东北大学matlab上机作业Word格式文档下载.docx
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A=[1,2,3,4;
4,3,2,1;
2,3,4,1;
3,2,4,1]
A=
1234
4321
2341
3241
A(5,6)=5
123400
432100
234100
324100
000005
B=[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+4j]
B=
1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i
4.0000+1.0000i3.0000+2.0000i2.0000+3.0000i4.0000+1.0000i
2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i4.0000+1.0000i
3.0000+2.0000i2.0000+3.0000i4.0000+1.0000i1.0000+4.0000i
3、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)
642361606757
955541213515016
1747462021434224
4026273736303133
3234352928383925
4123224445191848
4915145253111056
858595462631
B=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。
formatlong;
sum(2.^[0:
63])
ans=
1.844674407370955e+019
symsk;
symsum(2^k,0,200)
3213876088517980551083924184682325205044405987565585670602751
5、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,yy);
z=1./(sqrt((1-x).^2+y.^2))+1./(sqrt((1+x).^2+y.^2));
surf(x,y,z),shadingflat;
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)
symsx;
f=(3^x+9^x)^(1/x);
limit(f,x,inf)
9
symsxy;
f=x*y/(sqrt(x*y+1)-1);
limit(limit(f,x,0),y,0)
2
(3)
f=(1-cos(x^2+y^2))*exp(x^2+y^2)/(x^2+y^2);
limit(limit(f,x,0),y,0)
8、已知参数方程
,试求出
symst;
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*pi*3^(1/2)
9、假设
,试求
symsxyt;
f=int(exp(-t^2),t,0,x*y);
x/y*diff(f,x,2)-2*diff(diff(f,x),y)+diff(f,y,2);
simple(ans)
-2*exp(-x^2*y^2)*(-x^2*y^2+1+x^3*y)
10、试求出下面的极限。
symskn;
symsum(1/((2*k)^2-1),k,1,inf)
1/2
limit(n*symsum(1/(n^2+k*pi),k,1,n),n,inf)
1
11、试求出以下的曲线积分。
,
为曲线
为
正向上半椭圆。
symsat;
symsapositive;
x=a*(cos(t)+t*sin(t));
y=a*(sin(t)-t*cos(t));
f=x^2+y^2;
I=int(f*sqrt(diff(x,t)^2+diff(y,t)^2),t,0,2*pi)
I=
2*a^3*pi^2+4*a^3*pi^4
symsxyabct;
x=c*cos(t)/a;
y=c*sin(t)/b;
P=y*x^3+exp(y);
Q=x*y^3+x*exp(y)-2*y;
ds=[diff(x,t);
diff(y,t)];
I=int([PQ]*ds,t,0,pi)
-2/15*c*(-2*c^4+15*b^4)/a/b^4
12、试求出Vandermonde矩阵
的行列式,并以最简的形式显示结果。
edit
functionA=vander1(v)
n=length(v);
v=v(:
);
A=sym(ones(n));
forj=n-1:
-1:
1,A(:
j)=v.*A(:
j+1);
end
symsabcde;
C=[abcde];
A=vander1(C)
[a^4,a^3,a^2,a,1]
[b^4,b^3,b^2,b,1]
[c^4,c^3,c^2,c,1]
[d^4,d^3,d^2,d,1]
[e^4,e^3,e^2,e,1]
>
det(A)
