MAAB数学实验第二版答案胡良剑

1、数学实验答案Chapter 1Page20,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

2、，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.A4-2.Ax; fmin,min_index=min(f)最小值 最小值点编址 x(min_index)ans =绝对值最小的点0.6500 最小值点 f1,x1_index=min(abs(f)求近似根 -f1 =0.0328x1_index =24 x(x1_index)ans =-0.8500

3、x(x1_i ndex)=;f=x.A4-2.Ax;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 =0.0630x2_index =65 x(x2_index) ans =1.2500Page20,ex5 z=magic(10)z = 92 99 1 8 15 67 74 51 58 4098 80 7 14 16 73 55 57 64 414 81 88 20 22 54 56 63 70 4785 87 19 21 3 60 62 69 71 2886 93 25 2 9 61 68 75 52 3417

4、24 76 83 90 42 49 26 33 6523 5 82 89 91 48 30 32 39 6679 6 13 95 97 29 31 38 45 7210 12 94 96 78 35 37 44 46 5311 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 2Page 45 ex1先在编辑器窗口写下列 M函数，保存为eg2_1.mfunction xbar,s=ex2_1(x)n=length(x);xbar=sum(x)/n;s=sqrt(su

5、m(x42)-n*xbaA2)/( n-1);例如x=81 70 65 51 76 66 90 87 61 77;xbar,s=ex2_1(x)Page 45 ex2s=log(1);n=0;while sek=k+1;F(k)=F(k-1)+F(k-2); x=F(k)/F(k-1);enda,x,k计算至 k=21 可满足精度Page 45 ex4clear;tic;s=0;for i=1:1000000s=s+sqrt(3)/29;ends,toctic;s=0;i=1;while i1.1)+x.*(x=-1.1)-1.1*(x1);p=p+b*exp(-y.A2-6*x.A2).*(

6、x+y-1).*(x+y=1);p=p+a*exp(-0.75*y.A2-3.75*x.A2+1.5*x).*(x+y A=1 2 3;4 5 6;7 8 0;C=2 -5 -22;-5 -24 -56;-22 -56 -16; X=lyap(A,C)X =1.0000 -1.0000 -0.0000-1.0000 2.0000 1.0000-0.0000 1.0000 7.0000Chapter 3Page65 Ex1 a=1,2,3;b=2,4,3;a./b,a.b,a/b,abans =0.5000 0.5000 1.0000ans =2 2 1ans =0.6552 一元方程组 x2,

7、4,3=1,2,3 的近似解ans =0 0 00 0 0的特解0.6667 1.3333 1.0000矩阵方程 1,2,3x11,x12,x13;x21,x22,x23;x31,x32,x33=2,4,3Page65 Ex 2(1) A=4 1 -1;3 2 -6;1 -5 3;b=9;-2;1; rank(A), rank(A,b) A,b为增广矩阵ans =ans =3 可见方程组唯一解 x=Abx =2.38301.48942.0213(2) A=4 -3 3;3 2 -6;1 -5 3;b=-1;-2;1; rank(A), rank(A,b)ans =3ans =3 可见方程组唯一

8、解 x=Ab-0.4706-0.29410(3) A=4 1;3 2;1 -5;b=1;1;1; rank(A), rank(A,b)ans =2ans =3 可见方程组无解 x=Ab0.3311-0.1219 最小二乘近似解注意 b 的写法 a=2,1,-1,1;1,2,1,-1;1,1,2,1;b=1 2 3;% rank(a),rank(a,b)ans =3ans =3 rank(a)=rank(a,b) abans =1010 一个特解Page65 Ex3 a=2,1,-1,1;1,2,1,-1;1,1,2,1;b=1,2,3; x=null(a),x0=abx =-0.62550.6

