1 Computer Mathematics Languages — An Overview

01-01 Main Contents of the Course随堂测验

1、Scientific computing is in fact the solution of mathematical problems.

2、“Computing ”of Scientific computing includes analytical and numerical computation of mathematical problems.

01-02 Why Should We Learn Computer Mathematics Languages随堂测验

1、The analytical solution to the determinant of any given matrix exists.

2、The determinant of n×n matrix can be obtained from the algebraic sum of many determinants of 1×1 matrices by algebraic complements .

01-03 Analytical and Numerical Solutions随堂测验

1、Which of the following functions can solve the analytical solution?
    A、solve()
    B、none()
    C、zero()
    D、exp()

2、The irrational number π has closed-form solution.

01-04 A Brief Review of the Development of Computer Mathematics Languages随堂测验

1、Cleve Moler and Jack Little co-founded The MathWorks Inc. in 1984 to develop the MATLAB language.

01-05 Limitations of Conventional Computer Languages随堂测验

1、Conventional numerical algorithm is the best method for the solutions to mathematical problems.

01-06 Three-step Methodologies in Scientific Computing随堂测验

1、The three steps of Three-step Strategy of Scientific computing are "what is it", "how to describe it"and"solution".

Unit Test

1、There are three leading computer mathematics languages in the world with high reputations. Which three are the right options?
    A、EISPACK
    B、MATLAB of MathWorks Inc.
    C、Mathematica of Wolfram Research
    D、Maple of Waterloo Maple

2、The main functions of MATLAB include
    A、Numerical computation
    B、programming
    C、widely used in symbolic operation
    D、numerical simulation

3、Which of the following is the advantage of MATLAB language?
    A、Low integration, good scalability and strong numerical solution ability
    B、Programming complexity, similar to other languages, such as C
    C、powerful system simulation capability ,Simulink
    D、It is the international preferred computer language in the field of control and many fields

4、What are the outstanding features of MATLAB compared with other computer languages
    A、Poor openness
    B、Powerful functions
    C、Rich library functions
    D、Rich library functions

5、Which of the following situations does the analytic solution not exist
    A、Solving indefinite integral problems
    B、Circular constant
    C、The analytic expression of function
    D、Bivariate first order equations with roots

Unit Assignment

1、In order to understand the three-phase learning stage, please revisit Example 1.5, and see which statements belong to the second and third phases. Also please think about what should be done for the first phase.

2 Fundamentals of MATLAB Programming

02-01 Data Structures随堂测验

1、1. The correct one of the following variable names is()
    A、1Name
    B、_Name
    C、Name_1
    D、Name1-

2、2. Which of the following data types has the value range(0,255)()
    A、int8
    B、uint8
    C、int16
    D、uint16

3、3. Variable name and Name are the same variable()

4、4. Output string data 321, use command A = sym(321)()

5、5. To use the symbolic data structure to represent the value 34939383474488382, use the command sym (34939383474488382).()

02-02 Input of Matrices and Vectors随堂测验

1、Which is the wrong way to input matrix( )
    A、[1 2;3 4]
    B、[1,2;3,4]
    C、[1 2;3,4]
    D、[1;2;3;4]

2、4. Which are the correct ways to input matrix
    A、[1 2;3 4]
    B、[1;2;3;4]
    C、[1,2;3,4]
    D、[1 2;3,4]

3、1. To use MATLAB to represent matrix enter A=[1 2;3,4]()

4、2. Generate a vector between A ∈ [0,200] with a step size of 1, the command that should be entered is A = [0: 200]()

5、3. Generate a vector between A ∈ [1,111] with a step size of 2, the command that should be entered is A = [1: 2: 111]()

02-03 Algebraic Operations of Matrices随堂测验

1、1. To solve the linear equations AX = B, the MATLAB command used is X = B / A.()

2、2. A is a 3x3 matrix. Using the command A.*A, can achieve the direct calculation of the corresponding elements of matrix A()

3、3.

4、4.

5、5.

02-04 Other Fundamental Operations随堂测验

1、1.Please compute A & B where A = [2,6;7,8], B = [2,0;0,1].
    A、[1,0;0,1]
    B、[0,1;1,0]
    C、[1,1;1,1]
    D、[1,0;0,0]

2、2. Please list all the prime numbers in the interval [1, 1000].
    A、a=1:1000; b=a(primes(a))
    B、a=1:1000; b=b(primes(a))
    C、a=1:1000; b=a(isprime(b))
    D、a=1:1000; b=a(isprime(a))

3、4. Please choose the wrong command.
    A、syms s; P=(s+3)^2*(s^2+3*s+2)*(s^3+12*s^2+48*s+64); P1=simplify(P)
    B、syms s; P=(s+3)^2*(s^2+3*s+2)*(s^3+12*s^2+48*s+64); P2=expand(P)
    C、syms s; P=(s+3)^2*(s^2+3*s+2)*(s^3+12*s^2+48*s+64); P3=factor(P)
    D、syms s; P=(s+3)^2*(s^2+3*s+2)*(s^3+12*s^2+48*s+64); P4=prod(P3)

4、5. Please choose the correct command to substitute the variable x in the original function f(x) with variable x1.
    A、f1=subs(f,x1,x)
    B、f1=subs('f',x,x1)
    C、f1=subs(f,x,x1)
    D、f1=subs('f',x1,x)

5、3. The command: i = find(A>=5) can find all the indices in A whose value is larger than 5.

02-05 Flow Control Structures随堂测验

1、5. Please choose the correct commands .()
    A、tic, s=0; for i=1:10000000, s=s+1/2^i+1/3^i; end; toc
    B、tic, s=0; for i=1:10000000, s=s+1/2^i+1/3^i; end; tic
    C、toc, s=0; for i=1:10000000, s=s+1/2^i+1/3^i; end; toc
    D、toc, s=0; for i=1:10000000, s=s+1/2^i+1/3^i; end; tic

2、1.
    A、s1=0; for i=1:100, s1=s1+i; end; s1
    B、s1=0; for i=1:100, s1=s1+i, i=i+1; end; s1
    C、s2=0; i=1; while (i<=100), s2=s2+i; i=i+1; end; s2
    D、s2=0; i=1; while (i<=100), s2=s2+i; end; s2

3、4.
    A、s=0; m=0; while (s<=10000), m=m+1; s=s+m; end, m
    B、s=0; m=0; while (s<=10000), s=s+m; m=m+1; end, m
    C、s=0; for i=1:10000, s=s+i; if s>10000, break; end, s
    D、s=0; for i=1:10000, s=s+i; if s>10000, break; end, end, s

4、2. The difference between the for loop structure and the while loop structure is that the for loop structure itself can set an exit. ()

5、3.

02-06 Programming of Functions随堂测验

1、1. Please choose the difference between the M-function program and the M-script program.()
    A、The M-function program has no function definition, the M-script program has function definition.
    B、The M-script program has no function definition, the M-function program has function definition.
    C、Both the M-script program and the M-function program have function definition.
    D、Neither the M script file nor the M function file has function definition.

2、2. Please choose the correct statements. ()
    A、The M-script program can call the M-function program.
    B、The naming rules of file name are consistent with the naming rules of variable name.
    C、The first line of the M-function program must start with “function”.
    D、The first line of the M-script program must start with “function”.

3、3. Calling functions to solve similar problems needs to modify the source program.()

4、4. MATLAB functions can be called recursively, i.e., a function may call itself.()

5、5. M-scripts process the data in MATLAB workspace, and the results are returned back to MATLAB workspace.()

02-07 Two-dimensional Graphics随堂测验

1、1.Single choice:The command to add dimensions at the location specified in the drawing is( )
    A、title(x,y,y=sin(x))
    B、xlabel(x,y,y=sin(x))
    C、text(x,y,y=sin(x))
    D、legend(x,y,y=sin(x))

2、2. The command statement x=-1:0.1:1; plot([x+i*exp(-x.^2);x+i*exp(-2*x.^2);x+i*exp(-4*x.^2)]') draws ( ) curves.
    A、1
    B、3
    C、20
    D、4

3、5. In the settings of the line shape format, the character b represents the () color.
    A、red
    B、yellow
    C、white
    D、blue

4、3.

5、4.A is a two-dimensional numerical array with 1000 rows and 2 columns. Now we need to take the first column data of A as the abscissa and the second column data of a as the ordinate to draw a curve. Then the MATLAB statement is plot(A(:,2),A(:,1))

02-08 Special Two-dimensional Graphics随堂测验

1、1. Which command can draw implicit function image?()
    A、subplot
    B、ezplot
    C、draw
    D、contour

2、4. Which of the following functions is used to draw histogram? ()
    A、hist ()
    B、feather ()
    C、polar ()
    D、loglog ()

3、2. Divide a drawing window into four different areas, and display the image in the first area, using the command plot (2,4,1) .( )

4、3. Read the data in the excel table, you can use the ‘load’ command()

5、5. The subplot (m, n, k) function can be used to split a plot window into several different areas()

02-09 Three-dimensional Graphics随堂测验

1、1. In MATLAB, which of the following options is a command for drawing spherical surfaces? ( )
    A、cylinder
    B、sphere
    C、zero
    D、exp

2、3. In MATLAB, what function is used to draw a three-dimensional space curve? ()
    A、polar()
    B、plot()
    C、subplot()
    D、plot3()

3、4. In MATLAB, what function is used to draw a three-dimensional surface graph? ()
    A、plot ()
    B、subplot ()
    C、surf ()
    D、plot3 ()

4、2. The function for drawing a three-dimensional trajectory graph is comet3()

5、5. Three-dimensional surface implicit function drawing can call ezimplot3 () .()

02-10 Special Three-dimensional Graphics随堂测验

1、1. In MATLAB, the function of drawing contour lines of 3D data is: ( )
    A、surf
    B、plot
    C、plot3
    D、contour

2、2. In MATLAB, the function of drawing 3D implicit function graph is: ( )
    A、surf
    B、plot
    C、ezimplot3
    D、ezplot3

3、3. Directly use the toolbar to change the perspective of the graph. ( )

4、4. The contour command is related to the contour drawing of the curved surface. ( )

5、5. The view function can realize the rotation of the 3D surface. ( )

02-11 Four-dimensional Graphics随堂测验

1、1. When drawing four-dimensional graphics, the correct format of the meshgrid function is: ( )
    A、[x, y, z] = meshgrid ( 0 : 0.1 : 2 )
    B、[x, y, z] = meshgrid ( 0 : 0.1 )
    C、[x, y] = meshgrid ( 0 : 0.1 : 2 )
    D、[x, y] = meshgrid ( 0 : 0.1 )

2、2. The steps to draw a 3D solid slice are: ( )
    A、Generate grid data
    B、Calculate the function value of each point of the grid
    C、Drawing
    D、Spin

3、3. When drawing four-dimensional graphics, in order to easily observe the cross-sectional view, MATLAB provides a graphical user interface vol_visual4d. ( )

4、4. To draw a three-dimensional volume slice, you can use the command slice. ( )

5、5. Known mathematical function V = f (x, y, z), you can call the function vol_visual4d (x, y, z, V) to set the slice. ( )

Unit Test

1、Which of the following factorial calculation methods is wrong?
    A、factorial(sym(n))
    B、gamma(1+n)
    C、prod(1+n)
    D、gamma(1+sym(n)

2、what command is used to divide a drawing window into 4 different areas and display the image in the first area? ()
    A、subplot (2,4,1)
    B、plot (2,2,1)
    C、subplot (2,2,1)
    D、plot (2,4,1)

3、Which of the following functions is used to draw polar coordinates? ()
    A、hist ()
    B、feather ()
    C、polar ()
    D、loglog ()

4、Which of the following functions can draw a three-dimensional waterfall graphics? ()
    A、surfc ()
    B、ezmesh ()
    C、waterfall ()
    D、contour ()

5、MATLAB provides the rotation transformation method of the surface itself, and the rotation transformation can be implemented by the ( ) function
    A、plot
    B、rotate
    C、slice
    D、meshgrid

6、In the function slice (x, y, z, V, x1, y1, z1), the data describing the slices is ()
    A、x, y, z
    B、x, y, z, V
    C、V
    D、x1, y1, z1

7、The correct ones of the following variable names are()
    A、V_alue
    B、Value-
    C、Value1
    D、1_Value

8、Choose the flow control structures provided in MATLAB. ()
    A、switch structures
    B、conditional control structures
    C、trial structures
    D、loop structures

9、Mulpitle choice:In graphic decoration and property settings, what functions can be used to set and obtain the properties of objects?
    A、set()
    B、plotxx()
    C、get()
    D、plotyy()

10、To find the first 20 significant digits of 10/7, use command A = 10/7 , vpa(A,20)()

11、Generate a vector between A ∈ [0,45] with a step size of 1, the command that should be entered is A = [0: 45]()

12、Generate a vector between A ∈ [0,200] with a step size of 4, the command that should be entered is A = [0: 4:200]()

13、A is a 3x3 matrix. Using the command A * A, can achieve the direct calculation of the corresponding elements of matrix A()

14、

15、List all the prime numbers in the interval [1, 1000]. The command is a = 1:1000. ()

16、The polynomial P can be simplified with the command: simplify(P).()

17、

18、The naming rules of file name are consistent with the naming rules of variable names.( )

19、Both the M-script program and the M-function program have function definitions.()

20、Define an M function my_fact(n),which can calculate n!,then the command my_fact(99) can be used to calculate 99!

21、Both x and y are matrices. When using the command plot (x, y), the number of rows and columns of x and y should be the same.

22、contour () function can draw three-dimensional contour graphics ()

23、If you want to change the viewing angle to observe 3D graphics, you can use the view function ()

24、When drawing four-dimensional graphics, the calculation of the volume data V of the ternary function needs to use point operation ()

25、If a polynomial P (s) is given by P (s) = (s + 3)2(s2 + 3s + 2)(s3 + 12s2 + 48s + 64), it can be simplified by using the simplify() function.()

Unit Assignment

1、

3 Calculus Problems

03-01 Computations of Limits随堂测验

1、
    A、syms t; f=tan(t); L1=limit(f,t, pi/2),’left’)
    B、syms t; f=tan(t); L1=limit(f,t, pi/2),’right’)
    C、syms t; f=tan(t); L1=limit(f,t, π/2),’left’)
    D、syms t; f=tan(t); L1=limit(f,t, pi/2),’right’)

2、
    A、exp(x)/(2*(x^2+1))
    B、exp(x)/(x^2 + 1)
    C、0
    D、

3、
    A、6
    B、9
    C、18
    D、81

4、
    A、-1/2
    B、-1/6
    C、1/2
    D、1/6

5、
    A、f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,inf)
    B、syms n; f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,inf)
    C、f=n^(2/3)*sin(n!)/(n+1); F=limit(f,n,inf)
    D、syms n; f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,0)

03-02 Interval Limits and Multivariate Limits随堂测验

1、
    A、6,6
    B、6,3
    C、3,3
    D、0,0

2、
    A、0
    B、1
    C、2
    D、non-existence

3、
    A、1
    B、2
    C、4
    D、non-existence

4、
    A、-10
    B、10
    C、non-existence
    D、0

5、f=symvar( ) is written to describe piecewise functions.( )

03-03 Derivatives of Univariate Functions随堂测验

1、
    A、sym x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simple(diff(f,x,4))
    B、syms x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simplify(diff(f,x,4))
    C、sym x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simple(diff(f))
    D、syms x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simplify(diff(f))

2、
    A、syms x;f1=sqrt(x*cos(x)*sqrt(1-exp(2x))); F1=simplify(diff(f1))
    B、syms x;f1=sqrt(x*cos(x)*sqrt(1-exp(2x))); F1=simplify(diff(f1, x, 1))
    C、syms x;f1=sqrt(x*cos(x)*sqrt(1-exp(2x))); F1=simplify(diff(f1, x))
    D、f1=sqrt(x*cos(x)*sqrt(1-exp(2x))); F1=simplify(diff(f1))

3、
    A、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f)
    B、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f,4)
    C、sym x; f=cos(x)/(x^2+2*x+1);f4=diff(f,x)
    D、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f,x,4)

4、y = diff(fun,x,n) evaluate the n-th order derivative. If there is only one variable in the function, the independent variable name can not be omitted.

