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、5. 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))
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.（）
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.
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);
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、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
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)
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()
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
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.
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)
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