东华大学MATLAB数学实验第二版解答

数学实验答案

Chapter 1

Page20,ex1

(5) 等于[exp(1),exp(2);exp(3),exp(4)]

(7) 3=1*3, 8=2*4

(8) a为各列最小值，b为最小值所在的行号

(10) 1>=4,false, 2>=3,false, 3>=2, ture, 4>=1,ture

(11) 答案表明：编址第2元素满足不等式(30>=20)和编址第4元素满足不等式(40>=10)

(12) 答案表明：编址第2行第1列元素满足不等式(30>=20)和编址第2行第2列元素满足不等式(40>=10)

Page20, ex2

(1)a, b, c的值尽管都是1，但数据类型分别为数值，字符，逻辑，注意a与c相等，但他们不等于b

(2)double(fun)输出的分别是字符a,b,s,(,x,)的ASCII码

Page20,ex3

>> r=2;p=0.5;n=12;

>> T=log(r)/n/log(1+0.01*p)

Page20,ex4

>> x=-2:0.05:2;f=x.^4-2.^x;

>> [fmin,min_index]=min(f)

最小值最小值点编址

>> x(min_index)

ans =

0.6500 最小值点

>> [f1,x1_index]=min(abs(f)) 求近似根--绝对值最小的点

f1 =

0.0328

x1_index =

24

>> x(x1_index)

ans =

-0.8500

>> x(x1_index)=[];f=x.^4-2.^x; 删去绝对值最小的点以求函数绝对值次小的点

>> [f2,x2_index]=min(abs(f)) 求另一近似根--函数绝对值次小的点

f2 =

0.0630

x2_index =

65

>> x(x2_index)

ans =

1.2500

>> z=magic(10)

z =

92 99 1 8 15 67 74 51 58 40

98 80 7 14 16 73 55 57 64 41

4 81 88 20 22 54 56 63 70 47

85 87 19 21 3 60 62 69 71 28

86 93 25 2 9 61 68 75 52 34

17 24 76 83 90 42 49 26 33 65

23 5 82 89 91 48 30 32 39 66

79 6 13 95 97 29 31 38 45 72

10 12 94 96 78 35 37 44 46 53

11 18 100 77 84 36 43 50 27 59

>> sum(z)

>> sum(diag(z))

>> z(:,2)/sqrt(3)

>> z(8,:)=z(8,:)+z(3,:)

Chapter 2

Page 45 ex1

先在编辑器窗口写下列M函数，保存为eg2_1.m function [xbar,s]=ex2_1(x)

n=length(x);

xbar=sum(x)/n;

s=sqrt((sum(x.^2)-n*xbar^2)/(n-1));

例如

>>x=[81 70 65 51 76 66 90 87 61 77];

>>[xbar,s]=ex2_1(x)

Page 45 ex2

s=log(1);n=0;

while s<=100

n=n+1;

s=s+log(1+n);

end

m=n

Page 40 ex3

clear;

F(1)=1;F(2)=1;k=2;x=0;

e=1e-8; a=(1+sqrt(5))/2;

while abs(x-a)>e

k=k+1;F(k)=F(k-1)+F(k-2); x=F(k)/F(k-1);

end

a,x,k

计算至k=21可满足精度

clear;tic;s=0;

for i=1:1000000

s=s+sqrt(3)/2^i;

end

s,toc

tic;s=0;i=1;

while i<=1000000

s=s+sqrt(3)/2^i;i=i+1;

end

s,toc

tic;s=0;

i=1:1000000;

s=sqrt(3)*sum(1./2.^i);

s,toc

Page 45 ex5

t=0:24;

c=[15 14 14 14 14 15 16 18 20 22 23 25 28 ...

31 32 31 29 27 25 24 22 20 18 17 16];

plot(t,c)

Page 45 ex6

(1)

x=-2:0.1:2;y=x.^2.*sin(x.^2-x-2);plot(x,y)

y=inline('x^2*sin(x^2-x-2)');fplot(y,[-2 2]) (2)参数方法

t=linspace(0,2*pi,100);

x=2*cos(t);y=3*sin(t); plot(x,y)

(3)

x=-3:0.1:3;y=x;

[x,y]=meshgrid(x,y);

z=x.^2+y.^2;

surf(x,y,z)

(4)

x=-3:0.1:3;y=-3:0.1:13;

[x,y]=meshgrid(x,y);

z=x.^4+3*x.^2+y.^2-2*x-2*y-2*x.^2.*y+6;

surf(x,y,z)

(5)

t=0:0.01:2*pi;

x=sin(t);y=cos(t);z=cos(2*t);

plot3(x,y,z)

(6)

theta=linspace(0,2*pi,50);fai=linspace(0,pi/2,20); [theta,fai]=meshgrid(theta,fai);