1、A=1,2,3,4;4,3,2,1;2,3,4,1;3,2,4,1A = 1 2 3 4 4 3 2 1 2 3 4 1 3 2 4 1A(5,6)=5 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 0 5B=1+4j,2+3j,3+2j,4+j;4+j,3+2j,2+3j,j+4;2+3j,3+2j,4+j,j+4;3+2j,2+3j,4+j,1+4jB = 1.0000 + 4.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 4.0000 + 1.0000i
2、3.0000 + 2.0000i 2.0000 + 3.0000i 4.0000 + 1.0000i 2.0000 + 3.0000i 3.0000 + 2.0000i 4.0000 + 1.0000i 4.0000 + 1.0000i 3.0000 + 2.0000i 2.0000 + 3.0000i 4.0000 + 1.0000i 1.0000 + 4.0000i3、 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。A=magic(8) 64 2 3 61 60 6 7 57 9 55 54 12 13 51
3、 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 1B=A(2:2:8,:)4、 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。format long;sum(2.0:63)ans =1.844674407370955e+019s
4、yms k;symsum(2k,0,200) 32138760885179805510839241846823252050444059875655856706027515、 选择合适的步距绘制出下面的图形。(1),其中; (2)。t=-1:0.02:1;y=sin(1./t);plot(t,y)(2)t=-pi:0.05:pi;y=sin(tan(t)-tan(sin(t);6、 试绘制出二元函数的三维图和三视图。xx=-2:.1:-1.2,-1.1:-0.9,-0.8:0.1:0.8,0.9:1.1,1.2:2;yy=-1:-0.2,-0.1:0.1,0.2: x,y=meshgrid(xx
5、,yy); z=1./(sqrt(1-x).2+y.2)+ 1./(sqrt(1+x).2+y.2);surf(x,y,z),shading flat;zlim(0,15) z=1./(sqrt(1-x).2+y.2)+1./(sqrt(1+x).2+y.2); subplot(224),surf(x,y,z);subplot(221),surf(x,y,z),view(0,90);subplot(222),surf(x,y,z),view(90,0);subplot(223),surf(x,y,z),view(0,0);7、 试求出如下极限。 (3) (1)syms x; f=(3x+9x)
6、(1/x); limit(f,x,inf)9syms x y;f=x*y/(sqrt(x*y+1)-1); limit(limit(f,x,0),y,0)2(3)f=(1-cos(x2+y2)*exp(x2+y2)/(x2+y2);limit(limit(f,x,0),y,0)8、 已知参数方程,试求出syms t; x=log(cos(t); y=cos(t)-t*sin(t);diff(y,t)/diff(x,t)-(-2*sin(t)-t*cos(t)/sin(t)*cos(t)f=diff(y,t,2)/diff(x,t,2); subs(f,t,sym(pi)/3)3/8-1/24*
7、pi*3(1/2)9、 假设,试求syms x y t;f=int(exp(-t2),t,0,x*y);x/y*diff(f,x,2)-2*diff(diff(f,x),y)+diff(f,y,2);simple(ans)-2*exp(-x2*y2)*(-x2*y2+1+x3*y)10、 试求出下面的极限。syms k n; symsum(1/(2*k)2-1),k,1,inf)1/2limit(n*symsum(1/(n2+k*pi),k,1,n),n,inf)111、 试求出以下的曲线积分。,为曲线 为正向上半椭圆。syms a t;syms a positive;x=a*(cos(t)+
8、t*sin(t);y=a*(sin(t)-t*cos(t);f=x2+y2;I=int(f*sqrt(diff(x,t)2+diff(y,t)2),t,0,2*pi)I = 2*a3*pi2+4*a3*pi4syms x y a 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); I=int(P Q*ds,t,0,pi)-2/15*c*(-2*c4+15*b4)/a/b412、 试求出Vandermonde矩阵的行列式,并以最简的形式显示 结果。editfunc