5、

03-04 Computations of Partial Derivatives随堂测验

1、
    A、syms t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(y,x,t,3))
    B、syms x y t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(x,y,t,3))
    C、syms t; y=cos(t)/(t+2)^3; x=sin(t)/(t+3)^3; f=simplify(paradiff(y,x,t,3))
    D、syms t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(x,y,t,2))

2、
    A、syms x y;f=x^2+2*x*y+y^2-5; f1=diff(f,x,y,2)
    B、syms x y;f=x^2+2*x*y+y^2-5; f2=int(f,x,y,2)
    C、syms x y;f=x^2+2*x*y+y^2-5; f3=paradiff(f,x,y,2)
    D、syms x y;f=x^2+2*x*y+y^2-5; f4=impldiff(f,x,y,2)

3、
    A、syms x y z; f=sin(x*y^2)*exp(-x*y^2+z^2);df=diff(diff(f,y),z);
    B、syms x y z; f=sin(x*y^2)*exp(-x*y^2+z^2);df=diff(f,x,y,z);
    C、syms x y z; f=sin(x*y^2)*exp(-x*y^2+z^2);df=diff(f,y,z);
    D、syms x y z; f=sin(x*y^2)*exp(-x*y^2+z^2);df=diff(diff(f,y,1),z,1);

4、

5、

03-05 Computations of Integrals随堂测验

1、
    A、syms x; f=(2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)); I1=int(f)
    B、syms x; f=(2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)); I1=diff(f)
    C、syms x; I1=jacobian((2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)))
    D、syms x; I1=impldiff((2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)))

2、
    A、syms x; f=5/x/sqrt(1-log(x)^2); I=int(f,dx,2,e)
    B、syms x; f=5/x/sqrt(1-log(x)^2); I=inf(f,x,2,exp(sym(1)))
    C、syms x; f=5/x/sqrt(1-log(x)^2); I=diff(f,x,2,e)
    D、syms x; f=5/x/sqrt(1-log(x)^2); I=int(f,x,2,exp(sym(1)))

3、
    A、syms x; I1=int(exp(-3*x^2/2),x,0,inf)
    B、syms x; I1=int(exp(-3*x^2/2),x,0,inf);vpa(I1)
    C、syms x; I1=diff(exp(-3*x^2/2),x,0,inf)
    D、syms x; I1=diff(exp(-3*x^2/2),x,0,inf);vpa(l1)

4、

5、

03-06 Fourier Series Approximations随堂测验

1、given a periodic function f (x), x∈[L, L], and a period of T = 2L, write it in the form of a Fourier series as needed. If x∈(a, b), it can be calculated The minimum period is:
    A、L = (b -a)/2
    B、L = (b +a)/2
    C、L = (b +a)*2
    D、L = (b -a)*2

2、For the function f (x), x∈ [-L, L], if a new variable x1 = x + L + a is introduced, then f (x1) can be mapped to a function on the interval (), and the Fourier level Expand the number and map it back to the x function.
    A、(-L/2,L/2)
    B、(L,2L)
    C、(- L, L)
    D、(L/2,L)

3、If [F, A, B] = fseries (f, x, p, a, b) is a function for solving Fourier coefficients and series, for a given function y = x (x -π) (x -2π) , Fourier series expansion of x ∈ (0, 2π), the correct one is:
    A、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,-pi/2,pi/2);
    B、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,pi,2*pi);
    C、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,-pi,pi);
    D、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,0,2*pi);

4、Fourier series fitting is performed on the square wave signal in the [-π, π] interval, the higher the order, the more significant the fitting effect

03-07 Taylor Series Approximations随堂测验

1、For the function f (x) = sin x / (x2 + 4x + 3), find the first 9 terms of the power series expansion when a = 0, the syntax is correct
    A、syms x; f=sin(x)/(x^2+4*x+3); y=taylor(f,x,'Order',9)
    B、syms x; f=sin(x)/(x^2+4*x+3); y=taylor(f,x,'Order',6)
    C、syms x; f=sin(x)/(x^2+4*x+3); y=taylor(f,x,1,'Order',9)
    D、syms x; f=sin(x)/(x^2+4*x+3); y=taylor(f,x,1,'Order',6)

2、taylor () can directly expand Taylor series of multivariable functions. The calling format is F = taylor (f, [x1, x2, ..., xn], [a1, a2, ..., an], 'Order', k), the highest order of expansion is:
    A、k
    B、k+1
    C、k-1
    D、2k

3、For f (x, y) = x cos y, if x = a, y = b, the first 4 items of Taylor power series expansion, the syntax is correct:
    A、syms x y a b; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)
    B、syms a b; f=x*cos(y); F=taylor(f,[x,y],[0,0],’Order’,4)
    C、syms x y a b; f=x*cos(2y); F=taylor(f,[x,y],[a,b],’Order’,4)
    D、syms x y ; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)

4、For the function ln ((1 + x) / (1-x)), the correct statement for Taylor power series expansion is:
    A、syms x; f=log((1-x)/(1-x)), F2=taylor(f,x,15);
    B、syms x; f=log((1+x)/(1+x)), F2=taylor(f,x,5);
    C、syms x; f=log((1-x)/(1+x)), F2=taylor(f,x,15);
    D、syms x; f=log((1+x)/(1-x)), F2=taylor(f,x,15);

5、Multivariable functions cannot be expanded by Taylor power series

03-08 Series Sums and Sequence Products随堂测验

1、The () function provided in the Symbolic Operation Toolbox can be used to sum finite or infinite series of known terms.
    A、symsum()
    B、plus()
    C、add()
    D、sub()

2、Which of the following codes can lead to the product of an infinite number of items in a sequence?
    A、syms x y ; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)
    B、syms k;P2=symprod(1+1/k^3,k,1,inf); P2=simplify(P2)
    C、syms n x; s1=symsum(2/((2*n+1)*(2*x+1)^(2*n+1)),n,0,inf); simplify(s1)
    D、syms k n; P1=symprod(1+1/k^3,k,1,n); P1=simplify(P1)

3、Which instruction does not meet the code specification for solving the series sum and sequence quadrature synthesis problem?
    A、syms n k; S=simplify(limit(symsum((1+k/n^2)*sin(k*pi/n^2),k,1,n-1),n,inf))
    B、syms n k x; S1=symsum(x^n/symprod(1+x^k,k,1,n),n,1,inf)
    C、syms n k; L1=limit(symsum(1/((2*k)^2-1),k,1,n))
    D、syms n; P1=symprod((2*n+1)*(2*n+7)/(2*n+3)/(2*n+5),n,1,inf)

4、The new version of the MATLAB symbolic operation toolbox provides a solution function () Directly find the sequence quadrature problem.
    A、sub()
    B、prod()
    C、sun()
    D、symprod()

03-09 Path Integrals and Surface Integrals随堂测验

1、
    A、2π
    B、4π
    C、π/2
    D、π/4

2、What is the solution function for surface integrals ( )
    A、path_integral()
    B、sin()
    C、surf_integral()
    D、diff()

3、Which of the following is the MATLAB call format for path integrals ( )
    A、
    B、
    C、
    D、

4、

5、

03-10 Numerical Differentiations随堂测验

1、Given the prototype function, the analytic solution of each derivative can be obtained by the function.
    A、path_integral()
    B、sin()
    C、surf_integral()
    D、diff()

2、Which of the following functions can be used to find the bivariate gradient ( )
    A、diff()
    B、gradient()
    C、sin()
    D、path_integral()

3、Assume that there is a set of measured data (ti, yi) with evenly distributed time instances Δt, if Δt → 0, the difference between two divided by interval Δ t is the derivative of this point.

4、

5、In some applications where the original function is not known, only experimental data are given. In this case, numerical methods must be used to get the derivatives from the experimental data.

03-11 Numerical Integrals of Univariate Functions随堂测验

1、Which of the following call formats of intel() function is correct?
    A、I=integral(f,a,b,property setting pair)
    B、I=integral(a,b,property setting pair)
    C、I=integral(f,a,b)
    D、I=integral(f,a,property setting pair)

2、Which of the following methods can be used to describe integrand functions with intermediate variables?
    A、Inline() function
    B、M function
    C、Integral() function
    D、Anonymous function

3、
    A、>> f=@(t)exp(-t)*sin(3*t+1)*(pi-t)^(1/4); F1=integral(f,0,pi)
    B、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).^(1/4), F1=integral(f,0,pi)
    C、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).^(1/4); F1=integral(f,pi)
    D、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).*(1/4); F1=integral(f,0,pi)

4、What are the ways to describe the integrand?
    A、Inline() function
    B、M function
    C、Integral() function
    D、Anonymous function

5、

03-12 Numerical Double Integrals随堂测验

1、Which of the following is the standard call format for the integral2() function?
    A、
    B、
    C、
    D、

2、
    A、>> tic, f=@(y,x)exp(-x^2/2)*sinh(x^2+y); fh=@(y)sqrt(1-y^2); fl=@(y)-sqrt(1-y^2); I=integral2(f,-1,1,fl,fh,'RelTol',1e-20), toc
    B、>> tic, f=@(y,x)exp(-x.^2/2)*sinh(x^2+y); fh=@(y)sqrt(1-y^2); fl=@(y)-sqrt(1-y^2); I=integral(f,-1,1,fl,fh,'RelTol',1e-20), toc
    C、>> tic, f=@(y,x)exp(-x.^2/2).*sinh(x.^2+y); fh=@(y)sqrt(1-y.^2); fl=@(y)-sqrt(1-y.^2); I=integral(f,-1,1,fl,fh,'RelTol',1e-20), toc
    D、>> tic, f=@(y,x)exp(-x.^2/2).*sinh(x.^2+y); fh=@(y)sqrt(1-y.^2); fl=@(y)-sqrt(1-y.^2); I=integral2(f,-1,1,fl,fh,'RelTol',1e-20), toc

3、Which of the following is the most commonly used function for solving numerical solutions of double definite integrals?
    A、integral()
    B、integral2()
    C、Integral3()
    D、Integral4()

4、

5、It is not necessary to pay attention to the order of integration when calling the integral () function.

03-13 Numerical Triple and n-tuple Integrals随堂测验

1、Which one of the following functions can be used to solve the definite integral problem of multiple ultra-rectangular boundaries?
    A、quadndg() function
    B、intfunc() function
    C、integral2() function
    D、Integral3() function

2、When using quadndg () of the NIT toolbox to solve the numerical solution of multiple integrals, only one of the following methods can be used to describe the integrand?
    A、Inline() function
    B、M function
    C、Integral() function
    D、Anonymous function

3、
    A、>> f1=@(x,y)sqrt(4-x^2-y^2)*exp(-x^2-y^2); f1M=@(x)exp(-x^2/2); f1m=@(x)0; I1=quad2dggen(f1,f1m,f1M,0,2)
    B、>> f1=@(x,y)sqrt(4-x^2-y^2)*exp(-x^2-y^2); f1M=@(x)exp(-x^2/2); f1m=@(x)0; I1=quad2dggen(f1,f1m,f1M)
    C、>> f1=@(x,y)sqrt(4-x.^2-y.^2).*exp(-x.^2-y.^2); f1M=@(x)exp(-x.^2/2); f1m=@(x)0; I1=quad2dggen(f1,f1m,f1M)
    D、>> f1=@(x,y)sqrt(4-x.^2-y.^2).*exp(-x.^2-y.^2); f1M=@(x)exp(-x.^2/2); f1m=@(x)0; I1=quad2dggen(f1,f1m,f1M,0,2)

4、
    A、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(f,0,2,0,2,0,2)
    B、>> f=@(x,y,z)z.*(x.^2+y.^2)*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(f,0,2,0,2,0,2)
    C、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z) I2=triplequad(f,0,2,0,2,0,2)
    D、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(0,2,0,2,0,2)

5、

Unit Test

1、
    A、f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,inf)
    B、syms n; f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,inf)
    C、f=n^(2/3)*sin(n!)/(n+1); F=limit(f,n,inf)
    D、syms n; f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,0)

2、
    A、exp(x)/(2*(x^2+1)
    B、exp(x)/(x^2 + 1)
    C、0
    D、

3、
    A、-10
    B、10
    C、non-existence
    D、0

4、
    A、sym x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simple(diff(f,x,4))
    B、syms x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simplify(diff(f,x,4))
    C、sym x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simple(diff(f))
    D、syms x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simplify(diff(f))

5、
    A、syms t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(y,x,t,3))
    B、syms x y t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(x,y,t,3))
    C、syms t; y=cos(t)/(t+2)^3; x=sin(t)/(t+3)^3; f=simplify(paradiff(y,x,t,3))
    D、syms t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(x,y,t,2))

6、
    A、syms x; f=(2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)); I1=int(f)
    B、syms x; f=(2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)); I1=diff(f)
    C、syms x; I1=jacobian((2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)))
    D、syms x; I1=impldiff((2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)))

7、For the function f (x), x∈ [-L, L], if a new variable x1 = x + L + a is introduced, then f (x1) can be mapped to a function on the interval (), and the Fourier level Expand the number and map it back to the x function.
    A、(-L/2,L/2)
    B、(L,2L)
    C、(- L, L)
    D、(L/2,L)

8、If [F, A, B] = fseries (f, x, p, a, b) is a function for solving Fourier coefficients and series, for a given function y = x (x -π) (x -2π) , Fourier series expansion of x ∈ (0, 2π), the correct one is:
    A、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,-pi/2,pi/2);
    B、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,pi,2*pi);
    C、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,-pi,pi);
    D、syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,0,2*pi);

9、taylor () can directly expand Taylor series of multivariable functions. The calling format is F = taylor (f, [x1, x2, ..., xn], [a1, a2, ..., an], 'Order', k), the highest order of expansion is:
    A、k
    B、k+1
    C、k-1
    D、2k

10、Single choice: For f (x, y) = x cos y, if x = a, y = b, the first 4 items of Taylor power series expansion, the syntax is correct:
    A、syms x y a b; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)
    B、syms a b; f=x*cos(y); F=taylor(f,[x,y],[0,0],’Order’,4)
    C、syms x y a b; f=x*cos(2y); F=taylor(f,[x,y],[a,b],’Order’,4)
    D、syms x y ; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)

11、Which instruction does not meet the code specification for solving the series sum and sequence quadrature synthesis problem
    A、syms n k; S=simplify(limit(symsum((1+k/n^2)*sin(k*pi/n^2),k,1,n-1),n,inf))
    B、syms n k x; S1=symsum(x^n/symprod(1+x^k,k,1,n),n,1,inf)
    C、syms n k; L1=limit(symsum(1/((2*k)^2-1),k,1,n))
    D、syms n; P1=symprod((2*n+1)*(2*n+7)/(2*n+3)/(2*n+5),n,1,inf)

12、get the combination of instructions used in the finite product and infinite product of the sequence
    A、syms k n; P=symprod(1+1/k^3,k,1,n); P=simplify(P)
    B、syms k;P=symprod(1+1/k^3,k,1,inf); P=simplify(P)
    C、syms n x; s=symsum(2/((2*n+1)*(2*x+1)^(2*n+1)),n,0,inf); simplify(s)
    D、syms x y ; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)

13、Which of the following call formats of intel() function is correct?
    A、I=integral(f,a,b,property setting pair)
    B、I=integral(a,b,property setting pair)
    C、I=integral(f,a,b)
    D、I=integral(f,a,property setting pair)

14、
    A、>> f=@(t)exp(-t)*sin(3*t+1)*(pi-t)^(1/4); F1=integral(f,0,pi)
    B、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).^(1/4), F1=integral(f,0,pi)
    C、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).^(1/4); F1=integral(f,pi)
    D、>> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).*(1/4); F1=integral(f,0,pi)