9、255-0.20850.4170x0 =1010通解 kx+x0Page65 Ex 4 x0=0.2 0.8;a=0.99 0.05;0.01 0.95; x1=a*x, x2=aA2*x, x10=aA10*x x=x0;for i=1:1000,x=a*x;end,x0.8333x =0.1667 x0=0.8 0.2; x=x0;for i=1:1000,x=a*x;end,xx =0.83330.1667 v,e=eig(a)v =0.9806 -0.70710.1961 0.7071e =1.0000 00 0.9400 v(:,1)./xans =1.17671.1767 成比例，

10、说明 x 是最大特征值对应的特征向量Page65 Ex5用到公式 (3.11)(3.12) B=6,2,1;2.25,1,0.2;3,0.2,1.8;x=25 5 20; C=B/diag(x)C =0.2400 0.4000 0.05000.0900 0.2000 0.01000.1200 0.0400 0.0900 A=eye(3,3)-CA =0.7600 -0.4000 -0.0500-0.0900 0.8000 -0.0100-0.1200 -0.0400 0.9100 D=17 17 17;x=AD37.569625.786224.7690Page65 Ex 6(1) a=4 1

11、-1;3 2 -6;1 -5 3;det(a),inv(a),v,d=eig(a)ans =-94ans =0.2553 -0.0213 0.04260.1596 -0.1383 -0.22340.1809 -0.2234 -0.0532v =0.0185 -0.9009 -0.3066-0.7693 -0.1240 -0.7248-0.6386 -0.4158 0.6170-3.0527 0 00 3.6760 00 0 8.3766(2) a=1 1 -1;0 2 -1;-1 2 0;det(a),inv(a),v,d=eig(a) ans =1ans =2.0000 -2.0000 1.

12、00001.0000 -1.0000 1.00002.0000 -3.0000 2.0000v =-0.5773 0.5774 + 0.0000i 0.5774 - 0.0000i-0.5773 0.5774 0.5774-0.5774 0.5773 - 0.0000i 0.5773 + 0.0000i1.0000 0 00 1.0000 + 0.0000i 00 0 1.0000 - 0.0000i(3) A=5 7 6 5;7 10 8 7;6 8 10 9;5 7 9 10 A =5 7 6 57 10 8 76 8 10 95 7 9 10 det(A),inv(A), v,d=eig

13、(A) ans =1ans =68.0000 -41.0000 -17.0000 10.0000-41.0000 25.0000 10.0000 -6.0000-17.0000 10.0000 5.0000 -3.000010.0000 -6.0000 -3.0000 2.0000v =0.8304 0.0933 0.3963 0.3803-0.5016 -0.3017 0.6149 0.5286-0.2086 0.7603 -0.2716 0.55200.1237 -0.5676 -0.6254 0.5209d =0.0102 0 0 00 0.8431 0 00 0 3.8581 00 0

14、 0 30.2887（以n=5为例）方法一（三个 for ）n=5;for i=1:n, a(i,i)=5;end for i=1:(n-1),a(i,i+1)=6;endfor i=1:(n-1),a(i+1,i)=1;enda方法二(一个 for )n=5;a=zeros(n,n);a(1,1:2)=5 6;for i=2:(n-1),a(i,i-1,i,i+1)=1 5 6;enda(n,n-1 n)=1 5;a方法三(不用 for )n=5;a=diag(5*ones(n,1);b=diag(6*ones(n-1,1);c=diag(ones(n-1,1);a=a+zeros(n-1,

15、1),b;zeros(1,n)+zeros(1,n);c,zeros(n-1,1)列计算 det(a) ans =665 inv(a)ans =0.3173 -0.5865 1.0286 -1.6241 1.9489-0.0977 0.4887 -0.8571 1.3534 -1.62410.0286 -0.1429 0.5429 -0.8571 1.0286-0.0075 0.0376 -0.1429 0.4887 -0.58650.0015 -0.0075 0.0286 -0.0977 0.3173 v,d=eig(a)v =-0.7843 -0.7843 -0.9237 0.9860 -

