东北大学matlab作业汇总.docx

1、东北大学matlab作业汇总第一部分：1、安装MATLAB软件，应用demo命令了解主要功能，熟悉基本功能，会用help命令。2、用MATLAB语句输入矩阵和 ， 前面给出的是矩阵，如果给出命令将得出什么结果？解： A=1 2 3 4;4 3 2 1;2 3 4 1;3 2 4 1B=1+4j 2+3j 3+2j 4+1j;4+1j 3+2j 2+3j 1+4j;2+3j 3+2j 4+1j 1+4j;3+2j 2+3j 4+1j 1+4jA = 1 2 3 4 4 3 2 1 2 3 4 1 3 2 4 1B = 1.0000 + 4.0000i 2.0000 + 3.0000i 3.000

2、0 + 2.0000i 4.0000 + 1.0000i 4.0000 + 1.0000i 3.0000 + 2.0000i 2.0000 + 3.0000i 1.0000 + 4.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i 3.0000 + 2.0000i 2.0000 + 3.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i A(5,6)=5A = 1 2 3 4 0 0 4 3 2 1 0 0 2 3 4 1 0 0 3 2 4 1 0 0 0 0 0 0

3、 0 53、假设已知矩阵，试给出相应的MATLAB命令，将其全部偶数行提取出来，赋给矩阵，用命令生成矩阵，用上述命令检验一下结果是不是正确。解： A=magic(8)A = 64 2 3 61 60 6 7 57 9 55 54 12 13 51 50 16 17 47 46 20 21 43 42 24 40 26 27 37 36 30 31 33 32 34 35 29 28 38 39 25 41 23 22 44 45 19 18 48 49 15 14 52 53 11 10 56 8 58 59 5 4 62 63 1 B=A(2:2:end, :)B = 9 55 54 12

4、13 51 50 16 40 26 27 37 36 30 31 33 41 23 22 44 45 19 18 48 8 58 59 5 4 62 63 14、用数值方法可以求出，试不采用循环的形式求出和式的数值解。由于数值方法是采用double形式进行计算的，难以保证有效位数字，所以结果不一定精确。试采用运算的方法求该和式的精确值。解： syms S S=sum(sym(2).0:63) S = 184*7095516155、选择合适的步距绘制出下面的图形。（1），其中； （2），其中。解:（1） t=-1:0.001:1;y=sin(1./t);plot(t,y)(2) t=-pi:0.

5、001:pi;y=sin(tan(t)-tan(sin(t);plot(t,y)6、试绘制出二元函数的三维图和三视图。解: x,y=meshgrid(-2:.1:2);z=1./(sqrt(1-x).2+y.2)+1./(sqrt(1+x).2+y.2); surf(x,y,z),shading flat7、试求出如下极限。（1）； （2）； （3）。解:（1） syms x;f=(3x+9x)(1/x);limit(f,x,inf) ans = 9（2） syms x y;f=x*y/(x*y+1)(0.5)-1);limit(limit(f,x,0),y,0) ans = 2（3） sym

6、s x y;f=(1-cos(x2+y2)/(x2+y2)*exp(x2+y2);limit(limit(f,x,0),y,0) ans = 08、已知参数方程，试求出和。解: syms t;x=log(cos(t);y=cos(t)-t*sin(t); diff(y,t)/diff(x,t) ans = (cos(t)*(2*sin(t) + t*cos(t)/sin(t) f=diff(y,t,2)/diff(x,t,2);subs(f,t,sym(pi/3) ans = 3/8 - (pi*3(1/2)/249、假设，试求解: syms x y tf=int(exp(-t2),t,0,x

7、*y);x/y*diff(f,x,2)-2*diff(diff(f,x),y)+diff(f,y,2) ans = (2*x2*y2)/exp(x2*y2) - (2*x3*y)/exp(x2*y2) - 2/exp(x2*y2)10、试求出下面的极限。 （1）；（2）。解:（1） syms k n;limit( symsum(1/(2*k)2-1),k,1,n),n,inf) ans = 1/2（2） syms k nlimit(n*symsum(1/(n2+k*pi),k,1,n),n,inf) ans = 111、试求出以下的曲线积分。 （1），为曲线， 。 （2），其中为正向上半椭圆。