15、
    A、>> tic, f=@(y,x)exp(-x^2/2)*sinh(x^2+y); fh=@(y)sqrt(1-y^2); fl=@(y)-sqrt(1-y^2); I=integral2(f,-1,1,fl,fh,'RelTol',1e-20), toc
    B、>> tic, f=@(y,x)exp(-x.^2/2)*sinh(x^2+y); fh=@(y)sqrt(1-y^2); fl=@(y)-sqrt(1-y^2); I=integral(f,-1,1,fl,fh,'RelTol',1e-20), toc
    C、>> tic, f=@(y,x)exp(-x.^2/2).*sinh(x.^2+y); fh=@(y)sqrt(1-y.^2); fl=@(y)-sqrt(1-y.^2); I=integral(f,-1,1,fl,fh,'RelTol',1e-20), toc
    D、>> tic, f=@(y,x)exp(-x.^2/2).*sinh(x.^2+y); fh=@(y)sqrt(1-y.^2); fl=@(y)-sqrt(1-y.^2); I=integral2(f,-1,1,fl,fh,'RelTol',1e-20), toc

16、Which of the following is the most commonly used function for solving numerical solutions of double definite integrals?
    A、integral()
    B、integral2()
    C、Integral3()
    D、Integral4()

17、
    A、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(f,0,2,0,2,0,2)
    B、>> f=@(x,y,z)z.*(x.^2+y.^2)*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(f,0,2,0,2,0,2)
    C、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z) I2=triplequad(f,0,2,0,2,0,2)
    D、>> f=@(x,y,z)z.*(x.^2+y.^2).*exp(-x.^2-y.^2-z.^2-x.*z); I2=triplequad(0,2,0,2,0,2)

18、
    A、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f)
    B、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f,4)
    C、sym x; f=cos(x)/(x^2+2*x+1);f4=diff(f,x)
    D、syms x; f=cos(x)/(x^2+2*x+1);f4=diff(f,x,4)

19、
    A、syms x; I1=int(exp(-3*x^2/2),x,0,inf)
    B、syms x; I1=int(exp(-3*x^2/2),x,0,inf);vpa(I1)
    C、syms x; I1=diff(exp(-3*x^2/2),x,0,inf)
    D、syms x; I1=diff(exp(-3*x^2/2),x,0,inf);vpa(l1)

20、f=symvar( ) is written to describe piecewise functions.( )

21、

22、

23、

24、Assume that there is a set of measured data (ti, yi) with evenly distributed time instances Δt, if Δt → 0, the difference between two divided by interval Δ t is the derivative of this point.

25、In some applications where the original function is not known, only experimental data are given. In this case, numerical methods must be used to get the derivatives from the experimental data.

Unit Assignment

1、

2、

4 Linear Algebra Problems

04-01 Input of Special Matrices随堂测验

1、Which one is written to generate a 4 × 4 identity matrix. ( )
    A、ones(4)
    B、eye(4)
    C、zeros(4)
    D、rand(4)

2、
    A、V
    B、V1
    C、V2
    D、V3

3、
    A、V
    B、V1
    C、V2
    D、V3

4、
    A、V
    B、V1
    C、V2
    D、V3

5、zeros(4) is written to generate a 4 × 4 zero matrix.( )

04-02 Property Analysis of Matrices随堂测验

1、which of the following functions is to evaluate the determinant of a matrix()
    A、inv
    B、diag
    C、det
    D、eig

2、Which of the following functions is to evaluate the inverse matrix of a matrix()
    A、inv
    B、diag
    C、det
    D、eig

3、Running commands :A=[15 3 2 13; 5 18 10 8; 9 7 6 12; 4 14 15 1]; n1=norm(A), we can get the equation: n1=34. ()

4、Running commands :A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; n2=norm(A,Inf), we can get the equation: n2=34.()

5、The following commands :syms x y; P=x*(x+2*y)^8; p=coeffs(P,x),can extract coeffiffifficients of x in P. ()

04-03 Inverse Matrices and Pseudo Inverse Matrices随堂测验

1、For any given matrix A, there exists a unique matrix M such that some conditions below are satisfified.()
    A、AMA=A
    B、MAM=M
    C、both AM and MA are Hermite symmetric matrix
    D、AM=E

2、Running commands :A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; B=inv(A), we can get the exact inverse matrix.

3、Run commands :H1=[H eye(4)]; H2=rref(H1), H3=H2(:,5:8), and H3 is the inverse matrix of H.

4、Run commands :H1=[H eye(4)]; H2=rref(H1), H4=H2(:,1:4), and H4 is the identity matrix.

5、Given B=pinv(A), there is pinv(B)=A.()

04-04 Eigenvalues and Eigenvectors随堂测验

1、[V ,D]=eig(A), What are the meanings of V and D respectively?( )
    A、Eigenvalues and eigenvectors of A
    B、Eigenvectors and eigenvalues of A
    C、Rank and trace of A
    D、Trace and rank of A

2、The eigenvalue and eigenvector of matrix can be easily obtained by the ( ) function provided by MATLAB.
    A、norm()
    B、rref()
    C、eig()
    D、pinv()

3、If the characteristic polynomial can be exactly known, the function roots() can also be used in evaluating the eigenvalues of the matrix.()

4、In MATLAB, the function eig() can be used to compute directly the generalized eigenvalues and eigenvectors such that d = eig(A,B).()

5、The eig() function provided in the Symbolic Math Toolbox can also be used to evaluate the eigenvalues and eigenvectors of a given matrix. Even for large-sized matrices, results with very high accuracy can be obtained.()

04-05 Similarity Transforms and Triangular Factorizations随堂测验

1、Consider a symmetrical matrix A, perform numerical and analytical Cholesky factorizations. A=[9,3,4,2; 3,6,0,7; 4,0,6,0; 2,7,0,9]()
    A、chol(A)
    B、D = chol(A)
    C、cholsym(sym(A))
    D、D = cholsym(sym(A))

2、By using analytic solution function, matrix A can be triangulated. Please choose the correct command.()
    A、[L,U]=lu(sym(A))
    B、A=sym(A); [L,U]=lu(A)
    C、A=sym(A); [L,U]=lu(sym(A))
    D、[L,U]=lusym (A)

3、A MATLAB function Q = orth(A) can be used to construct the orthonormal basis for the column space of matrix A.()

4、The MATLAB function [D,p] = chol(A) can also be used to check whether a matrix is positive-definite or not, where for positive-definite matrix A, p = 0 will be returned.()

5、The matrix A can be transformed back if the statement inv(P)*L*U is used.()

04-06 Jordanian Transforms and Singular Value Decompositions随堂测验

1、
    A、A=[3,2,2,2; 1,2,-2,-2; -1,-2,0,-2; 0,1,3,5]; [d,v]=eig(sym(A)); A1=inv(v)*v*A
    B、A=[3,2,2,2; 1,2,-2,-2; -1,-2,0,-2; 0,1,3,5]; [d,v]=eig(sym(A)); A1=inv(v)*A*v
    C、A=[3,2,2,2; 1,2,-2,-2; -1,-2,0,-2; 0,1,3,5]; [v,d]=eig(sym(A)); A1=inv(v)*A*v
    D、A=[3,2,2,2; 1,2,-2,-2; -1,-2,0,-2; 0,1,3,5]; [v,d]=eig(sym(A)); A1=inv(d)*d*A

2、
    A、
    B、
    C、
    D、

3、
    A、34.0000
    B、17.8885
    C、4.4721
    D、0.0000

4、When a general matrix is transformed into a companion matrix, a column vector x can be randomly generated to determine whether the generated T matrix is singular or not. If it is not, the random column vector should be regenerat

5、Singular value decomposition is not possible for matrices with n≠m.

04-07 Linear Equation Solutions随堂测验

1、
    A、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(A*x-B)
    B、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(B)*A, e1=norm(A*x-B)
    C、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(B*x-A)
    D、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(x*A-B)

2、
    A、r
    B、n
    C、n-r
    D、n+r

3、
    A、x0=null(sym(A)*B)
    B、
    C、
    D、

4、
    A、x=[0.5400,0.4550,0.0434,-0.0473]T
    B、x=[0.5400,0.4550,0.0443,-0.0473]T
    C、x=[0.5466,0.4550,0.0434,-0.0473]T
    D、x=[0.5466,0.4550,0.0443,-0.0473]T

5、If A matrix is singular or near singular, inv (A) may produce wrong results.

04-08 Lyapunov Equations随堂测验

1、A continuous Lyapunov equation can be expressed as ().
    A、AX + XAT = −C
    B、AX + XAT = C
    C、AX - XAT = C
    D、AX - XAT = −C

2、When solving Lyapunov equation, what is the calling format of lyap() function? ()
    A、X=lyap (A,)
    B、X=lyap (A, C)
    C、X=lyap (B)
    D、X=lyap (A, B, C)

3、The Lyapunov equation can be rewritten as a simple linear equation:(A⊗I+I⊗A) x =−c

4、The typical form of Stein equation is:AXB+X+Q=0

5、A⊗B is the Kronecker product of matrix A and B, which is expressed by MATLAB function as follows: C=kron(A, B)

04-09 Sylvester Equations and Riccati Equations随堂测验

1、A Sylvester equation takes the general form:
    A、AX+XB=−C
    B、AX+XB=C
    C、AX−XB=C
    D、AX−XB=−C

2、When solving Sylvester equation, what is the calling format of lyap() function? ()?
    A、X=lyap (A,)
    B、X=lyap (A, C)
    C、X=lyap (B)
    D、X=lyap (A, B, C)

3、The specific call format of lyapsym() function is?
    A、X=lyapsym(sym(A),C)
    B、X=lyapsym(sym(A),-inv(B),Q*inv(B))
    C、X=lyapsym(sym(A),-inv(A'),Q*inv(A'))
    D、X=lyapsym(sym(A),B,C)

4、If (A ⊗ I m + I n ⊗ BT) is nonsingular, the Sylvester equation has a unique solution.

5、The original discrete Lyapunov equation can be rewritten as: AX + X[−(AT) −1] = −Q(AT) −1

04-10 Matrix Exponentials and Trigonometric Functions随堂测验

1、Which of the following functions is not element based nonlinear computing in matrices: ( )
    A、abs
    B、sqrt
    C、exp
    D、expm

2、In the following functions, the trigonometric functions of the matrix can be implemented by: ( )
    A、exp
    B、expm
    C、funm
    D、sin

3、For any form of matrix A, you can use expm (A*t) to solve eAt. ( )

4、There is no direct function to perform trigonometric operation on matrix in MATLAB ( )

5、The expression sin (A) can realize the analytical solution of matrix trigonometric functions ( )

04-11 Computations of Arbitrary Matrix Functions随堂测验

1、In the following description of calculating Arbitrary Matrix Functions, the correct one is: ( )
    A、Functions in MATLAB can directly solve Arbitrary Matrix Functions
    B、No need to use Jordan matrix factorization when solving Arbitrary Matrix Functions
    C、The nilpotent matrix is the identity matrix
    D、It is also necessary to use the nilpotent matrix when solving Ak

2、The following expressions about calculating matrix functions are correct:()
    A、sin A=funm(A, ’sin’)
    B、eA=exp(A)
    C、sin A=sin(A)
    D、e Acos(At) = funm (A, exp (x*cos(x*t)), x)

3、The function of funm () can find the analytical solution of any function:( )

4、Jordan matrix factorization is required when solving Arbitrary Matrix Functions:( )

5、In MATLAB, there is no direct function to compute Ak. ( )

Unit Test

1、
    A、V
    B、V1
    C、V2
    D、V3

2、
    A、V
    B、V1
    C、V2
    D、V3

3、If the characteristic polynomial can be exactly known, the function()can also be used in evaluating the eigenvalues of the matrix.
    A、norm()
    B、rref()
    C、roots()
    D、pinv()

4、Matrix A is triangulated by MATLAB. Find the upper triangular matrix and the lower triangular matrix. Please choose the correct command.()
    A、[V ,D]=eig(A)
    B、[L,U]=lu(A)
    C、[D ,V]=eig(A)
    D、[L,U]=lu(A)

5、A MATLAB function()can be used to construct the orthonormal basis for the column space of matrix A.()
    A、Q = orth(A)
    B、Q = chol(A)
    C、Q = eig(A)
    D、Q = lu(A)

6、
    A、
    B、
    C、
    D、

7、
    A、xT=[0.0790,0.1915,0.2415,-0.0710]
    B、xT=[0.0780,0.2915,0.2415,-0.0710]
    C、xT=[0.0780,0.1925,0.2415,-0.0710]
    D、xT=[0.0790,0.1925,0.2415,-0.0710]

8、A discrete Lyapunov equation can be expressed in the form:
    A、AXAT+X+Q=0
    B、AXAT−X+Q=0
    C、AXAT−X−Q=0
    D、AXAT+X−Q=0

9、A Riccati equation is a quadratic matrix equation which can be written as:
    A、ATX − XA − XBX − C = 0
    B、ATX + XA − XBX + C = 0
    C、ATX + XA − XBX − C = 0
    D、ATX − XA − XBX + C = 0

10、MATLAB provides the rotation transformation method of the surface itself, and the rotation transformation can be implemented by the () function
    A、e A = exp (A)
    B、sin A = sin (A)
    C、sin At = sin (A*t)
    D、e At= expm (A*t)

11、For any given matrix A, there exists a unique matrix M such that some conditions below are satisfified. ( )
    A、AMA=A
    B、AM与MA均为Hermite对称矩阵
    C、MAM=A
    D、MAM=M

12、Running commands :A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; n2=norm(A,2), we can get the equation: n2=34. ( )

13、Running commands :A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; n4=norm(A,’fro’), we can get the equation: n4=34. ( )

14、Run commands :H1=[H eye(5)]; H2=rref(H1), H3=H2(:,6:10), and H3 is the inverse matrix of H.

15、In the commond [V ,D]=eig(A), V is the eigenvectors of A and D is the eigenvalues of A. ()

16、The sub diagonal element of Jordan matrix is the eigenvalue of matrix, and the main diagonal element is 1.

17、MATLAB can't deal with complex matrix equally, so matrix with complex eigenvalue can't get complex diagonal matrix and complex similar transformation matrix.

18、The call format of dlyap() function is X=dlyap(A,Q)

19、The specific call format of are() function is X=are(A,B,C)

20、When solving numerical solutions of matrix trigonometric functions, the expression funm (A, 'function name') can be used ()

21、In MATLAB, the funm () function can calculate Ak ()

22、When calculating Ak, you need to use Jordan matrix factorization ()

Unit Assignment

1、Compute the eigenvalues and eigenvectors of the matrix A=[3,2,2;2,4,6,;1,3,3].

5 Integral Transforms and Complex Variable Functions

05-01 Laplace Transforms随堂测验

1、
    A、syms a b c u; f=exp(b*u)*sin(a*u+c); F=laplace(f,u,s)
    B、syms a b c u; f= exp(b*u)*sin(a*u+c); F=laplace(f)
    C、syms a b c t; f= exp(b*t)*sin(a*t+c); F=laplace(f,u)
    D、syms a b c t; f= exp(b*t)*sin(a*t+c); F=laplace(f)

2、The meaning of the parameters in the function laplace(f,v,u) is ( )
    A、f: Function name; v: Complex variable; u: Time variable
    B、f: Function name; v: Time variable; u: Complex variable
    C、f: Complex variable; v: Function name; u: Time variable
    D、f: Time variable; v: Function name; u: Complex variable

3、
    A、
    B、
    C、
    D、

4、
    A、
    B、
    C、
    D、

5、

05-02 Numerical Laplace Transforms随堂测验

1、
    A、The function can be used in finding numerical solutions of inverse Laplace transforms.
    B、The original function can be expressed by f, which is a string containing s.
    C、Both t0 and tn can take any value.
    D、N is the number of points of evaluation.

2、In general, numerical Laplace transform has higher precision and slower speed than analytical solution ( )

3、

4、If the analytical solution to the Laplace transform of the input u(t) cannot be obtained, numerical approaches should also be used as well.

