915230MATLAB第三版实验答案Word下载.docx
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实验2MATLAB矩阵处理
%第1题
E=eye(3);
R=rand(3,2);
O=zeros(2,3);
S=diag([2,3]);
A=[E,R;
O,S];
A^2
B=[E,(R+R*S);
O,S^2]
%第2题
A=fix(10*rand(5))
H=det(A)
Trace=trace(A)
Rank=rank(A)
Norm=norm(A)
H=hilb(5)
P=pascal(5)
Hh=det(H)
Hp=det(P)
Th=cond(H)
Tp=cond(P)
A=[-29,6,18;
20,5,12;
-8,8,5]
[V,D]=eig(A)
%数学意义略
%第5题方法一
%
(1):
A=[1/2,1/3,1/4;
1/3,1/4,1/5;
1/4,1/5,1/6];
b=[0.95,0.67,0.52]'
x=inv(A)*b
%
(2):
B=[0.95,0.67,0.53]'
x=inv(A)*B
%(3):
cond(A)
%第5题方法二
A=hilb(4)
A(:
1)=[]
A(4,:
)=[]
B=[0.95,0.67,0.52]'
X=inv(A)*B
B1=[0.95,0.67,0.53]'
X1=inv(A)*B1
N=cond(B)
N1=cond(B1)
Na=cond(A)%矩阵A为病态矩阵
实验3顺序结构程序设计
%程序(略)
实验4选择结构程序设计
%第1题程序一
x=[-5.0,-3.0,1.0,2.0,2.5,3.0,5.0];
y=[];
%建立存放所有y值的矩阵
forx0=x
ifx0<
0&
x0~=-3
y=[y,x0*x0+x0-6];
elseifx0>
=0&
x0<
5&
x0~=2&
x0~=3
y=[y,x0*x0-5*x0+6];
else
y=[y,x0*x0-x0-1];
end
end
x%输出所有x
y%输出所有y
%第1题程序二
x=[-5,-3,1,2,2.5,3,5];
fora=1:
7
ifx(a)<
x(a)~=-3
y=[y,(x(a))^2+x(a)-6];
elseifx(a)>
x(a)<
x(a)~=2&
x(a)~=3
y=[y,(x(a))^2-5*x(a)+6];
else
y=[y,x(a)*x(a)-x(a)-1];
%第2题程序一
x=input('
请输入一个百分制成绩:
'
ifx>
100|x<
disp('
您输入的成绩不是百分制成绩,请重新输入。
ifx<
=100&
x>
=90
elseifx<
=89&
=80
B'
=79&
=70
C'
=69&
60
D'
E'
%第2题程序二
s=input('
请输入一个成绩(0分到100分之间):
%s用于存放成绩
while1%判断输入成绩的合理性
ifs<
0|s>
100
disp('
输入的成绩需在0到100之间,请重新输入:
)
s=input('
break;
switchfix(s/10)%对成绩做出等级判断
case{9,10}
case8
case7
case6
otherwise
n=input('
请输入员工工号:
h=input('
该员工工作时数是:
ifh>
120
x=(h-120)*84*(1+0.15)+120*84;
elseifh<
x=h*84-700;
x=h*84;
disp([num2str(n),'
号员工'
'
的应发工资为'
num2str(x)]);
%第4题(还可以用switch语句实现)
a=fix(10+(99-10)*rand(1,2))%产生两个随机整数
x=a
(1);
y=a
(2);
t=input('
请输入运算符号:
s'
ift=='
+'
z=x+y;
elseift=='
-'
z=x-y;
*'
z=x*y;
/'
z=x/y;
disp([num2str(x),t,num2str(y),'
num2str(z)])%输出运算结果
a=rand(5,6)%产生5x6的随机矩阵
请输入您要输出矩阵的第几行:
ifn>
5
超出了矩阵的行数,矩阵的最后一行为:
a(5,:
disp(['
矩阵的第'
num2str(n),'
行为:
])
a(n,:
实验5循环结构程序设计
y=0;
n=?
fori=1:
n
y=y+1/(2*i-1)/3^(2*i-1);
y
log
(2)/2
i=1:
n;
y=1./(2*i-1)./3.^(2*i-1);
y=sum(y)
n=1;
whiley<
3
y=y+1/(2*n-1);
n=n+1;
y=y-1/(2*(n-1)-1)
n=n-2
a=input('
a=?
b=input('
b=?
