中南大学材料学院MATLAB题库答案30版.docx
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中南大学材料学院MATLAB题库答案30版.docx
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中南大学材料学院MATLAB题库答案30版
操作题55plotyy
>>t=1:
6
t=
123456
>>sr=[245620321900245028902280];
>>ll=[12.511.310.214.514.315.1];
>>[AX,H1,H2]=plotyy(t,sr,t,ll)
AX=
174.0037190.0039
H1=
175.0079
H2=
191.0042
>>legend('销售收入','边际利润率')
操作题56圆锥螺线的绘制
%office2013抽风,把做的十多道题都搞没了,怒罢工.
不妨取v=2a=pi/6w=3
>>symst
>>v=2;
>>a=pi/6;
>>w=3;
>>x=v*t*sin(a)*cos(w*t);
>>y=v*t*sin(a)*sin(w*t);
>>z=v*t*cos(w);
>>ezplot3(x,y,z,[0,10])%[0,10]为t的取值范围
操作题57求函数的零点
>>f=inline('exp(x)-x-5')
f=
Inlinefunction:
f(x)=exp(x)-x-5
>>fzero(f,2)
%初值点取在区间及区间附近都可以,据老师说最好取到区间内
ans=
1.9368
操作题58
>>f=inline('1./((x-0.3).^2+0.01)+1./((x-0.9).^2+0.04)-6')
f=
Inlinefunction:
f(x)=1./((x-0.3).^2+0.01)+1./((x-0.9).^2+0.04)-6
>>fzero(f,1)
ans=
1.2995
操作题59.插值法求点
>>t=0:
0.125:
0.5;
>>i=[06.247.754.850];
>>k=0:
50;
>>t1=0.01*k;
>>i1=interp1(t,i,t1)
i1=
Columns1through10
00.49920.99841.49761.99682.49602.99523.49443.99364.4928
Columns11through20
4.99205.49125.99046.30046.42126.54206.66286.78366.90447.0252
Columns21through30
7.14607.26687.38767.50847.62927.75007.51807.28607.05406.8220
Columns31through40
6.59006.35806.12605.89405.66205.43005.19804.96604.65604.2680
Columns41through50
3.88003.49203.10402.71602.32801.94001.55201.16400.77600.3880
Column51
0
操作题60.三次hermite插值
>>x=-1:
0.5:
1;
>>y=1./(1+25.*x.^2);
>>x1=-1:
0.1:
1;
>>pchip(x,y,x1)
ans=
Columns1through10
0.03850.04310.05640.07720.10480.13790.25040.46710.71370.9161
Columns11through20
1.00000.91610.71370.46710.25040.13790.10480.07720.05640.0431
Column21
0.0385
%此题用interp1(x,y,xi,’p’)亦可
操作题61.
>>x=-1:
0.5:
1;
%初值取步长多少不影响差值结果
>>y=1./(1+25.*x.^2);
>>x1=-1:
0.1:
1;
>>spline(x,y,x1)
%或者interp1(x,y,x1,'spline')
ans=
Columns1through10
0.0385-0.1817-0.2520-0.2023-0.06230.13790.36870.60010.80240.9456
Columns11through20
1.00000.94560.80240.60010.36870.1379-0.0623-0.2023-0.2520-0.1817
Column21
0.0385
操作题62.线性插值
>>t=[020405668808496104110];
