1、P.28 ex 2.1 數值變量(binling)的運算 format short e clear muw0=1.785e-3; a=0.03368; b=0.000221; t=0:20:80; muw=muw0./(1+a*t+b*t.2)muw = 1.7850e-003 1.0131e-003 6.6092e-004 4.6772e-004 3.4940e-004p.31 ex 2.2 數值(shz)駐足和字符串轉換 a=1:5; b=num2str(a); aa = 1 2 3 4 5 bb =1 2 3 4 5 b*2ans =98 64 64 100 64 64 102 64 6

2、4 104 64 64 106P.44 ex 2.9 比較用左除和右除分別求解恰定方程（線性方程組如果方程數等于未知數個數，叫做恰定方程組，如果方程多于未知數，叫做超定方程組，反之稱為(chn wi)欠定。換個角度說，系數矩陣如果是方陣，就是恰定方程組）的解見課本P.48 ex 2.14 計算矩陣的指數 并比較不同函數的結果 b=magic(3); expm(b)ans = 1.0e+006 * 1.0898 1.0896 1.0897 1.0896 1.0897 1.0897 1.0896 1.0897 1.0897 expmdemo2(b)ans = 1.0e+006 * 1.0898 1

3、.0896 1.0897 1.0896 1.0897 1.0897 1.0896 1.0897 1.0897 expm1(b)ans = 1.0e+003 * 2.9800 0.0017 0.4024 0.0191 0.1474 1.0956 0.0536 8.1021 0.0064 expmdemo3(b)ans = 1.0e+006 * 1.0898 1.0896 1.0897 1.0896 1.0897 1.08971.0896 1.0897 1.0897P50 ex 2.18 計算(j sun)矩陣(j zhn)的特征值條件數 a=rand(3)a = 0.9649 0.9572 0.

4、1419 0.1576 0.4854 0.4218 0.9706 0.8003 0.9157 V,D,s=condeig(a)V = 0.4913 0.6696 0.6696 0.3158 -0.4476 + 0.2831i -0.4476 - 0.2831i 0.8117 -0.2332 - 0.4655i -0.2332 + 0.4655iD = 1.8146 0 0 0 0.2757 + 0.3061i 0 0 0 0.2757 - 0.3061is = 1.1792 1.2366 1.2366P62 ex 2.29矩陣(j zhn)的抽取、三角(snjio)抽取 a=pascal(4)

5、a = 1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20 diag(a,-2)ans = 1 4 v=diag(diag(a)v = 1 0 0 0 0 2 0 0 0 0 6 0 0 0 0 20%diag簡單(jindn)來說就是抽取矩陣各對角線上的元素，如上是抽取(chu q)主對角線以下第二條對角線之元素(yun s)，其另一功能是建立對角矩陣 tril(a)ans = 1 0 0 0 1 2 0 0 1 3 6 0 1 4 10 20 triu(a)ans = 1 1 1 1 0 2 3 4 0 0 6 10 0 0 0 20%triu&tril用法與diag非常

6、類似，用途是提取下、上三角矩陣P62 ex2.30 建立多項式之伴隨矩陣這道題有點凌亂了.求解釋P64 ex 2.31 數組的冪運算 a=2 1 -3 -1;3 1 0 7;-1 2 4 -2;1 0 -1 5; a3ans = 32 -28 -101 34 99 -12 -151 239 -1 49 93 8 51 -17 -98 139 a.3ans = 8 1 -27 -1 27 1 0 343 -1 8 64 -8 1 0 -1 125P66 ex 2.32 數組之邏輯運算 a=1:3;4:6;7:9; b=0 1 0;1 0 1;0 0 1; x=5;y=ones(3)*5; x a