16、0.92370.5546 -0.5546 -0.3771 -0.0000 0.3771-0.2614 -0.2614 0.0000 -0.1643 0.00000.0924 -0.0924 0.0628 -0.0000 -0.0628-0.0218 -0.0218 0.0257 0.0274 0.0257 d =0.7574 0 0 0 00 9.2426 0 0 00 0 7.4495 0 00 0 0 5.0000 00 0 0 0 2.5505Page65 Ex 7(1) a=4 1 -1;3 2 -6;1 -5 3;v,d=eig(a) v =0.0185 -0.9009 -0.306

17、6-0.7693 -0.1240 -0.7248-0.6386 -0.4158 0.6170d =-3.0527 0 00 3.6760 00 0 8.3766 det(v)ans =-0.9255 %v 行列式正常 , 特征向量线性相关，可对角化 inv(v)*a*v 验算ans =-3.0527 0.0000 -0.00000.0000 3.6760 -0.0000-0.0000 -0.0000 8.3766 v2,d2=jordan(a) 也可用 jordanv2 =0.0798 0.0076 0.91270.1886 -0.3141 0.1256-0.1605 -0.2607 0.42

18、13 特征向量不同d2 =8.3766 0 00 -3.0527 - 0.0000i 00 0 3.6760 + 0.0000i v2a*v2ans =8.3766 0 0.00000.0000 -3.0527 0.00000.0000 0.0000 3.6760 v(:,1)./v2(:,2) 对应相同特征值的特征向量成比例 ans =2.44912.44912.4491(2) a=1 1 -1;0 2 -1;-1 2 0;v,d=eig(a)-0.5773 0.5774 + 0.0000i 0.5774 - 0.0000i-0.5773 0.5774 0.5774-0.5774 0.577

19、3 - 0.0000i 0.5773 + 0.0000id =1.0000 0 00 1.0000 + 0.0000i 00 0 1.0000 - 0.0000i det(v)ans =-5.0566e-028 -5.1918e-017i v 的行列式接近 0, 特征向量线性相关，不可对角化 v,d=jordan(a)v =1 0 11 0 01 -1 0d =0 1 10 0 1 jordan 标准形不是对角的，所以不可对角化(3) A=5 7 6 5;7 10 8 7;6 8 10 9;5 7 9 10A =5 7 6 57 10 8 76 8 10 95 7 9 10 v,d=eig(A

20、)v =0.8304 0.0933 0.3963 0.3803-0.5016 -0.3017 0.6149 0.5286-0.2086 0.7603 -0.2716 0.55200.1237 -0.5676 -0.6254 0.52090.0102 0 0 00 0.8431 0 00 0 3.8581 00 0 0 30.2887 inv(v)*A*vans =0.0102 0.0000 -0.0000 0.00000.0000 0.8431 -0.0000 -0.0000-0.0000 0.0000 3.8581 -0.0000-0.0000 -0.0000 0 30.2887 本题用 j

21、ordan 不行 , 原因未知(4)参考 6(4) 和 7(1)Page65 Exercise 8只有 (3) 对称, 且特征值全部大于零 , 所以是正定矩阵 .Page65 Exercise 9 (1) a=4 -3 1 3;2 -1 3 5;1 -1 -1 -1;3 -2 3 4;7 -6 -7 0 rank(a)ans =3 rank(a(1:3,:)ans =2 rank(a(1 2 4,:) 1,2,4 行为最大无关组 ans =3 b=a(1 2 4,:);c=a(3 5,:); bc 线性表示的系数ans =-0.5000 1.00000 -5.0000Page65 Exerci

22、se 10 a=1 -2 2;-2 -2 4;2 4 -2 v,d=eig(a)v =0.3333 0.9339 -0.12930.6667 -0.3304 -0.6681-0.6667 0.1365 -0.7327 d =-7.0000 0 00 2.0000 00 0 2.0000 v*vans =1.0000 0.0000 0.00000.0000 1.0000 0 0.0000 0 1.0000 v 确实是正交矩阵Page65 Exercise 11 设经过 6个电阻的电流分别为 i1, ., i6.列方程组如下20-2i1=a; 5-3i2=c; a-3i3=c; a-4i4=b;