9、tion A=vander1(v)n=length(v);v=v(:);A=sym(ones(n);for j=n-1:-1:1,A(:,j)=v.*A(:,j+1);endsyms a b c d e;C=a b c d e;A=vander1(C) a4, a3, a2, a, 1 b4, b3, b2, b, 1 c4, c3, c2, c, 1 d4, d3, d2, d, 1 e4, e3, e2, e, 1 det(A)d4*b3*c2*e-d4*b3*e2*c+b4*c3*d2*e-b4*c3*e2*d-b4*d3*c2*e+b4*d3*e2*c+b4*e3*c2*d-b4*e3
10、*d2*c-c4*b3*d2*e+c4*b3*e2*d+c4*d3*b2*e-c4*d3*e2*b-c4*e3*b2*d+c4*e3*d2*b-d4*c3*b2*e+d4*c3*e2*b+d4*e3*b2*c-d4*e3*c2*b-e4*b3*c2*d+e4*b3*d2*c+e4*c3*b2*d-e4*c3*d2*b-e4*d3*b2*c+e4*d3*c2*b+d4*e3*a2*b+a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2
11、*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*e2*a-b4*d3*a2*c+b4*d3*a2*e+b4*d3*c2*a-
12、b4*d3*e2*a+b4*e3*a2*c-b4*e3*a2*d-b4*e3*c2*a+b4*e3*d2*a+c4*a3*b2*d-c4*a3*b2*e-c4*a3*d2*b+c4*a3*d2*e+c4*a3*e2*b-c4*a3*e2*d-c4*b3*a2*d+c4*b3*a2*e+c4*b3*d2*a-c4*b3*e2*a+c4*d3*a2*b-c4*d3*a2*e-c4*d3*b2*a+c4*d3*e2*a-c4*e3*a2*b+c4*e3*a2*d+c4*e3*b2*a-c4*e3*d2*a-d4*a3*b2*c+d4*a3*b2*e+d4*a3*c2*b-d4*a3*c2*e-d4*
13、a3*e2*b+d4*a3*e2*c+d4*b3*a2*c-d4*b3*a2*e-d4*b3*c2*a+d4*b3*e2*a-d4*c3*a2*b+d4*c3*a2*e+d4*c3*b2*a-d4*c3*e2*a-d4*e3*a2*c-d4*e3*b2*a+d4*e3*c2*a+e4*a3*b2*c-e4*a3*b2*d-e4*a3*c2*b+e4*a3*c2*d+e4*a3*d2*b-e4*a3*d2*c-e4*b3*a2*c+e4*b3*a2*d+e4*b3*c2*a-e4*b3*d2*a+e4*c3*a2*b-e4*c3*a2*d-e4*c3*b2*a+e4*c3*d2*a-e4*d3*
14、a2*b+e4*d3*a2*c+e4*d3*b2*a-e4*d3*c2*a simple(ans)simplify:radsimp:combine(trig):d4*b3*c2*e-d4*b3*e2*c+b4*c3*d2*e-b4*c3*e2*d-b4*d3*c2*e+b4*d3*e2*c+b4*e3*c2*d-b4*e3*d2*c-c4*b3*d2*e+c4*b3*e2*d+c4*d3*b2*e-c4*d3*e2*b-c4*e3*b2*d+c4*e3*d2*b-d4*c3*b2*e+d4*c3*e2*b+d4*e3*b2*c-d4*e3*c2*b-e4*b3*c2*d+e4*b3*d2*c+
15、e4*c3*b2*d-e4*c3*d2*b-e4*d3*b2*c+e4*d3*c2*b+d4*e3*a2*b+a4*b3*c2*d-a4*b3*c2*e-a4*b3*d2*c+a4*b3*d2*e+a4*b3*e2*c-a4*b3*e2*d-a4*c3*b2*d+a4*c3*b2*e+a4*c3*d2*b-a4*c3*d2*e-a4*c3*e2*b+a4*c3*e2*d+a4*d3*b2*c-a4*d3*b2*e-a4*d3*c2*b+a4*d3*c2*e+a4*d3*e2*b-a4*d3*e2*c-a4*e3*b2*c+a4*e3*b2*d+a4*e3*c2*b-a4*e3*c2*d-a4*e3*d2*b+a4*e3*d2*c-b4*a3*c2*d+b4*a3*c2*e+b4*a3*d2*c-b4*a3*d2*e-b4*a3*e2*c+b4*a3*e2*d+b4*c3*a2*d-b4*c3*a2*e-b4*c3*d2*a+b4*c3*e2*a-b
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