d^4*b^3*c^2*e-d^4*b^3*e^2*c+b^4*c^3*d^2*e-b^4*c^3*e^2*d-b^4*d^3*c^2*e+b^4*d^3*e^2*c+b^4*e^3*c^2*d-b^4*e^3*d^2*c-c^4*b^3*d^2*e+c^4*b^3*e^2*d+c^4*d^3*b^2*e-c^4*d^3*e^2*b-c^4*e^3*b^2*d+c^4*e^3*d^2*b-d^4*c^3*b^2*e+d^4*c^3*e^2*b+d^4*e^3*b^2*c-d^4*e^3*c^2*b-e^4*b^3*c^2*d+e^4*b^3*d^2*c+e^4*c^3*b^2*d-e^4*c^3*d^2*b-e^4*d^3*b^2*c+e^4*d^3*c^2*b+d^4*e^3*a^2*b+a^4*b^3*c^2*d-a^4*b^3*c^2*e-a^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*c-a^4*b^3*e^2*d-a^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*b-a^4*c^3*d^2*e-a^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*c-a^4*d^3*b^2*e-a^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*b-a^4*d^3*e^2*c-a^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*b-a^4*e^3*c^2*d-a^4*e^3*d^2*b+a^4*e^3*d^2*c-b^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*c-b^4*a^3*d^2*e-b^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*d-b^4*c^3*a^2*e-b^4*c^3*d^2*a+b^4*c^3*e^2*a-b^4*d^3*a^2*c+b^4*d^3*a^2*e+b^4*d^3*c^2*a-b^4*d^3*e^2*a+b^4*e^3*a^2*c-b^4*e^3*a^2*d-b^4*e^3*c^2*a+b^4*e^3*d^2*a+c^4*a^3*b^2*d-c^4*a^3*b^2*e-c^4*a^3*d^2*b+c^4*a^3*d^2*e+c^4*a^3*e^2*b-c^4*a^3*e^2*d-c^4*b^3*a^2*d+c^4*b^3*a^2*e+c^4*b^3*d^2*a-c^4*b^3*e^2*a+c^4*d^3*a^2*b-c^4*d^3*a^2*e-c^4*d^3*b^2*a+c^4*d^3*e^2*a-c^4*e^3*a^2*b+c^4*e^3*a^2*d+c^4*e^3*b^2*a-c^4*e^3*d^2*a-d^4*a^3*b^2*c+d^4*a^3*b^2*e+d^4*a^3*c^2*b-d^4*a^3*c^2*e-d^4*a^3*e^2*b+d^4*a^3*e^2*c+d^4*b^3*a^2*c-d^4*b^3*a^2*e-d^4*b^3*c^2*a+d^4*b^3*e^2*a-d^4*c^3*a^2*b+d^4*c^3*a^2*e+d^4*c^3*b^2*a-d^4*c^3*e^2*a-d^4*e^3*a^2*c-d^4*e^3*b^2*a+d^4*e^3*c^2*a+e^4*a^3*b^2*c-e^4*a^3*b^2*d-e^4*a^3*c^2*b+e^4*a^3*c^2*d+e^4*a^3*d^2*b-e^4*a^3*d^2*c-e^4*b^3*a^2*c+e^4*b^3*a^2*d+e^4*b^3*c^2*a-e^4*b^3*d^2*a+e^4*c^3*a^2*b-e^4*c^3*a^2*d-e^4*c^3*b^2*a+e^4*c^3*d^2*a-e^4*d^3*a^2*b+e^4*d^3*a^2*c+e^4*d^3*b^2*a-e^4*d^3*c^2*a
>
simple(ans)
simplify:
radsimp:
combine(trig):
d^4*b^3*c^2*e-d^4*b^3*e^2*c+b^4*c^3*d^2*e-b^4*c^3*e^2*d-b^4*d^3*c^2*e+b^4*d^3*e^2*c+b^4*e^3*c^2*d-b^4*e^3*d^2*c-c^4*b^3*d^2*e+c^4*b^3*e^2*d+c^4*d^3*b^2*e-c^4*d^3*e^2*b-c^4*e^3*b^2*d+c^4*e^3*d^2*b-d^4*c^3*b^2*e+d^4*c^3*e^2*b+d^4*e^3*b^2*c-d^4*e^3*c^2*b-e^4*b^3*c^2*d+e^4*b^3*d^2*c+e^4*c^3*b^2*d-e^4*c^3*d^2*b-e^4*d^3*b^2*c+e^4*d^3*c^2*b+d^4*e^3*a^2*b+a^4*b^3*c^2*d-a^4*b^3*c^2*e-a^4*b^3*d^2*c+a^4*b^3*d^2*e+a^4*b^3*e^2*c-a^4*b^3*e^2*d-a^4*c^3*b^2*d+a^4*c^3*b^2*e+a^4*c^3*d^2*b-a^4*c^3*d^2*e-a^4*c^3*e^2*b+a^4*c^3*e^2*d+a^4*d^3*b^2*c-a^4*d^3*b^2*e-a^4*d^3*c^2*b+a^4*d^3*c^2*e+a^4*d^3*e^2*b-a^4*d^3*e^2*c-a^4*e^3*b^2*c+a^4*e^3*b^2*d+a^4*e^3*c^2*b-a^4*e^3*c^2*d-a^4*e^3*d^2*b+a^4*e^3*d^2*c-b^4*a^3*c^2*d+b^4*a^3*c^2*e+b^4*a^3*d^2*c-b^4*a^3*d^2*e-b^4*a^3*e^2*c+b^4*a^3*e^2*d+b^4*c^3*a^2*d-b^4*c^3*a^2*e-b^4*c^3*d^2*a+b^4*c^3*e^2*a-b