8、解:（1） syms a t; x=a*(cos(t)+t*sin(t); y=a*(sin(t)-t*cos(t);f=x2+y2; S=int(f*sqrt(diff(x,t)2+diff(y,t)2),t,0,2*pi) S = 2*pi2*(2*pi2 + 1)*(a2)(3/2)（2） syms a t; x=a*(cos(t)+t*sin(t); y=a*(sin(t)-t*cos(t);f=x2+y2; S=int(f*sqrt(diff(x,t)2+diff(y,t)2),t,0,2*pi) S = 2*pi2*(2*pi2 + 1)*(a2)(3/2) syms x y a

9、b c t; x=c*cos(t)/a; y=c*sin(t)/b;P=y*x3+exp(y); Q=x*y3+x*exp(y)-2*y;ds=diff(x,t);diff(y,t); S=int(P Q*ds,t,0,pi) S = -(2*c*(15*b4 - 2*c4)/(15*a*b4)12、求出Vandermonde矩阵的行列式，并以最简的形式显示 结果。解: syms a b c d e; A=vander(a b c d e) A = a4, a3, a2, a, 1 b4, b3, b2, b, 1 c4, c3, c2, c, 1 d4, d3, d2, d, 1 e4, e

10、3, e2, e, 1 det(A),simplify(ans) ans = a4*b3*c2*d - a4*b3*c2*e - a4*b3*c*d2 + a4*b3*c*e2 + a4*b3*d2*e - a4*b3*d*e2 - a4*b2*c3*d + a4*b2*c3*e + a4*b2*c*d3 - a4*b2*c*e3 - a4*b2*d3*e + a4*b2*d*e3 + a4*b*c3*d2 - a4*b*c3*e2 - a4*b*c2*d3 + a4*b*c2*e3 + a4*b*d3*e2 - a4*b*d2*e3 - a4*c3*d2*e + a4*c3*d*e2 + a

11、4*c2*d3*e - a4*c2*d*e3 - a4*c*d3*e2 + a4*c*d2*e3 - a3*b4*c2*d + a3*b4*c2*e + a3*b4*c*d2 - a3*b4*c*e2 - a3*b4*d2*e + a3*b4*d*e2 + a3*b2*c4*d - a3*b2*c4*e - a3*b2*c*d4 + a3*b2*c*e4 + a3*b2*d4*e - a3*b2*d*e4 - a3*b*c4*d2 + a3*b*c4*e2 + a3*b*c2*d4 - a3*b*c2*e4 - a3*b*d4*e2 + a3*b*d2*e4 + a3*c4*d2*e - a3

12、*c4*d*e2 - a3*c2*d4*e + a3*c2*d*e4 + a3*c*d4*e2 - a3*c*d2*e4 + a2*b4*c3*d - a2*b4*c3*e - a2*b4*c*d3 + a2*b4*c*e3 + a2*b4*d3*e - a2*b4*d*e3 - a2*b3*c4*d + a2*b3*c4*e + a2*b3*c*d4 - a2*b3*c*e4 - a2*b3*d4*e + a2*b3*d*e4 + a2*b*c4*d3 - a2*b*c4*e3 - a2*b*c3*d4 + a2*b*c3*e4 + a2*b*d4*e3 - a2*b*d3*e4 - a2*

13、c4*d3*e + a2*c4*d*e3 + a2*c3*d4*e - a2*c3*d*e4 - a2*c*d4*e3 + a2*c*d3*e4 - a*b4*c3*d2 + a*b4*c3*e2 + a*b4*c2*d3 - a*b4*c2*e3 - a*b4*d3*e2 + a*b4*d2*e3 + a*b3*c4*d2 - a*b3*c4*e2 - a*b3*c2*d4 + a*b3*c2*e4 + a*b3*d4*e2 - a*b3*d2*e4 - a*b2*c4*d3 + a*b2*c4*e3 + a*b2*c3*d4 - a*b2*c3*e4 - a*b2*d4*e3 + a*b2

14、*d3*e4 + a*c4*d3*e2 - a*c4*d2*e3 - a*c3*d4*e2 + a*c3*d2*e4 + a*c2*d4*e3 - a*c2*d3*e4 + b4*c3*d2*e - b4*c3*d*e2 - b4*c2*d3*e + b4*c2*d*e3 + b4*c*d3*e2 - b4*c*d2*e3 - b3*c4*d2*e + b3*c4*d*e2 + b3*c2*d4*e - b3*c2*d*e4 - b3*c*d4*e2 + b3*c*d2*e4 + b2*c4*d3*e - b2*c4*d*e3 - b2*c3*d4*e + b2*c3*d*e4 + b2*c*