>>v=[12020388080100100125125];
>>t1=0:
5:
110;
>>interp1(t,v,t1)
ans=
Columns1through10
1.00005.750010.500015.250020.000020.000020.000020.000020.000025.6250
Columns11through20
31.250036.875052.000069.500080.000080.000080.0000100.0000100.0000100.0000
Columns21through23
112.5000125.0000125.0000
>>plot(t,v,’+’,t1,ans,’o’)
操作题63.插值SUMMARY
>>x=0:
0.5:
5;
>>x1=0:
0.1:
5;
>>y=x.^2;
>>interp1(x,y,x1);%线性插值
>>interp1(x,y,x1,’spline’);%三次样条插值
>>interp1(x,y,x1,’cubic’);%三次插值
>>interp1(x,y,x1,’pchip’);%hermit插值
操作题64线性插值求点
>>D=18:
2:
30;
>>S=[9.96177249.95436459.94680699.93909509.93122459.92319159.9149925];
>>interp1(S,D,9.935799)
ans=
24.837557969633686
%此种方法可求某点处的数值,还有种实现方法见helpexample3
操作题65
>>m=1:
12;
>>t=[80.967.267.150.53233.636.646.852.36264.171.2];
>>mi=1:
.2:
12;
>>ti=interp1(m,t,mi,'p');
>>plot(m,t,'-ok',mi,ti,'-r')
%使用hermite插值,得到其图像可知该地在一年的五月份左右日照时间最短,到了十二月份到一月份,日照时间最长
操作题67二维插值
>>x=1:
4;y=1:
4;
>>h=[6.366.976.234.77;6.987.126.314.78;6.836.735.994.12;6.616.255.533.34];
>>xi=1:
.1:
4;yi=1:
.1:
4;
>>hi=interp2(x,y,h,xi,yi','s');
>>surf(zi)
>>axis('equal')
>>axis('square')
%无论几维插值,其实都是类似的,即已知有限的几点和其定义域之后求取更加多的点
%67题处对xi/yi是否必须用meshgrid产生分歧,经我验证,两种结果一样
>>[x,y]=meshgrid(1:
4,1:
4);
>>z=[6.36,6.97,6.23,4.77;6.98,7.12,6.31,4.78;6.83,6.73,5.99,4.12;6.61,6.25,5.53,3.34];
>>[x1,y1]=meshgrid(1:
0.5:
4,1:
0.5:
4);
>>interp2(x,y,z,x1,y1)
ans=
6.36006.66506.97006.60006.23005.50004.7700
6.67006.85757.04506.65756.27005.52254.7750
6.98007.05007.12006.71506.31005.54504.7800
6.90506.91506.92506.53756.15005.30004.4500
6.83006.78006.73006.36005.99005.05504.1200
6.72006.60506.49006.12505.76004.74503.7300
6.61006.43006.25005.89005.53004.43503.3400
操作题68
>>x=[129140103.588185.5195105.5157.5107.57781162162117.5];
>>y=[7.5141.52314722.5137.585.5-6.5-81356.5-66.584-33.5];
>>z=[48686889988949];
>>[xi,yi]=meshgrid(75:
200,-50:
150);
>>zi=griddata(x,y,z,xi,yi);
>>mesh(zi)
[a,b]=find(zi<5);%找出插值后Z中高度小于5对应行列
fori=1:
128
X(i)=xi(a(i),b(i));
Y(i)=yi(a(i),b(i));%找出对应位置的x,y值
end
%griddata不规则点阵插值,对于后半部分的筛选,感觉有点问题,!
!
?
?