5、

05-03 Fourier Transforms随堂测验

1、
    A、syms t w; syms a positive, f=3/(t^2+a^2); F=fourier(f,w,t)
    B、syms t w; syms a positive, f=3/(t^2+a^2); F=fourier(f,t,w)
    C、syms t w; syms a positive, f=3/(t^2+a^2); F=ifourier(f,t,w)
    D、syms t w; syms a positive, f=3/(t^2+a^2); F=ifourier(f,t,w)

2、
    A、syms t w; syms a positive; f=sin(a*t)^2; INVLAP(f,t,w)
    B、syms t w; syms a positive; f=sin(a*t)^2; ifourier(f,t,w)
    C、syms t w; syms a positive; f=sin(a*t)^2; fourier(f,t,w)
    D、syms t w; syms a positive; f=sin(a*t)^2; laplace(f,t,w)

3、
    A、syms t w; syms a positive; f=cos(t); F=simplify(int(f*cos(w*t),t,0,a))
    B、syms t w; syms a positive; f=cos(t); F=simple(int(f*cos(w*t),t,0,a))
    C、f=piecewise('t<a and t>=0','cos(t)','t>=a','0'); F=int(f*cos(w*t),t,0,inf)
    D、f=fourier('t<a and t>=0','cos(t)','t>=a','0'); F=int(f*cos(w*t),t,0,inf)

4、
    A、syms t k; syms a positive, f1=t; f2=a-t; Fs=int(f1*sin(k*pi*t/a),t,0,a/2)+int(f2*sin(k*pi*t/a),t,a/2,a); simplify(Fs)
    B、f=piecewise('t<=a/2','t','t>a/2','a-t');Fs=simplify(int(f*sin(k*pi*t/a),t,0,a))
    C、assume(k,’integer’);k1=2*k;k2=2*k-1; Fs1=int(f1*sin(k1*pi*t/a),t,0,a/2)+int(f2*sin(k1*pi*t/a),t,a/2,a); Fs2=int(f1*sin(k2*pi*t/a),t,0,a/2)+int(f2*sin(k2*pi*t/a),t,a/2,a); F1=simplify(Fs1), F2=simplify(Fs2)
    D、f=assume('t<=a/2','t','t>a/2','a-t');Fs=simplify(int(f*sin(k*pi*t/a),t,0,a))

5、

05-04 Mellin and Hankel Transforms随堂测验

1、Compute the Mellin transform to f(t) = t/(t + a) with a > 0.
    A、syms t z; syms a positive; f=t/(t+a); M=simplify(int(f*t^(z-1),t,0,inf))
    B、syms t z; syms a positive; f=t/(t+a); M=simplify(Mellin(f*t^(z-1),t,0,inf))
    C、syms t z; syms a positive; f=t/(t+a); M=simplify(diff(f*t^(z-1),t,0,inf))
    D、syms t z; syms a positive; f=t/(t+a); M=simplify(iMellin(f*t^(z-1),t,0,inf))

2、
    A、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(diff(f*t^(z-1),t,0,inf)), end
    B、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(Mellin(f*t^(z-1),t,0,inf)), end
    C、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(Fourier(f*t^(z-1),t,0,inf)), end
    D、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(int(f*t^(z-1),t,0,inf)), end

3、
    A、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*int(0,w*t),t,0,inf); F=simplify(F)
    B、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*besselj(0,w*t),t,0,inf); F=simplify(F)
    C、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*diff(0,w*t),t,0,inf); F=simplify(F)
    D、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*hankel(0,w*t),t,0,inf); F=simplify(F)

4、

5、

05-05 Z Transform随堂测验

1、Similar to the Laplace and Fourier transforms, which are the properties of z transforms?
    A、Linear property
    B、Backward translation property
    C、Frequency-domain derivative property
    D、Frequency-domain integral property

2、Z transform and its inverse can be obtained directly with the functions () and() provided in the Symbolic Math Toolbox.
    A、ztrans()
    B、iztrans()
    C、symsum()
    D、isymsum()

3、

4、In MATLAB, the sum over (−∞,∞) interval is always supported by the symsum() function.

5、z transforms are for the sum n > 0, and also known as one sided z transform. If the range of n is extended to the entire set of integers, the bilateral z transforms can be got.

05-06 Complex Mapping and Riemann Surface随堂测验

1、Assume that a complex matrix Z is given, compute complex conjugate with()
    A、Z1 = real(Z)
    B、Z1 = conj(Z)
    C、Z1 = imag(Z)
    D、Z1 = abs(Z)

2、
    A、d3 = 0.8150 − j0.6646
    B、d3 = 0.9150 − j0.6646
    C、d3 = 0.8150 − j1.6646
    D、d3 = 0.9150 − j1.6646

3、The mapping graphics of complex-valued functions are different from the 3D graphics. One should generate polar grid with the ()function.
    A、real()
    B、conj()
    C、cplxgrid()
    D、abs()

4、
    A、cplxroot(n)
    B、conj(n)
    C、cplxgrid(n)
    D、abs(n)

5、The expected bilinear mapping can be obtained directly with function subs().

05-07 Singularities, Poles and Residues随堂测验

1、
    A、Multiplicity of poles, column vector
    B、Column vector, multiple of pole
    C、Multiplicity of poles, row vector
    D、Row vector, multiple of pole

2、If z = a is the m-fold singularity of the function f (z), what is the correct definition of the remainder of this point?
    A、
    B、
    C、
    D、

3、
    A、>> syms z, f=(sin(z)-z)/z^6, [p,m]=residuesym(f)
    B、>> syms z; f=(sin(z)-z)/z^6; [r,p,m]=residuesym(f)
    C、>> syms z; f=(sin(z)-z)/z^6; [p,m]=residuesym(f)
    D、>> syms z; f=(sin(z)-z)/z^6; [p,m]=residuesym(f)

4、If the function f (z) is single-valued at each point in the area of the complex plane, and its derivative is finite. Then the singular point that makes the f (z) denominator polynomial equal to zero is also called the pole.

5、Assuming that the singular point a and the multiplicity m are known, the corresponding residue can naturally be found using the following MATLAB statement. The statement is c=limit(diff(F*(z-a)ˆm,z,m)/prod(1:m),z,a).

05-08 Computations of Partial Fraction Expansions and Closed-Path Integrals随堂测验

1、To find the partial fraction expansion representation of the rational function G (x) = B (x) / A (x), the correct calling format is:
    A、residue(b,a)
    B、gcd(A,B)
    C、partfrac(f,s)
    D、poles(f,a,b)

2、Rational function coprime means that the polynomials A (x) and B (x) have no common divisor. To find the greatest common divisor C of two polynomials, the correct calling format is:
    A、C=poles(f,a,b)
    B、C=residue(b,a)
    C、C=partfrac(f,s)
    D、C=gcd(A,B)

3、For (x ^ x + y ^ y), find the integral on the forward curve enclosed by y = x and y = x ^ x. The statement is correct:
    A、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],y,0,1) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2
    B、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],x,1,0) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,0,1), I=I1+I2
    C、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],x,0,1) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2
    D、syms x; y=x^2; f=(x^2+y^2); I1=path_integral(f,[x,y],x,0,1) y=x;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2

4、For the condition of integration limit a> 0, what kind of instruction is required in the matlab statement?
    A、a>0
    B、a<0
    C、syms a negtive
    D、syms a positive

5、Judgment: Curve integration is generally divided into the first type of curve integration and the second type of curve integration in advanced mathematics. The calling format is I=path_integral(f,[x,y],t,tm,tM)

05-09 Solutions of Difference Equations随堂测验

1、The difference function can be directly obtained by calling the difference function. The general solution function of the difference equation is:
    A、y=diff(A,B,y0,U,d)
    B、y=diff_eq(A,B,y0,U,d)
    C、y=diff_eq(A,B,U,d)
    D、y=diff_eq(A,B,d)

2、Try to solve the difference equation 48y (n + 4) -76y (n + 3) + 44y (n + 2) -11y (n + 1) + y (n) = 2u (n + 2) + 3u (n + 1) + u (n), where y (0) = 1, y (1) = 2, y (2) = 0, y (3) = -1, and enter u (n) = (1/5) ^ n, the correct solution to the difference equation is:
    A、syms z n; u=(1/5)^n; y=diff_eq([48 -76 44 -11 1],[2 3 1],[1 2 0 -1])
    B、syms z n; u=(1/5)^n; y=diff_eq([48 -76 44 -11 1],[2 3 1],[1 2 0 -1],U)
    C、syms z n; u=(1/5)^n; U=ztrans(u);y=diff_eq([48 -76 44 -11 1],[2 3 1],[1 2 0 -1],U)
    D、syms z n; u=(1/5)^n;;y=diff_eq([48 -76 44 -11 1],[2 3 1],[1 2 0 -1],u)

3、Judgment: Linear difference equations are divided into linear time-varying difference equations and linear time-invariant difference equations.

4、Judgment: Assume that the explicit form of the difference equation is known, ie y (t) = f (t, y (t-1), ..., y (t-n), u (t), ..., u (t-m )) Then the equation can be solved directly by recursive or iterative methods to obtain the numerical solution of the equation.

5、Judgment: The expression of the kth power of the constant square matrix F calculated by the inverse z transformation is F ^ k = L ^ (-1) [z (zI-F)].

Unit Test

1、1. The meaning of the parameters in the function laplace(f,v,u) is ( )
    A、f: Function name; v: Complex variable; u: Time variable
    B、f: Function name; v: Time variable; u: Complex variable
    C、f: Complex variable; v: Function name; u: Time variable
    D、f: Time variable; v: Function name; u: Complex variable

2、
    A、
    B、
    C、
    D、

3、
    A、syms t w; syms a positive, f=3/(t^2+a^2); F=fourier(f,w,t)
    B、syms t w; syms a positive, f=3/(t^2+a^2); F=fourier(f,t,w)
    C、syms t w; syms a positive, f=3/(t^2+a^2); F=ifourier(f,t,w)
    D、syms t w; syms a positive, f=3/(t^2+a^2); F=ifourier(f,t,w)

4、
    A、syms t w; syms a positive; f=sin(a*t)^2; INVLAP(f,t,w)
    B、syms t w; syms a positive; f=sin(a*t)^2; ifourier(f,t,w)
    C、syms t w; syms a positive; f=sin(a*t)^2; fourier(f,t,w)
    D、syms t w; syms a positive; f=sin(a*t)^2; laplace(f,t,w)

5、Compute the Mellin transform to f(t) = t/(t + a) with a > 0.
    A、syms t z; syms a positive; f=t/(t+a); M=simplify(int(f*t^(z-1),t,0,inf))
    B、syms t z; syms a positive; f=t/(t+a); M=simplify(Mellin(f*t^(z-1),t,0,inf))
    C、syms t z; syms a positive; f=t/(t+a); M=simplify(diff(f*t^(z-1),t,0,inf))
    D、syms t z; syms a positive; f=t/(t+a); M=simplify(iMellin(f*t^(z-1),t,0,inf))

6、
    A、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(diff(f*t^(z-1),t,0,inf)), end
    B、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(Mellin(f*t^(z-1),t,0,inf)), end
    C、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(Fourier(f*t^(z-1),t,0,inf)), end
    D、syms t z; syms a positive;for i=1:8, f=1/(t+a)^i; disp(int(f*t^(z-1),t,0,inf)), end

7、
    A、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*int(0,w*t),t,0,inf); F=simplify(F)
    B、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*besselj(0,w*t),t,0,inf); F=simplify(F)
    C、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*diff(0,w*t),t,0,inf); F=simplify(F)
    D、syms t w a positive; f=exp(-a^2*t^2/3); F=int(f*t*hankel(0,w*t),t,0,inf); F=simplify(F)

8、The mapping graphics of complex-valued functions are different from the 3D graphics. One should generate polar grid with the ()function.
    A、real()
    B、conj()
    C、cplxgrid()
    D、abs()

9、
    A、cplxroot(n)
    B、conj(n)
    C、cplxgrid(n)
    D、abs(n)

10、
    A、Multiplicity of poles, column vector
    B、Column vector, multiple of pole
    C、Multiplicity of poles, row vector
    D、Row vector, multiple of pole

11、If z = a is the m-fold singularity of the function f (z), what is the correct definition of the remainder of this point?
    A、
    B、
    C、
    D、

12、To find the partial fraction expansion representation of the rational function G (x) = B (x) / A (x), the correct calling format is:
    A、residue(b,a)
    B、gcd(A,B)
    C、partfrac(f,s)
    D、poles(f,a,b)

13、Rational function coprime means that the polynomials A (x) and B (x) have no common divisor. To find the greatest common divisor C of two polynomials, the correct calling format is:
    A、C=poles(f,a,b)
    B、C=residue(b,a)
    C、C=partfrac(f,s)
    D、C=gcd(A,B)

14、For (x ^ x + y ^ y), find the integral on the forward curve enclosed by y = x and y = x ^ x. The statement is correct:
    A、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],y,0,1) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2
    B、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],x,1,0) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,0,1), I=I1+I2
    C、syms x; y=x; f=(x^2+y^2); I1=path_integral(f,[x,y],x,0,1) y=x^2;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2
    D、syms x; y=x^2; f=(x^2+y^2); I1=path_integral(f,[x,y],x,0,1) y=x;f=(x^2+y^2);I2=path_integral(f,[x,y],x,1,1), I=I1+I2

15、The difference function can be directly obtained by calling the difference function. The general solution function of the difference equation is:
    A、y=diff(A,B,y0,U,d)
    B、y=diff_eq(A,B,y0,U,d)
    C、y=diff_eq(A,B,U,d)
    D、y=diff_eq(A,B,d)

16、
    A、The function can be used in finding numerical solutions of inverse Laplace transforms.
    B、he original function can be expressed by f, which is a string containing s.
    C、Both t0 and tn can take any value.
    D、N is the number of points of evaluation.

17、
    A、syms t w; syms a positive; f=cos(t); F=simplify(int(f*cos(w*t),t,0,a))
    B、syms t w; syms a positive; f=cos(t); F=simple(int(f*cos(w*t),t,0,a))
    C、f=piecewise('t<a and t>=0','cos(t)','t>=a','0'); F=int(f*cos(w*t),t,0,inf)
    D、f=fourier('t<a and t>=0','cos(t)','t>=a','0'); F=int(f*cos(w*t),t,0,inf)

18、Z transform and its inverse can be obtained directly with the functions () and() provided in the Symbolic Math Toolbox.
    A、ztrans()
    B、iztrans()
    C、symsum()
    D、isymsum()

19、

20、In general, numerical Laplace transform has higher precision and slower speed than analytical solution ( )

21、

22、

23、In MATLAB, the sum over (−∞,∞) interval is always supported by the symsum() function.

24、The expected bilinear mapping can be obtained directly with function subs().

25、If the function f (z) is single-valued at each point in the area of the complex plane, and its derivative is finite. Then the singular point that makes the f (z) denominator polynomial equal to zero is also called the pole.

Unit Assignment

1、

2、

6 Nonlinear Equations and Optimization Problems

06-01 Graphical Solutions of Algebraic Equations随堂测验

1、The function ezplot() can be used to draw the curve from the implicit function f(x) =0.( )

2、The real solutions of univariate nonlinear equations can be identifified from the intersections of the curves with the line y = 0. ( )

3、The real solutions of nonlinear equations with two variables can be identifified from the intersections of the two sets of curves. ()

4、Graphical method can show all the solutions of algebraic equations. ( )

5、Graphical method applies only to equations with one and two unknowns.( )

06-02 Quansi-analytical Solutions of Polynomial Equations随堂测验

1、Polynomial equations of degrees 5 and above has no analytical solution method.()

2、Classical numerical methods are not accurate.()

3、Quasi-analytical Methods can find the analytical or high precision solutions. ()

4、Quasi-analytical Methods are suitable for polynomial-type equations.()

5、Quasi-analytical Methods are slower than conventional numerical algorithms.()

06-03 Numerical Solutions of Nonlinear Equations随堂测验

1、In the following options, the equations can be described with MATLAB by().
    A、M- function
    B、Anonymous function
    C、Inline functions
    D、univariate functions

2、Different initial values will yield same solutions.()

3、The function fsolve() can be used directly to solve the original equations and find a solution.