15、d4*e3 - b2*c*d3*e4 - b*c4*d3*e2 + b*c4*d2*e3 + b*c3*d4*e2 - b*c3*d2*e4 - b*c2*d4*e3 + b*c2*d3*e4 ans = (a - b)*(a - c)*(a - d)*(b - c)*(a - e)*(b - d)*(b - e)*(c - d)*(c - e)*(d - e)13、试对矩阵进行Jordan变换，并得出变换矩阵。解: A=-2,0.5,-0.5,0.5;0,-1.5,0.5,-0.5;2,0.5,-4.5,0.5;2,1,-2,-2; V J=jordan(sym(A) V = 0, 1/2,

16、 1/2, -1/4 0, 0, 1/2, 1 1/4, 1/2, 1/2, -1/4 1/4, 1/2, 1, -1/4 J = -4, 0, 0, 0 0, -2, 1, 0 0, 0, -2, 1 0, 0, 0, -214、试用数值方法和解析方法求取下面的Sylvester方程，并验证得出的结果。解:数值方法： A=3,-6,-4,0,5;1,4,2,-2,4;-6,3,-6,7,3;-13,10,0,-11,0;0,4,0,3,4; B=3,-2,1; -2,-9,2; -2,-1,9; C=-2,1,-1; 4,1,2; 5,-6,1; 6,-4,-4; -6,6,-3; X=ly

17、ap(A,B,C)X = -4.056896419147292 -14.512782077381612 1.565310728709521.0355* 9.488645270988460 25.932327650327640 -4.417733416157587 2.696922296480646 21.645009214025027 -2.885084137489283 7.722872389418908 31.909960533088562 -3.763408710201076 norm(A*X+X*B+C)ans = 3.435635978567079e-13解析方法： X=lyap(s

18、ym(A),B,C)X =-434641749950/107136516451,-4664546747350/321409549353, 503105815912/321409549353 3809507498/107136516451, 8059112319373/321409549353, -880921527508/321409549353 1016580400173/107136516451, 8334897743767/321409549353,-1419901706449/321409549353 288938859984/107136516451, 6956912657222/3

19、21409549353, -927293592476/321409549353 827401644798/107136516451,10256166034813/321409549353,-1209595497577/321409549353 A*X+X*B+C ans = 0, 0, 0 0, 0, 0 0, 0, 0 0, 0, 0 0, 0, 015、假设已知矩阵如下，试求出，。解: A=-4.5,0,0.5,-1.5;-0.5,-4,0.5,-0.5;1.5,1,-2.5,1.5;0,-1,-1,-3; A=sym(A),syms t;expm(A*t) A = -9/2, 0, 1/

20、2, -3/2 -1/2, -4, 1/2, -1/2 3/2, 1, -5/2, 3/2 0, -1, -1, -3 ans = exp(-3*t)/2 + exp(-5*t)/2 - (t*exp(-3*t)/2 + (t2*exp(-3*t)/2, exp(-5*t)/2 - exp(-3*t)/2 + t*exp(-3*t), (t*exp(-3*t)/2 + (t2*exp(-3*t)/2, exp(-5*t)/2 - exp(-3*t)/2 - (t*exp(-3*t)/2 + (t2*exp(-3*t)/2 exp(-5*t)/2 - exp(-3*t)/2 + (t*exp(-

21、3*t)/2, exp(-3*t)/2 + exp(-5*t)/2, (t*exp(-3*t)/2, exp(-5*t)/2 - exp(-3*t)/2 + (t*exp(-3*t)/2 exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2, exp(-3*t)/2 - exp(-5*t)/2, exp(-3*t) + (t*exp(-3*t)/2, exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2 -(t2*exp(-3*t)/2, -t*exp(-3*t), -(t*exp(-3*t)*(t + 2)/2, -(exp(-

22、3*t)*(t2 - 2)/2 A=sym(A);syms t sin(A*t) ans = -sin(9*t)/2), 0, sin(t/2), -sin(3*t)/2) -sin(t/2), -sin(4*t), sin(t/2), -sin(t/2) sin(3*t)/2), sin(t), -sin(5*t)/2), sin(3*t)/2) 0, -sin(t), -sin(t), -sin(3*t) A=sym(A);syms t expm(A*t)*sin(A2*expm(A*t)*t) ans = sin(t*(3*exp(-3*t)/2 - (25*exp(-5*t)/2 +

