1 Computer Mathematics Languages — An Overview

Quiz

1、判断题:
The three steps of Three-step Strategy of Scientific computing are "what is it", "how to describe it"and"solution".‎‌‎
选项:
A: 正确
B: 错误
答案: 【 正确

Unit Test

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

2、多选题:
‎The main functions of MATLAB include​
选项:
A: Numerical computation
B: programming
C: widely used in symbolic operation
D: numerical simulation
答案: 【 Numerical computation;
programming;
widely used in symbolic operation;
numerical simulation

3、多选题:
​Which of the following is the advantage of MATLAB language?‍
选项:
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
答案: 【 powerful system simulation capability ,Simulink;
It is the international preferred computer language in the field of control and many fields

4、多选题:
​‎What are the outstanding features of MATLAB compared with other computer languages​‎​
选项:
A: Poor openness
B: Powerful functions
C: Rich library functions
D: Rich library functions
答案: 【 Powerful functions;
Rich library functions;
Rich library functions

5、多选题:
​‌Which of the following situations does the analytic solution not exist​
选项:
A: Solving indefinite integral problems
B: Circular constant
C: The analytic expression of function
D: Bivariate first order equations with roots
答案: 【 Solving indefinite integral problems;
Circular constant

2 Fundamentals of MATLAB Programming

Quiz

1、单选题:
1.   When drawing four-dimensional graphics, the correct format of the meshgrid function is: ( )‌‌‌
选项:
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 )
答案: 【 [x, y, z] = meshgrid ( 0 : 0.1 : 2 )

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

3、判断题:
3.   When drawing four-dimensional graphics, in order to easily observe the cross-sectional view, MATLAB provides a graphical user interface vol_visual4d. ( )‍‌‍
选项:
A: 正确
B: 错误
答案: 【 正确

4、判断题:
4.   To draw a three-dimensional volume slice, you can use the command slice. ( )‌‍‌
选项:
A: 正确
B: 错误
答案: 【 正确

5、判断题:
5.   Known mathematical function V = f (x, y, z), you can call the function vol_visual4d (x, y, z, V) to set the slice. ( )‏‎‏
选项:
A: 正确
B: 错误
答案: 【 正确

Unit Test

1、单选题:
​Which of the following factorial calculation methods is wrong?‏
选项:
A: factorial(sym(n))
B: gamma(1+n)
C: prod(1+n)
D: gamma(1+sym(n)
答案: 【 prod(1+n)

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

3、单选题:
Which of the following functions is used to draw polar coordinates? ()‏‏‏
选项:
A: hist ()
B: feather ()
C: polar ()
D: loglog ()
答案: 【 polar ()

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

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

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

7、多选题:
The correct ones of the following variable names are()‍​‍
选项:
A: V_alue
B: Value-
C: Value1
D: 1_Value
答案: 【 V_alue;
Value1

8、多选题:
  Choose the flow control structures provided in MATLAB. ()‌‏‌
选项:
A: switch structures
B: conditional control structures
C: trial structures
D: loop structures
答案: 【 switch structures;
conditional control structures;
trial structures;
loop structures

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

10、判断题:
To find the first 20 significant digits of 10/7, use command  A = 10/7 , vpa(A,20)()‎​‎
选项:
A: 正确
B: 错误
答案: 【 正确

11、判断题:
 Generate a vector between A ∈ [0,45] with a step size of 1, the command that should be entered is A = [0: 45]()‍‌‍
选项:
A: 正确
B: 错误
答案: 【 正确

12、判断题:
  Generate a vector between A ∈ [0,200] with a step size of 4, the command that should be entered is A = [0: 4:200]()​‏​
选项:
A: 正确
B: 错误
答案: 【 正确

13、判断题:
 A is a 3x3 matrix. Using the command A * A, can achieve the direct calculation of the corresponding elements of matrix A()​​​
选项:
A: 正确
B: 错误
答案: 【 错误

14、判断题:

‌选项:
A: 正确
B: 错误
答案: 【 错误

15、判断题:
​‍List all the prime numbers in the interval [1, 1000]. The command is a = 1:1000. ()​
选项:
A: 正确
B: 错误
答案: 【 错误

16、判断题:
The polynomial P can be simplified with the command: simplify(P).()​‏​
选项:
A: 正确
B: 错误
答案: 【 正确

17、判断题:

‌选项:
A: 正确
B: 错误
答案: 【 正确

18、判断题:
 The naming rules of file name are consistent with the naming rules of variable names.( )‌‍‌
选项:
A: 正确
B: 错误
答案: 【 正确