Xn=1;
Xn1=a/(b+Xn);
n=0;
whileabs(Xn1-Xn)>
1e-5
Xn=Xn1;
Xn1=a/(b+Xn);
n=n+1;
ifn==500
Xn1
r1=(-b+sqrt(b*b+4*a))/2
r2=(-b-sqrt(b*b+4*a))/2
ifi==1
f(i)=1;
elseifi==2
f(i)=0;
elseifi==3
f(i)=f(i-1)-2*f(i-2)+f(i-3);
max(f)
min(f)
sum(f)
length(find(f>
0))
length(find(f==0))
length(find(f<
s=0;
fori=2:
49
b=i*(i+1)-1;
m=fix(sqrt(b));
forj=2:
m
ifrem(b,j)==0
break
ifj==m
s=s+b;
s
实验6函数文件
functiony=mat1(x)%建立函数文件mat1.m
y=[exp(x),log(x),sin(x),cos(x)];
%在命令窗口调用上述函数文件:
y=mat1(1+i)
function[a,b,N,M]=shiyanwu2(m,n,t)
A=[m*cos(t*pi/180),-m,-sin(t*pi/180),0;
m*sin(t*pi/180),0,cos(t*pi/180),0;
0,n,-sin(t*pi/180),0;
0,0,-cos(t*pi/180),1];
B=[0,9.8*m,0,9.8*n];
C=inv(A)*B'
a=C
(1);
b=C
(2);
N=C(3);
M=C(4);
%在命令窗口调用该函数文件:
m1=input('
m1='
m2=input('
m2='
theta=input('
theta='
[a1,a2,N1,N2]=shiyanwu2(m1,m2,theta)
functionX=mat2(m1,m2,t)
g=9.8;
A=[m1*cos(t*pi/180),-m1,-sin(t*pi/180),0;
m1*sin(t*pi/180),0,cos(t*pi/180),0;
0,m2,-sin(t*pi/180),0;
B=[0;
m1*g;
0;
m2*g];
X=inv(A)*B;
%在命令窗口调用该函数文件:
X=mat2(1,1,60)
functionflag=mat3(x)
flag=1;
sqrt(x)
ifrem(x,i)==0
flag=0;
break;
fori=10:
99
j=10*rem(i,10)+fix(i/10);
ifmat3(i)&
mat3(j)
disp(i)
functiony=fx(x)
y=1./((x-2).^2+0.1)+1./((x-3).^4+0.01);
y=fx
(2)
a=[1,2;
3,4];
y=fx(a)
functionf1=mat5(n)
f1=n+10*log(n*n+5);
%在命令窗口中调用该函数文件:
y=mat5(40)/(mat5(30)+mat5(20))
%
(2)方法一
functionf2=mat6(n)
f2=0;
f2=f2+i*(i+1);
%在命令窗口中调用该函数文件如:
y=mat6(40)/(mat6(30)+mat6(20))
%
(2)方法二
functionf2=mat7(n)
m=i.*(i+1);
f2=sum(m);
y=mat7(40)/(mat7(30)+mat7(20))
实验7绘图操作
x=linspace(0,2*pi,101);
y=(0.5+3*sin(x)./(1+x.^2)).*cos(x);
plot(x,y)
x=-5:
0.01:
5;
%起始设y为空向量
ifx0<
=0%不能写成x0=<
y=[y,(x0+sqrt(pi))/exp
(2)];
%将x对应的函数值放到y中
y=[y,0.5*log(x0+sqrt(1+x0^2))];
t=-2*pi:
2*pi;
r=10*sin(1+5*t);
polar(t,r)
x=linspace(-2*pi,2*pi,100);
y1=x.^2;
y2=cos(2*x);
y3=y1.*y2;
plot(x,y1,'
b-'
x,y2,'
r:
x,y3,'
y--'
text(4,16,'