23、c-5i5=b; b-3i6=0; i1=i3+i4;i5=i2+i3;i6=i4+i5;计算如下 A=1 0 0 2 0 0 0 0 0;0 0 1 0 3 0 0 0 0;1 0 -1 0 0 -3 0 0 0; 1 -1 0 0 0 0 -4 0 0;0 -1 1 0 0 0 0 -5 0;0 1 0 0 0 0 0 0 -3; 0 0 0 1 0 -1 -1 0 0;0 0 0 0 -1 -1 0 1 0;0 0 0 0 0 0 -1 -1 1;b=20 5 0 0 0 0 0 0 0; Abans =13.34536.44018.542000002CXI Hi 5 uv?)-舉*眾疤

24、)0)2匸6一-(60)|30|方一 AA9H冒 0000.9(0el)lunsLll6_(6a)luns.L42 AA10 8 匕9 9 寸oCXI匸H fA=(A-p(1)*eye(3,3)*(A-p(2)*eye(3,3)*(A-p(3)*eye(3,3) fA =1.0e-012 *0.0853 0.1421 0.02840.1421 0.1421 0-0.0568 -0.1137 0.1705 norm(fA) f(A) 范数接近 0ans =2.9536e-013Chapter 4Page84 Exercise 1(1)roots(1 1 1)(2)roots(3 0 -4 0 2

25、 -1)(3)p=zeros(1,24);p(1 17 18 22)=5 -6 8 -5;roots(p)(4)p1=2 3;p2=conv(p1, p1);p3=conv(p1, p2);p3(end)=p3(end)-4; % 原 p3 最后一个分量 -4roots(p3)Page84 Exercise 2fun=inlin e(x*log(sqrt(xA2-1)+x)-sqrt(xA2-1)-0.5*x);fzero(fun,2)Page84 Exercise 3fplot(fun,-2 2);grid on;fzero(fun,-1),fzero(fun,1),fminbnd(fun,

26、0.5,1.5)Page84 Exercise 4 fun=inline(x*sin(1/x),x);fplot(fun, -0.1 0.1);x=zeros(1,10);for i=1:10, x(i)=fzero(fun,(i-0.5)*0.01);end;x=x,-xPage84 Exercise 5fun=i nli ne(9*x(1F2+36*x (2) A2+4*x (3)A2-36;x(1)A2-2*x(2)A2-20*x(3);16*x(1)-x(1)A3-2*x (2)A2-16*x(3)A2,x);a,b,c=fsolve(fun,0 0 0)Page84 Exercise

27、 6fun=(x)x(1)-0.7*sin(x(1)-0.2*cos(x(2),x(2)-0.7*cos(x(1)+0.2*sin(x(2);a,b,c=fsolve(fun,0.5 0.5)Page84 Exercise 7clear; close; t=0:pi/100:2*pi;x1=2+sqrt(5)*cos(t); y1=3-2*x1+sqrt(5)*sin(t);x2=3+sqrt(2)*cos(t); y2=6*sin(t);plot(x1,y1,x2,y2); grid on; 作图发现 4 个解的大致位置，然后分别求解y仁fsolve(x(1)-2F2+(x (2)-3+2*

28、x(1)F2-5,2*(x(1)-3F2+(x (2) /3)八2-4,1.5,2)y2=fsolve(x(1)-2)A2+(x (2)-3+2*x(1)A2-5,2*(x(1)-3)A2+(x (2)/3)A2-4,1.8,-2)y3=fsolve(x(1)-2)A2+(x(2)-3+2*x(1)A2-5,2*(x(1)-3)A2+(x(2)/3)A2-4,3.5,-5)y4=fsolve(x(1)-2)A2+(x(2)-3+2*x(1)A2-5,2*(x(1)-3)A2+(x(2)/3)A2-4,4,-4)Page84 Exercise 8(1)clear;fun=inline(x.A2.