19、判断题:
  Both the M-script program and the M-function program have function definitions.()‎​‎
选项:
A: 正确
B: 错误
答案: 【 错误

20、判断题:
‎Define an M function my_fact(n),which can calculate n!,then the command my_fact(99) can be used to calculate 99!‏
选项:
A: 正确
B: 错误
答案: 【 错误

21、判断题:
‌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.​
选项:
A: 正确
B: 错误
答案: 【 正确

22、判断题:
 contour () function can draw three-dimensional contour graphics ()‍‏‍
选项:
A: 正确
B: 错误
答案: 【 正确

23、判断题:
 If you want to change the viewing angle to observe 3D graphics, you can use the view function ()‌​‌
选项:
A: 正确
B: 错误
答案: 【 正确

24、判断题:
When drawing four-dimensional graphics, the calculation of the volume data V of the ternary function needs to use point operation ()‌‏‌
选项:
A: 正确
B: 错误
答案: 【 正确

25、判断题:
‌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.()‎
选项:
A: 正确
B: 错误
答案: 【 正确

3 Calculus Problems

Quiz

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

2、单选题:
‏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?‏
选项:
A: Inline() function
B:  M function
C: Integral() function
D: Anonymous function
答案: 【  M function

3、单选题:

‏选项:
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)
答案: 【 >> 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、单选题:

‏选项:
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)
答案: 【 >> 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)

5、判断题:

‍选项:
A: 正确
B: 错误
答案: 【 正确

Unit Test

1、单选题:

‏选项:
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)
答案: 【  syms n; f=n^(2/3)*sin(factorial(n))/(n+1); F=limit(f,n,inf)

2、单选题:

‍选项:
A: exp(x)/(2*(x^2+1) 
B: exp(x)/(x^2 + 1)
C: 0
D:
答案: 【 exp(x)/(2*(x^2+1) 

3、单选题:

‍选项:
A: -10
B: 10
C: non-existence
D: 0
答案: 【 -10

4、单选题:

‍选项:
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))
答案: 【 syms x; f=sqrt((x-2)*(x-3)/(x-4)/(x-5)); D=simplify(diff(f,x,4))

5、单选题:

‌选项:
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)) 
答案: 【 syms t; y=sin(t)/(t+2)^3; x=cos(t)/(t+3)^3; f=simplify(paradiff(y,x,t,3))

6、单选题:

‍选项:
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)))
答案: 【 syms x; f=(2*sin(x)^2-4*sin(x)*cos(x)+6*cos(x)^2)/(sin(x)+3*cos(x)); I1=int(f) 

7、单选题:
‍ 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.‌‍‌
选项:
A: (-L/2,L/2)
B: (L,2L)
C: (- L, L)
D: (L/2,L)
答案: 【 (- L, L)

8、单选题:
‍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:‏
选项:
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);
答案: 【 syms x; f=x*(x-pi)*(x-2*pi); [F,A,B]=fseries(f,x,12,0,2*pi);

9、单选题:
‍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:‏
选项:
A: k 
B: k+1
C: k-1
D: 2k
答案: 【 k-1

10、单选题:
‎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:‌‎‌
选项:
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)
答案: 【 syms x y a b; f=x*cos(y); F=taylor(f,[x,y],[a,b],’Order’,4)

11、单选题:
‍Which instruction does not meet the code specification for solving the series sum and sequence quadrature synthesis problem‌
选项:
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)
答案: 【 syms n k; L1=limit(symsum(1/((2*k)^2-1),k,1,n))

12、单选题:
‌get the combination of instructions used in the finite product and infinite product of the sequence‏‌‏
选项:
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)
答案: 【 syms k n; P=symprod(1+1/k^3,k,1,n); P=simplify(P)

13、单选题:
‍ Which of the following call formats of intel() function is correct?‍
选项:
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)
答案: 【 I=integral(f,a,b,property setting pair)

14、单选题:

‌选项:
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)
答案: 【 >> f=@(t)exp(-t).*sin(3*t+1).*(pi-t).^(1/4), F1=integral(f,0,pi)

15、单选题:

‏选项:
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
答案: 【 >> 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、单选题:
​Which of the following is the most commonly used function for solving numerical solutions of double definite integrals?‎
选项:
A: integral() 
B: integral2()
C: Integral3()
D: Integral4()
答案: 【 integral2()

17、单选题:

‏选项:
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)
答案: 【      >> 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)

18、多选题:

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