4、For more complicated problems, the solution control option opts can be used to select methods and control accuracies in searching the solution .

5、The precision requirement should not be too demanding, otherwise it may not be reached.()

06-04 General Purposse Solutions for Matrix Equations with Multiple Solutions随堂测验

1、The user may terminate the function more_sols() at any time by pressing keys ( ).
    A、Shift-C
    B、Ctrl-C
    C、Ctrl-Z
    D、Shift-D

2、Among the following functions, ( ) cannot be used to solve the Riccati equation.
    A、evalin()
    B、vpasolve()
    C、fsolve()
    D、are()

3、Both generalized Riccati equation and Riccati-like equation are nonlinear matrix equations. ( )

4、The simplest command to solve the general nonlinear equation is x = solve(fun,x0). ( )

5、Function vpasolve() can be used to solve more accurately nonlinear solutions .( )

06-05 Unconstrained Optimization Problems随堂测验

1、Among the following functions, ( ) can be used to solve optimization problems.
    A、fminunc()
    B、fmincon()
    C、fminsearch()
    D、quadprog()

2、Among the following methods, ( ) can be used to describe the objective function.
    A、M-function
    B、anonymous function
    C、Inline function
    D、M-script

3、The physical meaning of unconstrained optimization problem is to find a vector x such that the value of the objective function f(x) is minimized. ( )

4、Among the three description methods of the objective function, the anonymous function can use the intermediate variable. ( )

5、In the mathematical description of unconstrained minimization problem, X is the optimization vector and f (x) is the objective function. f (x) is a scalar function. ( )

06-06 Global Optimum Solutions随堂测验

1、MATLAB Optimization Toolbox provides () function, which can directly find the minimax.
    A、Fminimax
    B、fsolve
    C、reshape
    D、solve

2、The single objective optimization problem assumes that the objective function f (x) is a scalar function. When the objective function is extended to a vector function, the optimization problem is transformed into a multi-objective optimization problem. ( )

3、The necessary condition for the existence of the minimum value is df (x) / dx = 0. The x value satisfying the condition is the global minimum. ( )

4、Sometimes, the convergence speed for solving optimization problems may be very low, and the exact optimum may not be obtained using the information provided in the objective function alone. Thus, the gradient information can be used to improve the optimization process. ( )

5、In general, function fminunc global() is likely to get the global optimal solution. ( )

06-07 Feasible Regions随堂测验

1、In the practical optimization problems, which of the following statements are correct?( )
    A、The constraints can be equality constraints or inequality constraints
    B、The constraints can be either linear or nonlinear
    C、Sometimes constraints can not be described by pure mathematical functions
    D、All constraints can be described by mathematical functions

2、The range of x satisfying the constraint G (x) < 0 is called the feasible solution region. ( )

3、For general multivariate problems, the optimal solution can be obtained directly by graphic method. ( )

4、There is no way to test the global optimality in solving complex problems by numerical method. ( )

5、For a general one-dimensional problem, the optimal solution of the problem cannot be obtained directly by graphic method. ( )

06-08 Linear Programming and Quadratic Programming随堂测验

1、What functions should be used to implement the simplex algorithm?( )
    A、oeshgrid()
    B、optimset()
    C、quadprog()
    D、linprog()

2、In linear programming, both the objective function and the constraint function are linear. ( )

3、In some research fields, decision variables are described by vectors instead of matrices,so it is necessary to consider the linear programming problem with double subscript decision variables.()

4、In solving quadratic programming problems, the constants in the objective function have influence on the optimization results, so it cannot be omitted. ( )

5、The constraints in quadratic programming are still linear equality constraints. ( )

06-09 Nonlinear Programming随堂测验

1、What is the call format of fmincon() function? ( )
    A、[x] = fmincon(problem)
    B、[x, fopt, flag, c] = fmincon(problem)
    C、[fopt, flag, c] = fmincon(problem)
    D、[x, flag] = fmincon(problem)

2、fmincon() function is specially used to solve optimization problems under various constraints.( )

3、If a structure is used to describe a general nonlinear programming problem, the solver member variable should be set to fmincon.( )

4、The general nonlinear programming problems are formulated as follows:( )

5、fmincon_global() function can solve the global optimal solution..( )

06-10 Enumerate Methods for Integer Programming Problems随堂测验

1、What is the call format of intlinprog() function? ( )
    A、[x]= intlinprog(problem)
    B、[x, key, c] = intlinprog(problem)
    C、[x, fm, key, c] = intlinprog(problem)
    D、[key, c] = intlinprog(problem)

2、In the structure variable problem, what are the necessary member variables? ( )
    A、f
    B、intcon
    C、solver
    D、options

3、The solution function of mixed integer linear programming is intlinprog ()

4、The result can be fine tuned by the statement of x(intcon)=round(x(intcon)) to get the integer decision variable.

5、The call format of function BNB20_new () is [err, f, x] =BNB20_new (fun, x0, intcon, xm, xM, A, B, Aeq, Beq, CFun)

06-11 Mixed Integer Programming Problems随堂测验

1、The solution function of mixed integer linear programming problems is: ( )
    A、fsolve
    B、fminunc
    C、linprog
    D、intlinprog

2、The result of the function intlinprog() needs to be fine-tuned with: ( )
    A、round
    B、expm
    C、funm
    D、slove

3、The function to solve Mixed-integer Nonlinear Programming Problems is : ( )
    A、intlinprog
    B、BNB20_new
    C、linprog
    D、fmincon

4、Branch and bound algorithm is a common algorithm for solving nonlinear integer programming problems ( )

5、The BNB20_new() function directly calls the fmincon() function ( )

06-12 Dynamic Programming and Optimal Path Problems随堂测验

1、In MATLAB, the function to directly solve the shortest path problems is: ( )
    A、biograph
    B、sparse
    C、graphshortestpath
    D、linprog

2、What statements are required to create a sparse incidence matrix:()
    A、a=[a1,a2,· · ·,am,n]
    B、b=[b1,b2,· · ·,bm,n]
    C、w=[w1,w2,· · ·,wm,0]
    D、R=sparse(a,b,w)

3、In graph theory, graphs are composed of nodes and edges:( )

4、The biograph () function can create directed graph objects:( )

5、Regular and sparse matrices can be converted to each other. ( )

Unit Test

1、Among the following methods, ( ) cannot be used to describe the objective function.
    A、M-function
    B、anonymous function
    C、Inline function
    D、M-script

2、In general, function ( ) is likely to get the global optimal solution.
    A、fmincon()
    B、Fminimax
    C、fminunc_global()
    D、fsolve

3、
    A、[x1, x2, · · · , xn] T
    B、[x1, x2, · · · , xn]
    C、[x1] T
    D、[x1]

4、What is the variable err returned by BNB20_new()? ( )
    A、function value
    B、Error message string
    C、Optimal solution
    D、others

5、What is the variable f returned by BNB20_new()?.( )
    A、function value
    B、Error message string
    C、Optimal solution
    D、others

6、Which of the following syntax is correct in solving shortest path problems ()
    A、[d,p]=graphshortestpath(P)
    B、[d,p]=graphshortestpath(P , n1)
    C、[d,p]=graphshortestpath(P , n2)
    D、[d,p]=graphshortestpath(P , n1 , n2)

7、In function intlinprog(problem), the necessary member variables for struct problem are ( )
    A、f
    B、intcon
    C、solver
    D、options

8、The precision of graphical method is not high.( )

9、For equations with multiple solutions, graphical method can get one solution at a time.( )

10、Because two-dimensional graphs can only find the real solutions of equations, but not the complex conjugate solutions of equations, graphical methods can sometimes be used to draw wrong conclusions. ( )

11、The new function vpasolve() is quite effffective in finding all the solutions, real and complex, to polynomial-type equations,while the solve() function can only be used in finding analytical solutions, if they exist. ( )

12、The selection of initial values sometimes has a great influence on the solution of the whole problem, and even the solution cannot be found under some initial values. ( )

13、If a real initial value is selected, real root can be found, and if a complex initial value is selected, complex root can be found . ( )

14、We can use are (A,B,C) to solve Riccati equation directly. ( )

15、The user may terminate the function more_sols() at any time by pressing keys Ctrl-C. ( )

16、Among the three description methods of the objective function, the anonymous function cannot use the intermediate variable. ( )

17、MATLAB Optimization Toolbox provides function fminunc(), which can directly find the minimax. ()

18、For a general binary problem, the optimal solution can be obtained directly by graphic method. ( )

19、After drawing a three-dimensional figure, if you want to see the figure from the top down, you can use the view (0,90) command. ( )

20、If a formula in the constraint condition is a "≥" relationship, it needs to be multiplied by −1 on both sides of the unequal sign at the same time to convert it into a "≤" relationship. ( )

21、After the dual subscript decision variable linear programming problem is transformed into a standard linear programming problem, the solution needs to be replaced by the decision variable matrix. ( )

22、The call format of fmincon_global() function is [x, fmin]=fmincon_global(fun, a, b, n, N, others).( )

23、The intlinprog() function can be used to solve the 0-1 linear programming problems. ( )

24、When solving the optimal path problem, the incidence matrix used in the directed graph and the undirected graph is the same ()

Unit Assignmen

1、Find the solutions to the following equations, and verify the accuracy of the solutions.

7 Differential Equation Problems

07-01 Analytical Solutions of Differential Equations (I)随堂测验

1、
    A、
    B、
    C、
    D、

2、
    A、
    B、
    C、
    D、

3、
    A、y=dsolve('(2*x+3)^3*D3y+3*(2*x+3)*Dy-6*y=0'); y=simplify(y)
    B、y=dsolve('(2*x+3)^3*D3y+3*(2*x+3)*Dy-6*y=0','x'); y=simplify(y)
    C、syms x; simplify((2*x+3)^3*diff(y,x,3)+3*(2*x+3)*diff (y,x)-6*y)
    D、simplify((2*x+3)^3*diff(y,x,3)+3*(2*x+3)*diff(y,x)-6*y)

4、Analytical solutions can be found for linear differential equations, low-order special differential equations, and general nonlinear differential equations.

5、

07-02 Analytical Solutions of Differential Equations (II)随堂测验

1、
    A、syms t x(t) x=dsolve(diff(x)==x*(1-x^2))
    B、syms x(t); x=dsolve(diff(x)==x*(1-x^2))
    C、syms t x(t); x=dsolve(diff(x)==x*(1-x^2))
    D、syms t ; x=dsolve(diff(x)==x*(1-x^2))

2、
    A、
    B、
    C、
    D、

3、

4、Some nonlinear differential equations cannot be solved analytically with the dsolve () function.

5、The nonlinear differential equation can only be solved by numerical method, even the seemingly simple nonlinear differential equation has no analytical solution, only the very special nonlinear differential equation can be solved analytically.

07-03 Overview of ODE Solution Algorithms随堂测验

1、
    A、
    B、
    C、
    D、

2、Which of the following statements can improve the accuracy of numerical solutions?
    A、Choose the appropriate step
    B、Improve the accuracy of the approximation algorithm
    C、Using variable step size method
    D、Unlimited reduction of step size

3、

4、The Euler algorithm can be replaced by various more accurate interpolation methods to improve the accuracy of operation.

5、No matter how small the step size is, the resulting numerical solution will have a rounding error. Reducing the calculation step will increase the number of calculations, thereby increasing the number of rounding errors superimposed and passed throughout the calculation Large cumulative error.

07-04 Numerical Solutions of First-order Differential Equations随堂测验

1、The variable step size fourth-order fifth-level Runge–Kutta–Felhberg algorithm is implemented, and the calling format of the variable step size algorithm for solving differential equations is
    A、[t,x]=ode15s(f,[0,tn],x0)
    B、[t,x]=ode113(f,[0,tn],x0)
    C、[t,x]=ode23(f,[0,tn],x0)
    D、[t,x]=ode45(f,[0,tn],x0)

2、If you want to set the relative error to a smaller value of 10 to the negative 7th power, the following format is correct:
    A、options=odeset('RelTol',1e-7);
    B、options=odeset(1e-17);
    C、options=odeset; options.RelTol=1e-7;
    D、options=odeset; RelTol=1e-7;

3、In solving differential equations, which of the following measures can be taken to improve the numerical solution accuracy:
    A、Choose the appropriate step
    B、Improve accuracy of approximation algorithm
    C、Variable step size method
    D、Unlimited reduction of step size

4、Judgment: ode45 (), ode113 (), ode15s (), ode23 (), they not only have the same calling format, but also the same algorithm.

5、When solving a differential equation with additional parameters, the variable name must be exactly the same as the function itself when calling the function.

07-05 Standard Form Conversions of Differential Equations随堂测验

1、
    A、f=@(t,x,mu)[x(2); -mu*(x(1)^2-1)*x(2)-x(1)]
    B、f=@(t,x,mu)[x(1); -mu*(x(1)^2-1)*x(2)-x(1)]
    C、f=@(t,x,mu)[x(2); -mu*(x(1)^2-1)*x(1)-x(2)]
    D、f=@(t,x,mu)[x(2); -mu*(x(1)-1)*x(2)-x(1)]

2、A(x) is a non-singular matrix, let x = [x1, x2]T, then you can rewrite the original equation into a matrix form A(x)x′= B(x) transform the equation into a standard explicit one The system of order differential equations is correct:
    A、
    B、
    C、
    D、

3、Which of the following MATLAB functions can be directly used to solve implicit differential equations:
    A、cond()
    B、decic()
    C、odeset()
    D、ode15i()

4、The MATLAB statement for solving equation timing is:
    A、tic
    B、abs
    C、toc
    D、dev

5、The number of additional parameters in the ode45() call command may not exactly correspond to the number of additional parameters in the equation M function, and there will be no erroneous results.

07-06 Stiff Differential Equations随堂测验

1、The format of solving and calling rigid rigid equations in accordance with the grammatical rules is:
    A、[t,y]=ode15s(f,[0,tn],x0,ff,mu)
    B、[t,y]=ode15(f,[0,tn],x0,ff,mu)
    C、[t,y]=ode15s(f,x0,ff,mu)
    D、[t,y]=ode15s(f,[0,tn],mu)

2、The initial value of an ordinary differential equation is y1(0) = 0, y2(0) = 1. Taking the calculation interval as t∈(0, 100), consider replacing ode45() with ode15s(), and the correct format for the numerical solution of the equation is:
    A、[t1,y1]=ode15s(f,[0,100],[0;100],opt)
    B、[t1,y1]=ode15s(f,[0,1],[0;1],opt)
    C、[t1,y1]=ode45(f,[0,100],[0;1],opt)
    D、[t1,y1]=ode15s(f,[0,100],[0;1],opt)

3、For the variable step solution of rigid differential equations, the numerical solution is displayed by drawing a curve. The correct calling format is:
    A、toc
    B、plot(t1,y1)
    C、x1=exp(-2*t)
    D、tic

4、The solution of the rigid equation changes slowly and does not differ greatly, also known as the Stiff equation.

5、The format of the rigid differential equation is called grammatical judgment: the traditional rigid problem can not be solved directly by MATLAB's ordinary solution function, but the rigid problem must be selected.

07-07 Implicit Differential Equations随堂测验

1、
    A、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode15s(f,[0,10],[0; 0],opt);
    B、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=solve(f,[0,10],[0; 0],opt);
    C、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode15i(f,[0,10],[0; 0],opt);
    D、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode45(f,[0,10],[0; 0],opt);

2、
    A、
    B、
    C、
    D、

3、
    A、
    B、
    C、
    D、

4、the function fun can be used to describe the implicit equations. The function decic() can be used to solve the compatible undefined initial conditions. Then, the solver function ode15i() can be used to solve the implicit differential equations.