29、*sin(x.A2-x-2);fplot(fun,-2 2);grid on;作图观察x(1)=-2;x(5)=fminbnd(fun,1,2);fun 2=i nlin e(-x.A2.*si n(x.A2-x-2);x(2)=fminbnd(fun2,-2,-1);x(4)=fminbnd(fun2,-0.5,0.5);x(6)=2feval(fun,x)答案: 以上 x(1)(3)(5)是局部极小， x(2) (4) (6) 是局部极大， 从最后一句知道 x(1) 全局最小， x(2) 最大。(2)clear;fun=inline(3*x.A5-20*x.A3+10);fplot(fun

30、,-3 3);grid on;作图观察x(1)=-3;x(3)=fminsearch(fun,2.5);fun2=inline(-(3*x.A5-20*x.A3+10);x(2)=fminsearch(fun2,-2.5);x(4)=3;feval(fun,x)(3)fun=i nlin e(abs(xA3-xA2-x-2);fplot(fun,0 3);grid on;作图观察fminbnd(fun,1.5,2.5)fun2=inline(-abs(xA3-xA2-x-2);fminbnd(fun2,0.5,1.5)Page84 Exercise 9close;x=-2:0.1:1;y=-7

31、:0.1:1;x,y=meshgrid(x,y); z=y.A3/9+3*x.A2.*y+9*x.A2+y.A2+x.*y+9;mesh(x,y,z);grid on;作图观察fun=inline(x(2)A3/9+3*x(1)A2*x(2)+9*x(1)A2+x(2)A2+x(1)*x(2)+9);x=fminsearch(fun,0 0)求极小值fun 2=i nlin e(-(x (2)A3/9+3*x(1)A2*x (2)+9*x(1)H+x (2)A2+x(1)*x (2)+9);x=fminsearch(fun2,0 -5)求极大值Page84 Exercise 10 clear;

32、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;p2=polyfit(t,c,2)p3=polyfit(t,c,3) fun=inline(a(1)*exp(a(2)*(t-14).A2),a,t);a=lsqcurvefit(fun,0 0,t,c)初值可以试探f=feval(fun, a,t)norm(f-c) 拟合效果plot(t,c,t,f)作图检验fun2=inline(b(1)*sin(pi/12*t+b(2)+20,b,t);原题修改 f(x)+20b=lsq

33、curvefit(fun2,0 0,t,c) figure f2=feval(fun2, b,t) norm(f2-c) 拟合效果plot(t,c,t,f2) 作图检验Page84 Exercise 11fun=inline(1-x)*sqrt(10.52+x)-3.06*x*sqrt(1+x)*sqrt(5); x=fzero(fun, 0, 1)Page84 Exercise 12r=5.04/12/100;N=20*12;x=7500*180 房屋总价格y=x*0.3 首付款额x0=x-y 贷款总额a=(1+r)AN*r*x0/(1+r)AN-1)月付还款额r1=4.05/12/100;

34、x1=10*10000;公积金贷款a1=(1+r1)AN*r1*x1/(1+r1)AN-1)x2=x0-x1 商业贷款a2=(1+r)AN*r*x2/(1+r)AN-1)a=a1+a2Page84 Exercise 13列方程 th*RA2+(pi-2*th)*rA2-R*r*sin(th)=pi*A2/2化简得 sin(2*th)-2*th*cos(2*th)=pi/2以下 Matlab 计算clear;fun= inline(sin(2*th)-2*th*cos(2*th)-pi/2,th) th=fsolve(fun,pi/4)R=20*cos(th)Page84 Exercise 14