23、(9*t*exp(-3*t)/2)*(t*exp(-3*t)/2 + (t2*exp(-3*t)/2) + sin(t*(17*exp(-3*t)/2 + (25*exp(-5*t)/2 - (21*t*exp(-3*t)/2 + (9*t2*exp(-3*t)/2)*(exp(-3*t)/2 + exp(-5*t)/2 - (t*exp(-3*t)/2 + (t2*exp(-3*t)/2) + sin(t*(exp(-3*t) - 6*t*exp(-3*t) + (9*t2*exp(-3*t)/2)*(exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2 -

24、(t2*exp(-3*t)/2) + sin(t*(25*exp(-5*t)/2 - (15*exp(-3*t)/2 + (9*t*exp(-3*t)/2)*(exp(-5*t)/2 - exp(-3*t)/2 + t*exp(-3*t), sin(t*(9*exp(-3*t)/2 - (25*exp(-5*t)/2)*(t*exp(-3*t)/2 + (t2*exp(-3*t)/2) + sin(t*(25*exp(-5*t)/2 - (21*exp(-3*t)/2 + 9*t*exp(-3*t)*(exp(-3*t)/2 + exp(-5*t)/2 - (t*exp(-3*t)/2 + (

25、t2*exp(-3*t)/2) - sin(t*(6*exp(-3*t) - 9*t*exp(-3*t)*(exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2 - (t2*exp(-3*t)/2) + sin(t*(9*exp(-3*t)/2 + (25*exp(-5*t)/2)*(exp(-5*t)/2 - exp(-3*t)/2 + t*exp(-3*t), sin(t*(6*exp(-3*t) - (13*t*exp(-3*t)/2 - (11*t2*exp(-3*t)/2 + (11*t*exp(-3*t)*(t + 2)/2)*(t*exp(-3*t

26、)/2 + (t2*exp(-3*t)/2) - sin(t*(3*exp(-3*t) - (19*t*exp(-3*t)/2 - (5*t2*exp(-3*t)/2 + (5*t*exp(-3*t)*(t + 2)/2)*(exp(-5*t)/2 - exp(-3*t)/2 + t*exp(-3*t) - sin(t*(5*exp(-3*t) + 5*t*exp(-3*t) - (t2*exp(-3*t)/2 - 4*t*exp(-3*t)*(t + 2)*(exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2 - (t2*exp(-3*t)/2) - sin

27、(t*(2*exp(-3*t) - (21*t*exp(-3*t)/2 - (21*t2*exp(-3*t)/2 + 6*t*exp(-3*t)*(t + 2)*(exp(-3*t)/2 + exp(-5*t)/2 - (t*exp(-3*t)/2 + (t2*exp(-3*t)/2), sin(t*(25*exp(-5*t)/2 - (25*exp(-3*t)/2 + (9*t*exp(-3*t)/2 + (5*t2*exp(-3*t)/2 - (5*exp(-3*t)*(t2 - 2)/2)*(exp(-5*t)/2 - exp(-3*t)/2 + t*exp(-3*t) + sin(t*

28、(t2*exp(-3*t)/2 - 6*t*exp(-3*t) + 4*exp(-3*t)*(t2 - 2)*(exp(-3*t)/2 - exp(-5*t)/2 + (t*exp(-3*t)/2 - (t2*exp(-3*t)/2) + sin(t*(25*exp(-3*t)/2 - (25*exp(-5*t)/2 + (9*t*exp(-3*t)/2 - (11*t2*exp(-3*t)/2 + (11*exp(-3*t)*(t2 - 2)/2)*(t*exp(-3*t)/2 + (t2*exp(-3*t)/2) - sin(t*(25*exp(-3*t)/2 - (25*exp(-5*t)/2 + (21*t*exp(-3*t)/2 - (21*t2*exp(-3*t)/2 + 6*exp(-3*t)*(t2 - 2)*(exp(-3*t)/2 + exp(-5*t)/2 - (t*exp(-3*t)/2 + (t2*exp(-3*t)/2) sin(t*(17*exp(-3*t)/2 + (25*exp(-5*t)/2 - (21*t*exp(-3