5、The solution process of the implicit differential equations is the same as the explicit equations.they can be assigned arbitrarily.

07-08 Differential Algebraic Equations随堂测验

1、
    A、f=(t,x)[1-x(1);-x(2)]; M=@(t,x)[sin(x(1)),cos(x(2));-cos(x(2)),sin(x(1))]; options=odeset; options.Mass=M; options.RelTol=1e-6; [t,x]=ode45(f,[0,10],[0;0],options);
    B、f=(t,x)[1-x(1);-x(2)]; M=@(t,x)[sin(x(1)),cos(x(2));-cos(x(2)),sin(x(1))]; options=odeset; options.Mass=M; options.RelTol=1e-6; [t,x]=int(f,[0,10],[0;0],options);
    C、f=(t,x)[1-x(1);-x(2)]; M=@(t,x)[sin(x(1)),cos(x(2));-cos(x(2)),sin(x(1))]; options=odeset; options.Mass=M; options.RelTol=1e-6; [t,x]=fsolve(f,[0,10],[0;0],options);
    D、f=(t,x)[1-x(1);-x(2)]; M=@(t,x)[sin(x(1)),cos(x(2));-cos(x(2)),sin(x(1))]; options=odeset; options.Mass=M; options.RelTol=1e-6; [t,x]=diff(f,[0,10],[0;0],options);

2、
    A、fM=@(t,u)[1,0,0,0; 0,1,0,0; 0,0,2,cos(u(1)-u(2));... 0,0,cos(u(1)-u(2)),1]; g=9.81; x0=[45;30;0;0]; f=@(t,u)[u(3); u(4); -g*sin(u(1))-sin(u(1)-u(2))*u(4)^2;... -g*sin(u(2))+sin(u(1)-u(2))*u(3)^2]; ff=odeset; ff.Mass=fM; [t,x]=diff(f,[0,1.2],x0,ff);
    B、fM=@(t,u)[1,0,0,0; 0,1,0,0; 0,0,2,cos(u(1)-u(2));... 0,0,cos(u(1)-u(2)),1]; g=9.81; x0=[45;30;0;0]; f=@(t,u)[u(3); u(4); -g*sin(u(1))-sin(u(1)-u(2))*u(4)^2;... -g*sin(u(2))+sin(u(1)-u(2))*u(3)^2]; ff=odeset; ff.Mass=fM; [t,x]=int(f,[0,1.2],x0,ff);
    C、fM=@(t,u)[1,0,0,0; 0,1,0,0; 0,0,2,cos(u(1)-u(2));... 0,0,cos(u(1)-u(2)),1]; g=9.81; x0=[45;30;0;0]; f=@(t,u)[u(3); u(4); -g*sin(u(1))-sin(u(1)-u(2))*u(4)^2;... -g*sin(u(2))+sin(u(1)-u(2))*u(3)^2]; ff=odeset; ff.Mass=fM; [t,x]=ode45(f,[0,1.2],x0,ff);
    D、fM=@(t,u)[1,0,0,0; 0,1,0,0; 0,0,2,cos(u(1)-u(2));... 0,0,cos(u(1)-u(2)),1]; g=9.81; x0=[45;30;0;0]; f=@(t,u)[u(3); u(4); -g*sin(u(1))-sin(u(1)-u(2))*u(4)^2;... -g*sin(u(2))+sin(u(1)-u(2))*u(3)^2]; ff=odeset; ff.Mass=fM; [t,x]=solve(f,[0,1.2],x0,ff);

3、
    A、f=@(t,x)[-0.2*x(1)+x(2)*x(3)+0.3*x(1)*x(2); 2*x(1)*x(2)-5*x(2)*x(3)-2*x(2)*x(2); x(1)+x(2)+x(3)-1]; M=[1,0,0; 0,1,0; 0,0,0]; options=odeset; options.Mass=M; x0=[0.8; 0.1; 0.1]; [t,x]=ode15s(f,[0,20],x0,options);
    B、fDae=@(t,x)[-0.2*x(1)+x(2)*(1-x(1)-x(2))+0.3*x(1)*x(2);... 2*x(1)*x(2)-5*x(2)*(1-x(1)-x(2))-2*x(2)*x(2)]; x0=[0.8; 0.1]; [t1,x1]=ode45(fDae,[0,20],x0);
    C、f=@(t,x,xd)[xd(1)+0.2*x(1)-x(2)*x(3)-0.3*x(1)*x(2); xd(2)-2*x(1)*x(2)+5*x(2)*x(3)+2*x(2)^2; x(1)+x(2)+x(3)-1]; x0=[0.8;0.1;2]; x0F=[1;1;0]; xd0=[1;1;1]; xd0F=[]; [x0,xd0]=decic(f,0,x0,x0F,xd0,xd0F); [x0,xd0];res=ode15i(f,[0,20],x0,xd0);
    D、fDae=@(t,x)[-0.2*x(1)+x(2)*(1-x(1)-x(2))+0.3*x(1)*x(2);... 2*x(1)*x(2)-5*x(2)*(1-x(1)-x(2))-2*x(2)*x(2)]; x0=[0.8; 0.1]; [t1,x1]=solve(fDae,[0,20],x0);

4、Differential algebraic equation means that in the differential equation, certain variables satisfy the constraints of certain algebraic equations, so such an equation cannot be directly solved by the ordinary differential equation solution.

5、

07-09 Delayed Differential Equations随堂测验

1、
    A、f=@(t,x,Z)[1-5*x(1)-Z(2,1)-0.7*Z(1,2)^3-Z(1,2); x(3); 6*x(1)-2*x(2)-3*x(3)]; tau=[1 0.5]; tx=ode45(f,tau,zeros(3,1),[0,10]);
    B、f=@(t,x,Z)[1-5*x(1)-Z(2,1)-0.7*Z(1,2)^3-Z(1,2); x(3); 6*x(1)-2*x(2)-3*x(3)]; tau=[1 0.5]; tx=dde23(f,tau,zeros(3,1),[0,10]);
    C、f=@(t,x,Z)[1-5*x(1)-Z(2,1)-0.7*Z(1,2)^3-Z(1,2); x(3); 6*x(1)-2*x(2)-3*x(3)]; tau=[1 0.5]; tx=ddesd(f,tau,zeros(3,1),[0,10]);
    D、f=@(t,x,Z)[1-5*x(1)-Z(2,1)-0.7*Z(1,2)^3-Z(1,2); x(3); 6*x(1)-2*x(2)-3*x(3)]; tau=[1 0.5]; tx=ddensd(f,tau,zeros(3,1),[0,10]);

2、
    A、tau=@(t,x)[t-0.2*abs(sin(t)); t-0.8]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=ddensd(f,tau,zeros(3,1),[0,10]);
    B、tau=@(t,x)[t-0.2*abs(sin(t)); t-0.8]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=dde23(f,tau,zeros(3,1),[0,10]);
    C、tau=@(t,x)[t-0.2*abs(sin(t)); t-0.8]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=ode45(f,tau,zeros(3,1),[0,10]);
    D、tau=@(t,x)[t-0.2*abs(sin(t)); t-0.8]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=ddesd(f,tau,zeros(3,1),[0,10]);

3、
    A、tau=@(t,x)[t-0.1*abs(sin(t)); 0.8*t]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=ddesd(f,tau,zeros(3,1),[0,10]);
    B、tau=@(t,x)[t-0.1*abs(sin(t)); 0.8*t]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=pdepe(f,tau,zeros(3,1),[0,10]);
    C、tau=@(t,x)[t-0.1*abs(sin(t)); 0.8*t]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=ddensd(f,tau,zeros(3,1),[0,10]);
    D、tau=@(t,x)[t-0.1*abs(sin(t)); 0.8*t]; f=@(t,x,Z)[-2*x(2)-3*Z(1,1); -0.05*x(1)*x(3)-2*Z(2,2)+2; 0.3*x(1)*x(2)*x(3)+cos(x(1)*x(2))+2*sin(0.1*t^2)]; sol=bvp5c(f,tau,zeros(3,1),[0,10]);

4、
    A、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ddensd(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    B、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ddesd(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    C、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=dde23(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    D、A.A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ode45(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)

5、some of the signal contains not only the values at current time t, but also have values in the past, the differential equations are referred to as delay differential equations. MATLAB function dde23() is provided to solve numerically delay differential equations using implicit Runge–Kutta algorithms.

07-10 Boundary Value Problems of Differential Equations随堂测验

1、Which function provided by MATLAB can solve the boundary value problem of differential equations well?
    A、Linspace
    B、plot
    C、bvp5c
    D、bvpinit

2、
    A、linspace()
    B、etime()
    C、Colon expressions
    D、bvp5c()

3、Regarding the sol = bvp5c (@ fun1, @ fun2, sinit, options, additional parameters), which statements are correct ()
    A、This function can be used to solve boundary value problems.
    B、fun1.m and fun2.m are respectively the differential equations and the boundary values.
    C、fun1.m and fun2.m cannot be represented by anonymous functions. fun1.m和fun2.m
    D、The field sol.parameters stores the undetermined constant vector sol.parameters

4、

5、

07-11 Block Diagram Based Solutions of Differential Equations随堂测验

1、Which statements are correct?
    A、You can use open_system ('simulink') to open block library window of the Simulink.
    B、The Sine block can be used in generating sinusoidal signals. The block Step can be used in generating the step signal.
    C、
    D、

2、Regarding the integrator in Simulink, which statements are correct?
    A、
    B、Let each first derivative term of the ordinary differential equations be used as the input of each integrator module
    C、
    D、For high-order linear differential equations, it can also be modeled by Transfer Function blocks.

3、The Simulink model of differential equations is established, and the model can be solved with the sim () function to obtain the numerical solution of the differential equation

4、

5、

Unit Test

1、
    A、
    B、
    C、
    D、

2、
    A、syms t x(t) x=dsolve(diff(x)==x*(1-x^2))
    B、syms x(t); x=dsolve(diff(x)==x*(1-x^2))
    C、syms t x(t); x=dsolve(diff(x)==x*(1-x^2))
    D、syms t ; x=dsolve(diff(x)==x*(1-x^2))

3、
    A、
    B、
    C、
    D、

4、The variable step size fourth-order fifth-level Runge–Kutta–Felhberg algorithm is implemented, and the calling format of the variable step size algorithm for solving differential equations is
    A、[t,x]=ode15s(f,[0,tn],x0)
    B、[t,x]=ode113(f,[0,tn],x0)
    C、[t,x]=ode23(f,[0,tn],x0)
    D、[t,x]=ode45(f,[0,tn],x0)

5、A(x) is a non-singular matrix, let x = [x1, x2]T, then you can rewrite the original equation into a matrix form A(x)x′= B(x) transform the equation into a standard explicit one The system of order differential equations is correct:
    A、
    B、
    C、
    D、

6、For the variable step solution of rigid differential equations, the numerical solution is displayed by drawing a curve. The correct calling format is:
    A、toc
    B、plot(t1,y1)
    C、x1=exp(-2*t)
    D、tic

7、
    A、.f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode15s(f,[0,10],[0; 0],opt);
    B、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=solve(f,[0,10],[0; 0],opt);
    C、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode15i(f,[0,10],[0; 0],opt);
    D、f=@(t,x)inv([sin(x(1)) cos(x(2)); -cos(x(2)) sin(x(1))])*[2-x(1); -x(2)]; opt=odeset; opt.RelTol=1e-6; [t,x]=ode45(f,[0,10],[0; 0],opt);

8、
    A、
    B、
    C、
    D、

9、
    A、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ddensd(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    B、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ddesd(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    C、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=dde23(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)
    D、A1=[-13,3,-3; 106,-116,62; 207,-207,113]; A2=diag([0.02,0.03,0.04]); B=[0; 1; 2]; u=1; f=@(t,x,z1,z2)A1*z1+A2*z2+B*u; x0=zeros(3,1); sol=ode45(f,0.15,0.5,x0,[0,15]); plot(sol.x,sol.y)

10、Which function provided by MATLAB can solve the boundary value problem of differential equations well?
    A、Linspace
    B、plot
    C、bvp5c
    D、bvpinit

11、If you want to set the relative error to a smaller value of 10 to the negative 7th power, the following format is correct:
    A、options=odeset('RelTol',1e-7);
    B、options=odeset(1e-17);
    C、options=odeset; options.RelTol=1e-7;
    D、options=odeset; RelTol=1e-7;

12、
    A、f=@(t,x)[-0.2*x(1)+x(2)*x(3)+0.3*x(1)*x(2); 2*x(1)*x(2)-5*x(2)*x(3)-2*x(2)*x(2); x(1)+x(2)+x(3)-1]; M=[1,0,0; 0,1,0; 0,0,0]; options=odeset; options.Mass=M; x0=[0.8; 0.1; 0.1]; [t,x]=ode15s(f,[0,20],x0,options);
    B、fDae=@(t,x)[-0.2*x(1)+x(2)*(1-x(1)-x(2))+0.3*x(1)*x(2);... 2*x(1)*x(2)-5*x(2)*(1-x(1)-x(2))-2*x(2)*x(2)]; x0=[0.8; 0.1]; [t1,x1]=ode45(fDae,[0,20],x0);
    C、f=@(t,x,xd)[xd(1)+0.2*x(1)-x(2)*x(3)-0.3*x(1)*x(2); xd(2)-2*x(1)*x(2)+5*x(2)*x(3)+2*x(2)^2; x(1)+x(2)+x(3)-1]; x0=[0.8;0.1;2]; x0F=[1;1;0]; xd0=[1;1;1]; xd0F=[]; [x0,xd0]=decic(f,0,x0,x0F,xd0,xd0F); [x0,xd0];res=ode15i(f,[0,20],x0,xd0);
    D、fDae=@(t,x)[-0.2*x(1)+x(2)*(1-x(1)-x(2))+0.3*x(1)*x(2);... 2*x(1)*x(2)-5*x(2)*(1-x(1)-x(2))-2*x(2)*x(2)]; x0=[0.8; 0.1]; [t1,x1]=solve(fDae,[0,20],x0);

13、
    A、linspace()
    B、etime()
    C、Colon expressions
    D、bvp5c()

14、Regarding the integrator in Simulink, which statements are correct?
    A、
    B、Let each first derivative term of the ordinary differential equations be used as the input of each integrator module
    C、
    D、For high-order linear differential equations, it can also be modeled by Transfer Function blocks.

15、

16、Some nonlinear differential equations cannot be solved analytically with the dsolve () function.

17、The nonlinear differential equation can only be solved by numerical method, even the seemingly simple nonlinear differential equation has no analytical solution, only the very special nonlinear differential equation can be solved analytically.

18、The Euler algorithm can be replaced by various more accurate interpolation methods to improve the accuracy of operation.

19、When solving a differential equation with additional parameters, the variable name must be exactly the same as the function itself when calling the function.

20、The number of additional parameters in the ode45() call command may not exactly correspond to the number of additional parameters in the equation M function, and there will be no erroneous results.

21、The format of the rigid differential equation is called grammatical judgment: the traditional rigid problem can not be solved directly by MATLAB's ordinary solution function, but the rigid problem must be selected. The rules are:

22、Differential algebraic equation means that in the differential equation, certain variables satisfy the constraints of certain algebraic equations, so such an equation cannot be directly solved by the ordinary differential equation solution.

23、some of the signal contains not only the values at current time t, but also have values in the past, the differential equations are referred to as delay differential equations. MATLAB function dde23() is provided to solve numerically delay differential equations using implicit Runge–Kutta algorithms.