35、先在Editor窗口写M函数保存function x=secant(fname,x0,x1,e)while abs(x0-x1)e, x=x1-(x1-x0)*feval(fname,x1)/(feval(fname,x1)-feval(fname,x0);x0=x1;x1=x;end再在指令窗口fun=inlin e(x*log(sqrt(xA2-1)+x)-sqrt(xA2-1)-0.5*x);secant(fun,1,2,1e-8)Page84 Exercise 15作系数为a,初值为xo,从第m步到第n步迭代过程的M函数:function f=ex4_15fun(a,x0,m,n)x(

36、1)=x0; y(1)=a*x(1)+1;x(2)=y(1);if mm, plot(x(i),x(i),x(i+1),y(i-1),y(i),y(i); endendhold off;M脚本文件subplot(2,2,1);ex4_15fun(0.9,1,1,20);subplot(2,2,2);ex4_15fun(-0.9,1,1,20);subplot(2,2,3);ex4_15fun(1.1,1,1,20); subplot(2,2,4);ex4_15fun(-1.1,1,1,20);Page84 Exercise 16设夹角 t, 问题转化为 min f=5/sin(t)+10/co

37、s(t) 取初始值 pi/4, 计算如下 fun=(t)5/sin(t)+10/cos(t);t,f=fminsearch(fun, pi/4)t =0.6709f =20.8097Page84 Exercise 17提示：x(k+2)=f(x(k)=aA2*x(k)*(1-x(k)*(1-a*x(k)*(1-x(k) 计算平衡点 x|f(x)| ex4_18(0.9,1,20) ex4_18(-0.9,1,20) ex4_18(1.1,1,20) ex4_18(-1.1,1,20)Page84 Exercise 19 clear; close; x(1)=0; y(1)=0;for k=1:

38、3000x(k+1)=1+y(k)-1.4*x(kF2; y(k+1)=0.3*x(k);endplot(x(1000:1500),y(1000:1500),+g);hold on plot(x(1501:2000),y(1501:2000),.b);plot(x(2001:2500),y(2001:2500),*y);plot(x(2501:3001),y(2501:3001),.r);Chapter 5Page101 Exercise 1x=0 4 10 12 15 22 28 34 40;y=0 1 3 6 8 9 5 3 0;trapz(x,y)Page101 Exercise 2 x

39、=0 4 10 12 15 22 28 34 40;y=0 1 3 6 8 9 5 3 0; diff(y)./diff(x)Page101 Exercise 3 xa=-1:0.1:1;ya=0:0.1:2;x,y=meshgrid(xa,ya);z=x.*exp(-x42 -y.A3);px,py = gradient(z,xa,ya);pxPage101 Exercise 4 t=0:0.01:1.5;x=log(cos(t);y=cos(t)-t.*sin(t);dydx=gradient(y,x) x_1,id=min(abs(x-(-1);% 找最接近 x=-1 的点 dydx(i

40、d)Page101 Exercise 5(1)Fun=inline( 1/(sqrt(2*pi).*exp(-x42./2);Quadl(fun,0,1)(2)fun=i nlin e(exp(2*x).*cos(x).A3);quadl(fun,0,2*pi)或用 trapzx=linspace(0,2*pi,100); y=exp(2*x).*cos(x).A3;trapz(x,y)(3)fun=(x)x.*log(x.A4).*asin(1./x.A2); quadl(fun,1,3)或用 trapzx=1:0.01:3;y=feval(fun,x);trapz(x,y)(4)1e-10

41、 代替fun=(x)sin(x)./x;quadl(fun,1e-10,1) % 注意由于下限为 0，被积函数没有意义，用很小的(5)%参考 Exercise 5(4)(6)fun=i nlin e(sqrt(1+r.A2.*si n(th),r,th);dblquad(fun,0,1,0,2*pi)(7)首先建立 84 页函数 dblquad2clear;fun=(x,y)1+x+y.A2;clo=(x)-sqrt(2*x-x.A2);dup=(x)sqrt(2*x-x42);dblquad2(fun,0,2,clo,dhi,100)Page101 Exercise 6 t=linspace