操作题69多种基函数做拟合
>>xi=0:
.5:
3;
>>yi=[0.4794.8415.9815.9126.5985.1645];
>>x1=ones(7,1);x2=xi;x3=xi.^2;;x4=cos(xi);x5=exp(xi);x6=sin(xi);
>>x=[x1,x2',x3',x4',x5',x6'];
>>ab=x\yi'
ab=
0.3828
0.4070
-0.3901
-0.4598
0.0765
0.5653
>>y=ab
(1)+ab
(2)*xi+ab(3)*xi.^2+ab(4)*cos(xi)+ab(5)*exp(xi)+ab(6)*sin(xi);
>>plot(xi,y)
>>xi=0:
.05:
3;
>>y=ab
(1)+ab
(2)*xi+ab(3)*xi.^2+ab(4)*cos(xi)+ab(5)*exp(xi)+ab(6)*sin(xi);
>>plot(xi,y)
操作题70n次多项式的拟合
>>x=[0:
.1:
1];
>>y=[-0.4471.9783.286.167.077.347.669.569.489.3011.2];
>>y1=polyfit(x,y,1)
y1=
10.3193636363636381.438590909090908
>>y2=polyfit(x,y,2)
y2=
-9.80034965034965620.119713286713292-0.031461538461540
>>y8=polyfit(x,y,8)
y8=
1.0e+005*
Columns1through5
-0.1641512635755670.698101903041705-1.209172353370695.0937********
Columns6through9
.020*********
>>Y1=poly2sym(y1)
Y1=
(5809285278428491*x)/562949953421312+31649/22000
>>Y2=poly2sym(y2)
Y2=
(1415798957200675*x)/70368744177664-(28029*x^2)/2860-4534085532540663/144115188075855872
>>Y8=poly2sym(y8)
Y8=
-(1128038893846617*x^8)/68719476736+(2398659874271589*x^7)/34359738368-(8309369140727187*x^6)/68719476736+(3758228963595679*x^5)/34359738368-(7555371370282575*x^4)/137********2+(8264030631159095*x^3)/549755813888-(557033108521445*x^2)/274877906944+(2143007143072083*x)/175********416-4034526554172747/9007199254740992
%只用改变polyfit(x,y,n)中的n即可换多项式的次数~
操作题71线性拟合
>>w=[5:
5:
30];
>>l=[7.258.128.959.9010.911.8];
>>plot(w,l)
%作图观察适合用何种拟合,结果推测用线性拟合即可
>>holdon
>>p=polyfit(w,l,1)
p=
0.183********57146.282666666666665
>>li=(801*w)/4375+2356/375;
>>plot(w,li,'-+r')
%此题中要用到线性拟合,要注意在新版中不存在linefit,直接用一次多项式即可
操作题:
72simpson公式
>>quad('exp(-x.^2)',-1,1)
ans=
1.493648276062878
>>quad('exp(-x.^2)',-1,1,.1)
ans=
1.493619637572876
操作题73cotes公式积分(quad8)
%同理,可劲带公式就行
操作题74阻尼正波函数的积分
>>symsct;
>>a=atan(-c./sqrt(1-c.^2));
>>f=(exp(-c*t)./cos(a))*cos(t*sqrt(1-c.^2)+a);
>>f=subs(f,c,0.1)
f=
(10*11^(1/2)*cos((3*11^(1/2)*t)/10-1804455842471457/18014398509481984))/(33*exp(t/10))
>>int(f,0,20)
ans=
sin(1804455842471457/18014398509481984)+(11^(1/2)*cos(1804455842471457/18014398509481984))/33-(11^(1/2)*(cos(1804455842471457/18014398509481984-6*11^(1/2))+3*11^(1/2)*sin(1804455842471457/18014398509481984-6*11^(1/2))))/(33*exp
(2))
>>vpa(ans)
ans=
0.3021742148326484564240312198151
操作题75二重积分
>>f=inline('exp((-x.^2)./2).*sin(x.^2+y)');
>>F=dblquad(f,-2,2,-1,1)
F=
1.5745
操作题76三重积分
>>f=inline('4.*x.*z.*exp(-x.^2.*y-z.^2)');
>>F=triplequad(f,0,2,0,pi,0,pi)
F=
3.1081
操作题77各种重积分
1.
>>f=inline('sin(x+y)');
>>I1=dblquad(f,0,2,0,pi);
2.