24、

25、The Simulink model of differential equations is established, and the model can be solved with the sim () function to obtain the numerical solution of the differential equation

Unit Assignmen

1、

2、

8 Data Interpolation and Functional Approximation Problems

08-01 One-dimensional Interpolation Problems随堂测验

1、Which of the following is the default system interpolation method. ( )
    A、Spline
    B、pchip
    C、Nearest
    D、Linear

2、Which of the following interpolation methods has the higher interpolation accuracy. ( )
    A、y =interp1(x,y,x1)
    B、y=interp1(x,y, x1,'spline')
    C、y=interp1(x,y, x1,'nearest')
    D、y=interp1(x,y, x1, 'linear')

3、The one-dimensional interpolation function in MATLAB is interp1()

4、The function interp1() provided in MATLAB does not have the Runge phenomenon. ( )

5、Forecast problems are essentially the extrapolation problems, and can not be implemented in interp1() function. ( )

08-02 Two-dimensional and Multi-dimensional Interpolation Problems随堂测验

1、Which of the following functions is Two-dimensional interpolation function. ( )
    A、interp1()
    B、interp2()
    C、trapz()
    D、ginput()

2、Which of the following functions can solve two-dimensional discrete data interpolation. ( )
    A、interp1 ()
    B、interp2()
    C、griddata()
    D、trapz()

3、Which of the following functions can generate n-dimensional grid data. ( )
    A、meshgrid()
    B、ndgrid()
    C、contour ()
    D、contour 3()

4、The function interp2() can only handle the data given in grid format. ( )

5、The call format of griddata() function is z =griddata(x0,y0,z0,x,y,’v4’). ( )

08-03 Spline Interpolation Problems随堂测验

1、Which of the following functions is used to define a cubic spline object in the Spline Toolbox. ( )
    A、csapi()
    B、ndgrid()
    C、trapz()
    D、griddata()

2、Numerical differentiation and integration can’t be solved using the Spline Toolbox. ( )

3、The interpolation results of spline function objects can be drawn with the function fnplt().( )

4、The function csapi() can be used to establish the cubic spline object for multivariate data in the grid format.( )

5、If the samples are given in vectors x and y, the following statements can be used to define a B-spline object S with the syntax S = spapi(k,x,y), where k is the order of B-spline. ( )

08-04 Numerical Calculus Computations with Spline Interpolations随堂测验

1、Which of the following functions can take partial derivatives for multivariate functions.( )
    A、Sd = fnder(S,k)
    B、Sd = fnder(S,[k1,· · · ,kn])
    C、Sd=spapi(k,x,y)
    D、f=diff(diff(f,x,m),y,n)

2、What is the meaning of S in Sd = fnder(S,[k1,· · · ,kn]).( )
    A、the cubic spline object
    B、the B-spline object
    C、arbitrary function
    D、indetermination

3、The spline function-based numerical differentiation to the given sample points can be calculated from the function fnder().( )

4、The cubic splines are not applicable to the calculation of third-order derivatives. ( )

5、If the definite integral over the [a, b] interval is required, we can use I = diff(fnint(S,[a, b])).( )

08-05 Fitting Functions from Samples随堂测验

1、Which of the following functions can be used to convert the result of P = polyfit(x,y,n) to symbolic polynomials.( )
    A、polyval()
    B、poly2sym()
    C、poly ()
    D、polyder ()

2、In commands : x = [0.47, 0.96, 1.76, 2.53, 3.30, 3.74];y = [1.07, 1.75, 2.27, 2.31, 1.49, 0.74];p = polyfit(x,y, 2), we can get( )
    A、-0.5495 2.2250 0.1260
    B、-0.5495 2.3250 0.1260
    C、-0.5495 2.3250 0.3260
    D、-0.4495 2.3250 0.1260

3、A MATLAB function polyfit() can be used to solve polynomial fitting problems, with the syntax p = polyfit(x,y,n), where x and y are the vectors of sample points, n is the selected degree of polynomial fitting.( )

4、If the fitting result is very poor, the fitting accuracy can be solved by increasing the degree of polynomial.( )

5、Polynomial fittings are not always accurate.( )

08-06 Least Squares Curve Fitting随堂测验

1、Which of the following functions can solve the least square curve fitting problem. ( )
    A、polyfit()
    B、fnder()
    C、lsqcurvefit()
    D、fnint()

2、The MATLAB function [a,Jm] = lsqcurvefit(fun,a0,x,y, opts), fun is the MATLAB description to the prototype function, which functions can be used as prototype functions.( )
    A、M-function
    B、anonymous function
    C、inline function
    D、not sure

3、The objective of least square curve fitting is to find the value of undetermined constants so that the objective function is the minimum.( )

4、The function lsqcurvefit() can’t be used for least square fitting of multi-variable function.( )

5、The prototype function can only be described by M-functions. ( )

08-07 Rational Approximations of Functions随堂测验

1、Run commands: cf=contfrac(pi,20), we can get ( )
    A、cf = [3, 7, 15, 1, 292, 1, 1, 1, 3, 1, 2, 1, 14, 2, 1, 1, 2, 2, 2, 2],
    B、cf= [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3, 1, 1, 2, 2, 2, 2],
    C、cf = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2],
    D、cf= [3, 7, 15, 1, 291, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2],

2、
    A、syms x; f=sin(x)*exp(-x)/(x+1)^3; [cf,r]=contfrac(f,10)
    B、syms x; f=sin(x)*exp(-x)/(x+1)^3; G= padefcnsym(f,0,10)
    C、syms x; f=sin(x)*exp(-x)/(x+1)^3; G= padefcnsym(f,10,10)
    D、syms x; f=sin(x)*exp(-x)/(x+1)^3; [cf,r]=contfrac(f,0,10)

3、The default call format for function contfrac() assumes that the reference point is at 0.( )

4、There is no continued fraction expansion functions provided in MATLAB, while low-level support of MuPAD has a set of functions.( )

5、Padé approximation can process any function to get its rational approximation. ( )

08-08 Special Functions随堂测验

1、Which of the following is the calling format of the gamma function. ( )
    A、y = erf(z),
    B、y = erfc(z)
    C、y=gammainc(x,α)
    D、y = gamma(x),

2、Which of the following functions can directly compute the value of the first Bessel function.( )
    A、besselj()
    B、bessely()
    C、besselh()
    D、legendre()

3、Gamma functions can be evaluated directly with y = gamma(x), where x can only be a vector. ( )

4、Incomplete Beta functions cannot be directly calculated by MATLAB functions.( )

5、The Beta function is an integral analytic nonintegrable.( )

08-09 Mittag-Leffler Functions随堂测验

1、
    A、
    B、
    C、
    D、

2、
    A、syms z; I=mittag_leffler(5,z)
    B、syms z; I=mittag_leffler(3,z)
    C、syms z; I=mittag_leffler(1/sym(3),z)
    D、syms z; I=mittag_leffler(1/sym(5),z)

3、
    A、syms z, I=mittag_leffler(5,4,z)
    B、syms z, I=mittag_leffler(4,5,z)
    C、syms z, I=mittag_leffler(54,1,z)
    D、syms z, I=mittag_leffler(1,54,z)

4、The single parameter Mittag-Leffler function is a special case of the double parameter Mittag-Leffler function. ( )

5、Due to the limitations of symsum() function in the new version, the mittag_leffler() function sometimes may not yield correct results. ( )

08-10 Correlation Analysis of Signals随堂测验

1、Which of the following call formats can be used to obtain the correlation coefficients R of vectors x and y. ( )
    A、R = corrcoef(x,y)
    B、R = xcorr ([x,N])
    C、R = corrcoef([x,y])
    D、R = corrcoef([x,y,N])

2、Correlation analysis can’t be used to characterize both stochastic and deterministic signals. ( )

3、The correlation function is an even function. ( )

4、

5、The auto-correlation function and cross-correlation function can both be evaluated with the use of function xcorr() ( )

08-11 Signal Filters and Filter Design随堂测验

1、Which of the following filters can be called at the moving average (MA) filter in the control domain ( )
    A、FIR filter
    B、IIR filter
    C、ARMA filter
    D、Butterworth filter

2、Which quantity in the command y=filter(b,a,x) represents the signal to be filtered. ( )
    A、b
    B、a
    C、x
    D、y

3、If the filter is known, the function filter() can be used to analyze the magnitude of the filter.( )

4、The filtered signal will have a time delay compared with the original signal. ( )

5、As the natural frequency increases the bandwidth of the filter will increase and the delay will increase. ( )

Unit Test

1、For the gamma function, the following statement is false.( )
    A、
    B、
    C、
    D、

2、Which function is the establishment B-spline object.( )
    A、Nearest
    B、csapi
    C、spapi
    D、pchip

3、Which function can be used to create a cubic spline object. ( )
    A、csapi
    B、spapi
    C、pchip
    D、linear

4、Which function can be used to solve the least squares curve fitting problems. ( )
    A、padefcn()
    B、lsqcurvefit()
    C、contfrac()
    D、fnint()

5、The construction of Mittag-Leffler function is based on the power series expansion of ( ) function. ( )
    A、sine
    B、exponent
    C、tangent
    D、logarithmic

6、Which is the relationship between the error function and the complement error function.()
    A、erf(z)erfc(z)=1
    B、erf(z)+erfc(z)=0
    C、erf(z)+erfc(z)=1
    D、erf(z)=erfc-1(z)

7、Which of the following functions is used to compute the Padé rational approximation.( )
    A、padefcn
    B、lsqcurvefit
    C、contfrac
    D、fnder

8、Which of the following functions is the correlation function in MATLAB.( )
    A、xcorr()
    B、besselj()
    C、R = corrcoef()
    D、R =belssly()

9、Which quantity in the command y=filter(b,a,x) represents the signal to be filtered. ( )
    A、b
    B、a
    C、x
    D、y

10、Which of the following interpolation methods has the higher interpolation accuracy. ( )
    A、y =interp1(x,y,x1)
    B、y=interp1(x,y, x1,'spline')
    C、y=interp1(x,y, x1,'nearest')
    D、y=interp1(x,y, x1, 'linear')

11、Which of the following functions can solve two-dimensional discrete data interpolation. ( )
    A、interp1 ()
    B、interp2()
    C、griddata()
    D、trapz()

12、
    A、
    B、
    C、
    D、

13、The MATLAB function [a,Jm] = lsqcurvefit(fun,a0,x,y, opts), fun is the MATLAB description to the prototype function, which functions can be used as prototype functions.( )
    A、M-function
    B、anonymous function
    C、inline function
    D、not sure

14、Which of the following functions can take partial derivatives for multivariate functions.( )
    A、Sd = fnder(S,k)
    B、Sd = fnder(S,[k1,· · · ,kn])
    C、Sd=spapi(k,x,y)
    D、f=diff(diff(f,x,m),y,n)

15、Which of the following call formats can be used to obtain the correlation coefficients R of vectors x and y. ( )
    A、R = corrcoef(x,y)
    B、R = xcorr ([x,N])
    C、R = corrcoef([x,y])
    D、R = corrcoef([x,y,N])

16、The padefcn() function provided in the Optimization Toolbox can be used to solve the least squares curve fitting problems.( )

17、No need to know the function prototype when using least squares curve fitting. ( )

18、The interpolation curves can be drawn with the function fnplt(). ( )

19、The two-dimensional interpolation function interp2() is provided in MATLAB.( )

20、The single parameter Mittag-Leffler function is a special case of the double parameter Mittag-Leffler function. ( )

21、The interpolation results of spline function objects can be drawn with the function fnplt().( )

22、The spline function-based numerical differentiation to the given sample points can be calculated from the function fnder.( )

23、The specific call format of are() function is X=are(A,B,C)

24、The correlation function is an even function. ( )

25、Incomplete Beta functions cannot be directly calculated by MATLAB functions.( )

Unit Assignment

1、

2、

9 Probability and Mathematical Statistics Problems

09-01 Commonly Used Probability Distributions随堂测验

1、The cumulative probability function F(x) is satisfying.( )
    A、monotonic increasing function
    B、
    C、
    D、

2、Which of the following statements about keywords in functions are true. ( )
    A、The functions with suffiffiffixes of pdf are used to indicate the probability density function.
    B、The functions with suffiffiffixes of cdf are used to indicate the cumulative distribution function.
    C、The functions with suffiffiffixes of inv are used to indicate the inverse distribution function.
    D、The functions with suffiffiffixes of rnd are used to indicate the random number generator.

3、

4、

5、

09-02 Probability Computation随堂测验

1、Function hist() can be used to obtain the frequencies.()

2、

3、

4、Monte Carlo method is a statistical experiment to find the values of uncertain variables using a large number of random quantities, based on random distributions.()

5、

09-03 Statistical Quantity Computation and Analysis随堂测验

1、Let a set of measured data be expressed by vector x = [x1, x2, x3, · · · , xn]T. Choose the right one in the following statements.
    A、m = mean(x) can be used to evaluate the sample mean.
    B、s2 = std(x) can be used to evaluate the sample variance.
    C、s = var(x) can be used to evaluate the standard deviation.
    D、m1 = median(x) can be used to evaluate the median value.

2、

3、For a set of random samples x1, x2, · · · , xn, the command Br = moment(x, r) can be used to evaluate the raw moments of all given order. ( )

4、The command [m,s]=raylstat(0.45) can be used to evaluate the mean and variance of Rayleigh distribution with theparameter b=0.45.( )

5、For a set of random samples x1, x2, · · · , xn, the command Ak=sum(x.ˆk)/length(x) can be used to evaluate the raw moments of all given order. ( )

09-04 Covariance Computation随堂测验

1、Which of the following functions can be used to evaluate the joint PDF of multivariate normal distributions. ( )
    A、cov()
    B、covpdf()
    C、mvnrnd()
    D、mvnpdf()

2、The function cov() can be used to evaluate the covariance matrix in MATLAB, with the syntax C = cov(X).

3、The mvnrnd() function in MATLAB can be used to generate multivariate pseudorandom numbers under normal distribution, with the syntax R = mvnrnd(µ,Σ2,m,n), where the m sets of random numbers will be returned in an m × n matrix R, with each column corresponding to a random variable. ( )

4、The command P = random(30000,4);R = cov(P) can generate a matrix R, and theoretically, it should be an identity matrix. ( )

5、The command R = mvnrnd(µ,Σ2,m,n) can be used to generate a metrix R, with each row corresponding to a random variable.

09-05 Outliers Detection随堂测验

1、By which means can outliers be detected? ( )
    A、Direct observation
    B、Histogram
    C、Data distribution map
    D、All of the above

2、Which command can find the median vector? ( )
    A、q =quantile(v,3)
    B、q =quantile(3,v)
    C、q=outliers(v,3)
    D、q=outliers(3,v)

3、The box graph of data vector v can be drawn directly by function boxplot (v). ( )

4、When the boxplot() function is called, if v is a matrix of m rows, m Box graphs will be displayed at the same time. ( )

5、For multivariable problems, moutlier1 () can be used to detect outliers. ( )

09-06 Parameter Estimation and Interval Estimation随堂测验

1、Which is the parameter estimation function of gamma distribution? ( )
    A、raylfit()
    B、nifit()
    C、gamfit()
    D、poissfit()

2、The confidence interval will be affected by the different choice of confidence degree. We usually choose 90% confidence degree.( )

3、If some data are known to satisfy a certain distribution, we can call the normfit() function to estimate the mean value μ and variance σ2 of the distribution by the maximum likelihood method.()

4、When generating random numbers, the more random points are selected, the better. Because this will significantly improve the accuracy of parameter estimation. ( )

5、For the function normfit (x, Pci), the larger the value of Pci is, the larger the confidence interval will be. ( )

09-07 Statistical Hypothesis Tests随堂测验

1、
    A、
    B、
    C、
    D、

2、What is the general value of significance level? ( )
    A、α = 2%
    B、α = 3%
    C、α = 5%
    D、α = 7%

3、Which of the following MATLAB statements can find the value of T0 .( )
    A、
    B、
    C、
    D、

4、

5、

09-08 Analysis of Variance随堂测验

1、What are the common methods of Analysis of variance? ( )
    A、one-way ANOVA
    B、two-way ANOVA
    C、N-way ANOVA
    D、zero-way ANOVA

2、Analysis of variance is an analysis method proposed by Ronald Fischer, a British statistician and geneticist ()

3、

4、

5、

09-09 Principal Component Analysis随堂测验

1、When doing principal component analysis, you need to set up a covariance matrix with ().
    A、eig()
    B、fliplr()
    C、diag()
    D、corr()

2、What are the steps of principal component analysis: ( )
    A、Find the covariance matric R from X
    B、
    C、Compute the principal components and contributions
    D、New coordinates Z = X L

3、Principal component analysis can achieve dimension reduction : ( )

4、Principal component analysis achieves dimension reduction through appropriate linear transformation ( )

5、Any problem can be simplified by principal component analysis ( )

Unit Test

1、The problem that principal component analysis can solve is ( )
    A、Data dimension reduction
    B、Data fitting
    C、Data forecast
    D、Data decoupling

2、Which of the following statements about keywords in functions are true..( )
    A、The functions with suffiffiffixes of rnd are used to indicate the random number generator.
    B、The functions with suffiffiffixes of stat are used to indicate the statistics analysis.
    C、The functions with suffiffiffixes of fit are used to indicate the parametric estimation.
    D、The functions with suffiffiffixes of pdf are used to indicate the probability density function.