\leftarrowy1=x^2'
text(6*pi/4,-1,'
\downarrowy2=cos(2*x)'
text(-1.5*pi,-2.25*pi*pi,'
\uparrowy3=y1*y2'
subplot(1,3,1);
%分区
plot(x,y1);
title('
y1=x^2'
%设置标题
subplot(1,3,2);
plot(x,y2);
y2=cos(2*x)'
subplot(1,3,3);
plot(x,y3);
y3=x^2*cos(2*x)'
x=linspace(-2*pi,2*pi,20);
subplot(2,2,1);
bar(x,y1);
y1=x^2的条形图'
subplot(2,2,2);
stairs(x,y1);
y1=x^2的阶梯图'
subplot(2,2,3);
stem(x,y1);
y1=x^2的杆图'
subplot(2,2,4);
fill(x,y1,'
r'
%如果少了'
则会出错
y1=x^2的填充图'
%其他的函数照样做。
%第3题(略)
x=linspace(-5,5,21);
y=linspace(0,10,31);
[x,y]=meshgrid(x,y);
%在[-5,5]*[0,10]的范围内生成网格坐标
z=cos(x).*cos(y).*exp(-sqrt(x.^2+y.^2)/4);
subplot(2,1,1);
surf(x,y,z);
subplot(2,1,2);
contour3(x,y,z,50);
%其中50为高度的等级数,越大越密
ezsurf('
cos(s)*cos(t)'
cos(s)*sin(t)'
sin(s)'
[0,0.5*pi,0,1.5*pi]);
%利用ezsurf隐函数
shadinginterp%进行插值着色处理
实验8数据处理与多项式运算
A=rand(1,30000);
b=mean(A)
std(A,0,2)
max(A)
min(A)
30000
ifA(i)>
0.5
p=n/30000
A=45+51*rand(100,5);
[Y,U]=max(A)
[a,b]=min(A)
m=mean(A)
s=std(A)
sum(A,2)
[Y,U]=max(ans)
[a,b]=min(ans)
%(4)
[zcj,xsxh]=sort(ans)
p1=[1,2,4,0,5];
p2=[1,2];
p3=[1,2,3];
p=p1+[0,conv(p2,p3)]%为使两向量大小相同,所以补0
A=roots(p)
A=[-1,1.2,-1.4;
0.75,2,3.5;
0,5,2.5];
polyval(p,A)
polyvalm(p,A)
h=6:
2:
18;
x=6.5:
17.5;
t1=[18,20,22,25,30,28,24];
t2=[15,19,24,28,34,32,30];
T1=spline(h,t1,x)
T2=spline(h,t2,x)
x=1:
101;
y1=log10(x);
p=polyfit(x,y1,5)
y2=polyval(p,x);
:
实验9数值微分与积分
forx=1:
fx=[x,x^2,x^3;
1,2*x,3*x;
0,2,6*x];
diff(fx)
f1=@(x)sqrt(cos(x.*x)+4*sin((2*x).^2)+1);
I1=quad(f1,0,2*pi)
f2=@(x)log(1+x)./(1+x.^2);
I2=quadl(f2,0,1)
I2=integral(f2,0,1)
%第4题(略)
%第5题(略)
实验10方程数值求解
A=[6,5,-2,5;
9,-1,4,-1;
3,4,2,-2;
3,-9,0,2];
b=[-4;
13;
1;
11];
x1=A\b
x2=inv(A)*b
[L,U]=lu(A);
x3=U\(L\b)
%
(1)
z=fzero(@(x)3*x+sin(x)-exp(x),1.5)
%首先建立函数文件myfun.m。
functionF=myfun(X)
x=X
(1);
y=X
(2);
z=X(3);
F
(1)=sin(x)+y^2+log(z)-7;
F
(2)=3*x+2^y-z^3+1;
F(3)=x+y+z-5;