42、(0,2*pi,100);x=2*cos(t);y=3*sin(t);dx=gradient(x,t);dy=gradient(y,t);f=sqrt(dx.A2+dy.A2);trapz(t,f)Page101 Exercise 7xa=-1:0.1:1;ya=0:0.1:2;x,y=meshgrid(xa,ya);z=x.*exp(x.A2+y.A2);zx,zy=gradient(z,xa,ya);f=sqrt(1+zx.A2+zy.A2);s=0;for i=2:length(xa)for j=2:length(ya) s=s+(xa(i)-xa(i-1)*(ya(j)-ya(j-1)

43、*(f(i,j)+f(i-1,j)+f(i,j-1)+f(i-1,j-1)/4; end endsPage101 Exercise 8fun l=i nli ne(-(-x)402*cos(x);funr=inlin e(x.A0.2.*cos(x); quadl(funl,-1,0)+quadl(funr,0,1)Page101 Exercise 9( 以 I32 为例 )fun=(x)abs(sin(x);h=0.1;x=0:h:32*pi;y=feval(fun,x);t1=trapz(x,y)h=pi;x=0:h:32*pi;y=feval(fun,x);t2=trapz(x,y)%步

44、长与周期一致，结果失真q1=quad(fun,0,32*pi)q2=quadl(fun,0,32*pi)Page101 Exercise 10(2)先在程序编辑器，写下列函数，保存为 ex5_10_2ffunction d=ex5_10_2f(fname,a,h0,e)h=h0;d=(feval(fname,a+h)-2*feval(fname,a)+feval(fname,a-h)/(h*h); d0=d+2*e;while abs(d-d0)ed0=d;h0=h;h=h0/2;d=(feval(fname,a+h)-2*feval(fname,a)+feval(fname,a-h)/(h*

45、h);end再在指令窗口执行fun=i nlin e(x.A2*si n(x.A2-x-2) ,x);d=ex5_10_2f(fun,1.4,0.1,1e-3)Page101 Exercise 11提示：f上升时，fO;f 下降时，f0; f 极值，f=0.Page101 Exercise 12在程序编辑器，写下列函数，保存为 ex5_12f function I=ex5_12(fname,a,b,n) x=linspace(a,b,n+1);y=feval(fname,x);I=(b-a)/n/3*(y(1)+y(n+1)+2*sum(y(3:2:n)+4*sum(y(2:2:n); 再在指

46、令窗口执行ex5_12(i nlin e(1/sqrt(2*pi)*exp(-x.A2/2),0,1,50)Page101 Exercise 13fun=i nlin e(5400*v./(8.276*v.A2+2000),v); quadl(fun,15,30)Page101 Exercise 14重心不超过凳边沿。 1/2, 2/3, 3/4, .,n/(n+1)Page101 Exercise15利润函数 fun=inline(p-c0+k*log(M*exp(-a*p)*M*exp(-a*p),p); 求 p 使 fun 最大Page101 Exercise 16 clear; x=-

47、3/4:0.01:3/4;y=(3/4+x)*2.*sqrt(1-16/9.*x.A2)*9.8;P=trapz(x,y) % 单位：千牛Page101 Exercise 17clear; close;fplot(17-tA(2 -5-2*护(2/3), 0,20); grid; t=fzero(17-xA(2/3)-5-2*xA(2/3) ,7) t=0:0.1:8; y=17-t.A(2/3)-5-2*t.A(2/3);trapz(t,y)-20 % 单位：百万元Page101 Exercise 18曲面面积计算Chapter 6Page121 Exercise 1(1)fun=inline(x+y,x,y);中0不可缺t,y=ode45(fun,0 1 2 3,1) % 注意由于初值为 y(0)=1,0 1 2 3(3)令 y(1)=y,y(2)=y, 化为方程组y(1)=y( 2),y(2)=0.0