3、Which of the following is the correct call format for ztest() and ttest() functions? ( )
    A、
    B、
    C、
    D、

4、Which of the following functions can implement the Jarque–Bera and Lilliefors hypothesis testing algorithm? ( )
    A、jbtest()
    B、ztest()
    C、lillietest()
    D、ttest()

5、Two functions,rand() and randn(),are used for generating uniformly distributed and normally distributed random matrices..( )

6、

7、

8、For a set of random samples x1, x2, · · · , xn, the command Br = moment(x, r) can be used to evaluate the central moments of all given order. ( )

9、The command median (x) can be used to evaluate the mean of vector x. ( )

10、The function corr() can be used to evaluate the covariance matrix in MATLAB, with the syntax C = corr(X).

11、The function mvnpdf() can be used to evaluate the joint PDF of multivariate normal distributions.()

12、In the box graph, there are some cross marks, indicating the outliers of the data set. ( )

13、The call format of the function moutlier1() is moutlier1 (X, α), where X is a matrix of M columns and α is the significance level. ( )

14、If some data are known to satisfy a certain distribution, the normfit() function can estimate the confidence intervals Δμ and Δσ2 of the distribution. ( )

15、The function regress () can get the parameter estimation and confidence interval estimation of multivariate linear regression model. ( )

16、

17、

Unit Assignment

1、

The final exam

The final exam

1、Which of the following is an invalid variable name( )
    A、abcdef
    B、xyz_3
    C、x3yz
    D、3xyz

2、Given that A is a 3×5 matrix,after A(:,[2,4])=[ ] is executed( ).
    A、A becomes the row vector
    B、A becomes 3 rows and 2 columns
    C、A becomes 3 rows and 3 columns
    D、A becomes 2 rows and 2 columns

3、Create a 5×6 random matrix A whose elements are random integers in the range [100, 200]. The corresponding command is ( ).
    A、A= fix(100+200*rand(5,6))
    B、A= fix(200+100*rand(5,6)) 
    C、A= fix(100+300*rand(5,6))
    D、A=fix(100+101*rand(5,6))

4、If P is a polynomial coefficient vector and A is a square matrix, then the values of the functions Polyval (P,A) and Polyvalm (P,A) are ( ).
    A、One is a scalar and another is a square matrix
    B、Both are scalars
    C、the two values are not equal
    D、the two values are equal

5、In the following four interpolation calculation methods, the method of passing through each sample point is( ).
    A、linear
    B、nearest
    C、pchip
    D、spline

6、If a and b are polynomial coefficient vectors, a=[1,2] and b=[3,4,5], add the two polynomials, the following is correct ( ).
    A、a+b
    B、[0,a]+b
    C、[a,0]+b
    D、a+b(1:2)

7、
    A、V
    B、V1
    C、V2
    D、V3

8、The construction of the Mittag-Leffler function is based on the power series expansion of ( ) function.
    A、Logarithmic
    B、Exponential
    C、Sine
    D、Cosine

9、
    A、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(A*x-B)
    B、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(B)*A, e1=norm(A*x-B)
    C、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(B*x-A)
    D、A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2]; B=[5 1; 4 2; 3 3; 2 4]; x=inv(A)*B, e1=norm(x*A-B)

10、
    A、f=@(x)(x(1))^(1/3)*sqrt(x(2))*x(3)^2*x(4)^3*x(5); I=quadndg(f,[0 0 0 0 0],[5,4,3,1,2]);
    B、f=(x)(x(1))^(1/3)*sqrt(x(2))*x(3)^2*x(4)^3*x(5); I=quadndg(f,[0 0 0 0 0], [5,4,3,1,2]);
    C、f=@(x)(x(1))^(1/3)*sqrt(x(2))*x(3)^2*x(4)^3*x(5); I=quadndg(@f,[0 0 0 0 0],[5,4,1,2,3]);
    D、f=(x)(x(1))^(1/3)*sqrt(x(2))*x(3)^2*x(4)^3*x(5); I=quadndg(f,[5,4,1,2,3],[0 0 0 0 0]);

11、Defined a function file fun.m: function f=fun(n) f=sum(n.*(n+1)); The result of calling the fun function >> fun(1:5)  in the command window is ( ).
    A、30 
    B、50
    C、65
    D、70

12、If you use the command taylor(f,x,1,'Order',6) to perform Taylor expansion on f, the highest order of the expansion is ( ).
    A、6
    B、5
    C、4
    D、3

13、In the dsolve() function, if no argument is specified, the default argument is ( ).
    A、a
    B、x
    C、i
    D、t

14、The command subplot(2,2,3) means ( )
    A、The lower left picture of two rows and two columns
    B、The lower right picture of two rows and two columns
    C、Upper left picture with two rows and two columns
    D、Upper right picture with two rows and two columns

15、For linear equations Ax=b, when det(A)≠0, the solution of the equation is ( ).
    A、A/b
    B、b/A
    C、b\A
    D、A\b

16、
    A、
    B、
    C、
    D、

17、When entering commands in the MATLAB command window, you can use the line continuation character, which is written ( ).
    A、ellipsis(…)
    B、semicolon(;)
    C、three decimal points(...)
    D、Percent sign(%)

18、The meanings of f, v, u in the function laplace(f, v, u) are ( ).
    A、f is function name, v is time-domain variable, u is complex domain variable
    B、f is complex domain variable, v is function name, u is time-domain variable
    C、f is time-domain variable, v is function name, u is complex domain variable
    D、f is function name, v is complex domain variable, u is time-domain variable

19、The function used to create the B-spline interpolation object is ( ).
    A、spapi
    B、csapi
    C、Nearest
    D、pchip

20、
    A、
    B、
    C、
    D、

21、
    A、x = [0, 0.6667, 1.6667, 2.6667]T
    B、x = [0, 0.6667, 1.6667, 3.6667]T
    C、x = [0, 0.2857, 1.8571, 3.4286]T
    D、x = [0, 0.2857, 1.8571, 2.4286]T

22、
    A、
    B、
    C、
    D、

23、When using the S function, add ( ) in the model editing window.
    A、Sine Wave block
    B、S-Program block
    C、S-Function block
    D、Subsystem block

24、
    A、
    B、
    C、
    D、

25、
    A、3
    B、1
    C、0
    D、2

26、
    A、x = [0.3952, 2.3213, 0.75260, 5309, 1.5053, 0, 0]T
    B、x = [0.3952, 2.3213, 0.5309, 0, 0, 0.7526, 1.5053T
    C、x = [0, 0, 0.3952, 2.3213, 0.5309, 0.7526, 1.5053]T
    D、x= [0.3952, 2.3213, 0.5309, 0.7526, 1.5053, 0, 0]T

27、
    A、
    B、
    C、
    D、

28、
    A、
    B、
    C、
    D、

29、
    A、
    B、
    C、
    D、

30、
    A、- 1/3
    B、1/3
    C、- 1/6
    D、1/6

31、When creating a matrix, elements in the same row are separated by ( ).
    A、comma
    B、space
    C、semicolon
    D、square brackets

32、If the fpp.m file exists in both the current folder and search path, the wrong options in the following statement are ( ) when entering fpp in the command window.
    A、execute the fun1.m file in the search path at first, then execute the fun1.m file in the current folder
    B、only execute the fun1.m file in the search path
    C、execute the fun1.m file in the current folder at first, and then execute the fun1.m file in the search path
    D、only execute the fun1.m file in the current folder

33、The trace of a matrix is defined as the sum of diagonal elements, which of the following methods can find the matrix trace( ).
    A、trace(A)
    B、sum(diag(A))
    C、prod(eig(A))
    D、sum(eig(A))

34、Given that a =2:2:8 and b =2:5, the correct expression is ( ).
    A、a'*b
    B、a .*b
    C、a*b
    D、a-b

35、
    A、34.0000
    B、17.8885
    C、4.4721
    D、0.0000

36、Given three polynomials whose coefficient vectors are q, r, s respectively, the following commands can be used to take the product of them ( ).
    A、conv(q,r,s)
    B、conv(conv(q,r),s)
    C、conv(q,conv(r,s))
    D、conv(conv(s,r),q)

37、
    A、Create a function file tx.m. function dx=tx(t, x) dx=[ -8/3*x(1)+x(2)*x(3); -10*x(2)+10*x(3); -x(1)*x(2)+28*x(2)-x(3) ]; Call function file: >> [t, x]=ode45(@tx, [0, 20], [0, 1, 1]); >> plot3(x(:,1),x(:,2),x(:,3));
    B、Create a function file tx.m. function dx=tx(t, x) dx=[ -8/3*x(1)+x(2)*x(3); -10*x(2)+10*x(3); -x(1)*x(2)+28*x(2)-x(3) ]; Call function file: >> h=@tx; >> [t, x]=ode45(h, [0, 20], [0, 1, 1]); >> plot3(x(:,1),x(:,2),x(:,3));
    C、>>f=@(t,x)[-8/3*x(1)+x(2)*x(3); -10*x(2)+10*x(3); -x(1)*x(2)+28*x(2)-x(3)]; >>[t,x]=ode45(f,[0, 20], [0, 1, 1]); >> plot3(x(:,1),x(:,2),x(:,3));
    D、>>[t, x]=ode45(@(t, x) [-8/3*x(1)+x(2)*x(3); -10*x(2)+10*x(3); -x(1)*x(2) + 28 *x(2)-x(3)], [0, 20], [0, 1, 1]); >> plot3(x(:,1),x(:,2),x(:,3));

38、The specific call format of lyapsym() function is ( ).
    A、X=lyapsym(sym(A),C)
    B、X=lyapsym(sym(A),-inv(B),Q*inv(B))
    C、X=lyapsym(sym(A),-inv(A'),Q*inv(A'))
    D、X=lyapsym(sym(A),B,C)

39、Which of the following the description of commands are correct ( ).
    A、round( ) is round to nearest integer
    B、the result of floor(-2.3) is -2
    C、ceil( ) is round towards +∞
    D、the result of rem (x,y) is the remainder of x divided by y

40、Which of the following descriptions about stiff ordinary differential equations are correct ( ).
    A、Many conventional stiff equations, one may still try to use the ordinary ODE solvers rather than the stiff equation solver.
    B、The function ode45() is not suitable for stiff equations,an alternative function, ode15s() can be used instead.
    C、Some solutions of stiff ordinary differential equations change very rapidly while others may change very slowly.
    D、Stiff equations using ode45 () can get results faster, but the results are not accurate.

41、
    A、trace(A)=13
    B、rank(A)=3
    C、[V,D]=eig(A) means to find all the eigenvalues of matrix A to form the diagonal matrix D and the eigenvectors of A form the column vector V
    D、det(A)=78

42、MATLAB provides the solution of unconstrained optimization function, the correct call format is ( )
    A、x=fsolve(fun, x0)
    B、x=fminsearch(fun, x0)
    C、x=fminunc(fun, x0)
    D、x=fsolve(fun, x0,x1)

43、Which of the following operations is correct for matrix A,B ( )
    A、A.+B
    B、A.*B
    C、A+B
    D、A\B

44、The following statement is wrong ( ).
    A、A=[1 2;3 4];B=[3 7]; A*B;
    B、A=cell(2,3); A(1,2)=[4;5]
    C、A=[2 3 5 7;9 4 6 1;7 3 2 5];B=[1 7;0 5];A(2:end,2:2:end)
    D、x=-5:5;y=-5:5;z=x.*x-y.*y;surf(x,y,z)

45、
    A、P1=[5,0,3];P2=[1,-2,11];P3=[0,-7,-6];P=conv(conv(P1,P2),P3)
    B、P1=[5,0,3];P2=[1,-2,11];P3=[-7,-6,0];P=conv(conv(P1,P2),P3)
    C、P1=[5,0,3];P2=[1,-2,11];P3=[0,-7,-6];P=conv(P1,conv(P2,P3))
    D、P1=[5,0,3];P2=[1,-2,11];P3=[-7,-6,0];P=conv(conv(P3,P2),P1)

46、The following expressions about calculating matrix functions are correct( )
    A、sin A=funm(A, ’sin’)
    B、eA=exp(A)
    C、sin A=sin(A)
    D、e Acos(At) = funm (A, exp (x*cos(x*t)), x)

47、Which of the following are the process structures provided in matlab. ( )
    A、the loop structures
    B、conditional control structures
    C、switch structures
    D、test pause structures

48、Which of the following blocks are provided by Simulink ( )
    A、Input and output port blocks
    B、Pause blocks
    C、Transport delay blocks
    D、Gain blocks

49、What are the methods of interpolation ( ).
    A、Linear
    B、Spline
    C、Nearest
    D、pchip

50、Central-point difference algorithm call format is [dy,dx]=diff_ctr(y, Dt, n), the following statements are correct ( ).
    A、y is the vector containing measured data for evenly distributed points
    B、n specifies the order of derivativ
    C、the argument dx is the corresponding vector of independent variables.
    D、

51、The variable names are case-sensitive in MATLAB.

52、For a matrix A with 3 rows and 3 columns, A(4) represents the element in the first column of the second row in matrix A.

53、In MATLAB, the round() can round to nearest integer of arrays.

54、The statement to establish the 3rd order a matrix of ones is A=ones(3,1).

55、Any complex program is composed of three basic structures: sequential structure, selection structure and loop structure.

56、The command to add 30 to the diagonal elements of matrix A is A+30*eye(A).

57、A MATLAB function inv() can calculate the inverse matrix of singular matrix.

58、clc is used to clear space to save content, and clear is used to clear MATLAB display content.

59、No matter how many branches there are in the multi-branch if statement, after the program executes one branch, the remaining branches will not be executed again, and then the entire if statement ends.

60、In the curve color setting, b means black.

61、The text() can be used to add labels to coordinate axes.

62、Running commands A=[15 3 2 13; 5 18 10 8; 9 7 6 12; 4 14 15 1]; n1=norm(A), the characteristic value of A can be obtained.

63、If the polynomial coefficient vector p=[5,3,1] is known, the constant term of the polynomial is 5.

64、Comments start with % in MATLAB, followed by the content of the comment.

65、Padé approximation can process any function to get its rational approximation.

66、

67、If the characteristic polynomial can be exactly known, the function roots() can also be used in evaluating the eigenvalues of the matrix.

68、are(A,B,C) can solve the Riccati equation.

69、The diff() function can be used to find the partial derivative of the sign function.

70、In commands: H1=[H eye(5)]; H2=rref(H1), H3=H2(:,6:10), H3 is the inverse matrix of matrix H.

71、Incomplete Beta functions cannot be directly calculated by MATLAB functions.

72、If a certain vector of polynomial coefficients contains five elements, then the polynomial is a polynomial of degree 5.

73、The text() can be used to add labels to coordinate axes.

74、In the MATLAB environment, if you need to add grid lines to the already drawn graphics, you can use the hold on command.

75、The Beta function is an integral analytic nonintegrable.