X=fsolve(@myfun,[1,1,1],optimset('
Display'
'
off'
))
f=@(x)(x^3+cos(x)+x*log(x))/exp(x);
fminbnd(f,0,1)
%建立函数文件fx12.m:
functionf=fx12(u)
x1=u
(1);
x2=u
(2);
f=2*x1.^3+4*x1*x2.^3-10*x1.*x2+x2.^2;
[U,fmin]=fminsearch(@fx12,[0,0])
%建立函数文件ztf.m
functionyy=ztf(x,y)
yy=[(5*y
(1)-y
(2))/x;
y
(1)];
[x,y]=ode23(@ztf,[0,5],[0;
0])
%建立函数文件ztfun.m
functionyy=ztfun(t,y)
yy=[y
(2)*y(3);
-y
(1)*y(3);
-0.51*y
(1)*y
(2)];
[t,y]=ode23(@ztfun,[0,5],[0;
1])
plot3(y(:
1),y(:
2),y(:
3))
实验11符号计算对象与符号微积分
x=sym(6);
y=sym(5);
z=(x+1)/(sqrt(3+x)-sqrt(y))
symsxy
z=sym(x*x*x*x-y*y*y*y);
factor(z)
num=sym(5135);
factor(num)
symsbeta1beta2
f1=sym(sin(beta1)*sin(beta2)-cos(beta1)*cos(beta2));
simplify(f1)
symx
f2=sym((4*x*x+8*x+3)/(2*x+1));
simplify(f2)
symsabcdefghi
P1=[0,1,0;
1,0,0;
0,0,1];
P2=[1,0,0;
0,1,0;
1,0,1];
A=[a,b,c;
d,e,f;
g,h,i];
B=P1*P2*A
inv(B)
tril(B)
det(B)
symsxat
f1=(x*(exp(sin(x))+1)-2*(exp(tan(x))-1))/sin(x)^3
limit(f1,x,0)%求
(1)
f2=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1);
limit(f2,x,-1,'
right'
)%求
(2)
f3=(1-cos(2*x))/x;
diff(f3,x)
diff(f3,x,2)%求(3)
A=[power(a,x),t^3;
t*cos(x),log(x)];
diff(A,x)
diff(A,t,2)
diff(diff(A,x),t)%求(4)
f=(x*x-2*x)*exp(-x*x-y*y-x*y);
%求(5)
df51=-diff(f,y)/diff(f,x)
df52=diff(diff(f,x),y)
formatshorte
int(1/(1+x^4+x^8),x)
int(1/((asin(x))^2*sqrt(1-x*x)),x)
int((x*x+1)/(x^4+1),0,inf)
a=int(exp(x)*(1+exp(x))^2,0,log
(2))
eval(a)
实验12级数与方程符号求解
symsnx;
symsum(1/(2*n-1),n,1,10)
s=symsum(n^2*x^(n-1),n,1,inf)
x=sym(5);
x=1/x;
s=symsum(n^2*x^(n-1),n,1,inf)/5
x=sym('
x'
f=log(x);
taylor(f,6,1)
symsxy;
y=solve(log(1+x)-5/(1+sin(x))==2)
y=solve(x^2+9*sqrt(x+1)-1)
y=solve(3*x*exp(x)+5*sin(x)-78.5)
[xy]=solve([sqrt(x^2+y^2)-100,3*x+5*y-8])
y=dsolve('
D2y+4*Dy+29*y'
y(0)=0,Dy(0)=15'
[x,y,z]=dsolve('
Dx-2*x+3*y-3*z'
Dy-4*x+5*y-3*z'
Dz-4*x+4*y-2*z'
t'
实验13低层绘图操作
h=figure('
MenuBar'
figure'
color