>>f=inline('x.*sin(y+z)');
>>I2=triplequad(f,0,3,0,2,0,1);
操作题78
>>t=2:
2:
20;
>>v=[10182529322011520];
>>s=trapz(t,v)
s=
294
>>t=2:
2:
20;
v=[10182529322011520];
t1=0:
0.5:
20;
a=polyfit(t,v,4);%多次实验4次拟合比较好
plot(t,v,'-o',t1,polyval(a,t1))
>>f=poly2sym(a)
f=
x^4/384-(1171*x^3)/13728+(8402257696402027*x^2)/180********481984+(4511473053292677*x)/1125899906842624+6004799503144177/36028797018963968
>>I=int(f,0,20)
I=
390502119689659812155/1288029493427961856
>>vpa(I)
ans=
303.177********441423446064546923
操作题79数值法和符号法求微分方程
>>dsolve('Dy=4*exp(0.8*t)-0.5*y','y(0)=2')
ans=
(40*exp((13*t)/10))/(13*exp(t/2))-14/(13*exp(t/2))
%符号法求解,相当方便
>>f=inline('4*exp(0.8*t)-0.5*y');
>>ode23(f,[0:
4],2)
>>ode23(f,[0,4],2)
>>[t,y]=ode23(f,[0:
4],2)
t=
0
1
2
3
4
y=
2.000000000000000
6.193481793146627
14.839230669770473
33.665213911138977
75.315016303826766
%数值法,定义内联函数
操作题80四阶rk法解一阶微分方程组
rigid.m
functiondy=rigid(t,y)
dy=zeros(2,1);
dy
(1)=1.2*y
(1)-0.6*y
(1).*y
(2)
dy
(2)=-0.8*y
(2)+0.3*y
(1).*y
(2);
[t,y]=ode45('rigid',[012],[21]);
%本题显然题目中有错误,当两式相等时,与已知条件矛盾,
%此解法是将第二个微分方程中dy1改为dy2所得,当为正解
%此题和helpexamples中的题几乎一样的
50.
>>symsx
>>f=(5*x^3+3*x^2-2*x+7)/(-4*x^3+8*x+3);
>>diff(f)
ans=
(15*x^2+6*x-2)/(-4*x^3+8*x+3)+((12*x^2-8)*(5*x^3+3*x^2-2*x+7))/(-4*x^3+8*x+3)^2
51.
(1)
symsx
>>f=(x+sin(x))/(1+cos(x));
>>I1=int(f)
I1=
x*tan(x/2)
(2).
>>symsx
>>f=sqrt(log(1/x));
>>I2=int(f,0,1)
I2=
pi^(1/2)/2
>>vpa(I2)
ans=
0.88622692545275801364908374167057
52.
>>symsx
>>f=[cos(x)x^2;2^xlog(2+x)]
f=
[cos(x),x^2]
[2^x,log(x+2)]
>>I3=int(f)
I3=
[sin(x),x^3/3]
[2^x/log
(2),(log(x+2)-1)*(x+2)]
52.
>>symsx
>>y=sin(x);
>>taylor(y,4,1)
ans=
sin
(1)-(sin
(1)*(x-1)^2)/2+cos
(1)*(x-1)-(cos
(1)*(x-1)^3)/6
53.
>>symsxyuv
>>[u1,v1]=solve('x*u+y*v=0','y*u+x*v=1','u','v');
>>diff(diff(u1,x),y)
ans=
(2*x)/(x^2-y^2)^2+(8*x*y^2)/(x^2-y^2)^3
54.
>dsolve('D2y=cos(2*x)-y','y(0)=1','Dy(0)=0','x')
ans=
(5*cos(x))/3+sin(x)*(sin(3*x)/6+sin(x)/2)-(2*cos(x)*(6*tan(x/2)^2-3*tan(x/2)^4+1))/(3*(tan(x/2)^2+1)^3)
55.
>>x=1:
6;
>>y1=[245620231900245028902280];
>>y2=[12.511.310.214.514.315.1];
>>plotyy(x,y1,x,y2)
>>legend('销售收入','边际利润')
56.
不妨取v=2a=pi/6w=3
>>symst
>>v=2;
>>a=pi/6;
>>w=3;
>>x=v*t*sin(a)*cos(w*t);
>>y=v*t*sin(a)*sin(w*t);
>>z=v*t*cos(w);
>>ezplot3(x,y,z,[0,10])%[0,10]为t的取值范围
57.
>>f=inline('exp(x)-x-5')
f=
Inlinefunction:
f(x)=exp(x)-x-5
>>fzero(f,2)%初值点取在区间及区间附近都
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