7、b=a&bab = 0 1 0 1 0 1 0 0 1%此處為與運算，就是同真才為真（同為非零數） bans = 1 0 1 0 1 0 1 1 0%邏輯非運算，即全都非，真變假假變真；還有邏輯或運算，看下面即懂： a|bans = 1 1 1 1 1 1 1 1 1%總結多項式運算的函數：poly: Polynomial with specified roots特征多項式的生成p=poly(a)a為n階特征矩陣，所得一般為n階特征多項式；poly2sym數值2符號；polyval 求多項式的值；roots 求多項式的根；conv 多項式的乘法(向量之卷積)conv(p,d);polyder

8、多項式微分；polyfit 多項式擬合。P71 ex 2.41 多項式擬合(n h)，用5階多項式對正弦(zhngxin)函數進行(jnxng)最小二乘擬合 x=0:pi/20:pi/2; y=sin(x); a=polyfit(x,y,5); x1=0:pi/30:pi*2; y1=sin(x1); y2=a(1)*x1.5+a(2)*x1.4+a(3)*x1.2+a(4)*x1.2+a(5)*x1+a(6); plot(x,y,b-,x1,y2,r*) legend(原曲線,擬合曲線) axis(0,7,-1.2,4) axis(0,7,-1.2,1.5) %調整坐標軸顯示范圍 2.符號運

9、算命名和基本運算法則P 79 符號矩陣的運算 A=sym(a,b;c,d) A = a, b c, d syms a b c d B=a,b;c,d B = a, b c, d B-A ans = 0, 0 0, 0 A/B ans = 1, 0 0, 1 A2 ans = a2 + b*c, a*b + b*d a*c + c*d, d2 + b*c A.2 ans = a2, b2 c2, d2 det(A) ans = a*d - b*c %行列式 inv(A) ans = d/(a*d - b*c), -b/(a*d - b*c) -c/(a*d - b*c), a/(a*d - b*

10、c) %逆 rank(A) ans = 2%秩%SUMMARY 矩陣(j zhn)的分解：奇異(qy)值分解 U,S,V=svd(A)；特征值分解(fnji)V,D=eig(A)；正交分解Q,R=qr(A)；三角分解L,U=lu(A)；P88 ex 3.7 利用函數gradient繪制一個矢量圖 x,y=meshgrid(-2:.2:2,-2:.2:2); z=x.*exp(-x.2-y.2); px,py=gradient(z,.2,.2); contour(z),%等高線繪制(huzh)函數 hold on quiver(px,py)%矢量圖繪制(huzh)函數 %繪圖(hu t)SUMM

11、ARY 1.二維plot 不解釋；fplot：繪制y=f(x)圖形 fplot(fname,lims,s)；ezplot：繪制隱函數圖形 help吧；極坐標polar,對數坐標semilogx,semilogy,loglog;bar 條形圖，pie餅狀圖；hist 直方圖 有些疑惑！；grid on/off：控制是否畫網格線。box on/off： 控制是否加邊框線。hold on/off 控制是否刷新當前軸及圖形%2.三維：plot3; meshgrid函數：產生平面區域內的網格坐標矩陣;mesh 畫格子；surf 面；figure(n)開窗戶；subplot:割圖。3.二維圖形函數運用P9

12、8 基本繪圖命令 y=rand(100,1); plot(y) x=rand(100,1); z=x+y.*i; plot(z) P101 ex4.1 繪制帶有顯示屬性的二維屬性 x=1:0.1*pi:2*pi; y=sin(x); z=cos(x); plot(x,y,-k,x,z,-.rd) P104 ex4.5 條狀圖和矢量圖 x=1:10; y=rand(10,1); bar(x,y) x=0:0.1*pi:2*pi; x=0:0.1*pi:2*pi; y=x.*sin(x); feather(x,y) P104 ex4.6 函數圖形繪制 lim=0,2*pi,-1,1; fplot(

13、sin(x),cos(x),lim) P105 ex 4.7 繪制餅狀圖 x=2,4,6,8; pie(x,math,english,chinese,music) 4.三維圖形(txng)函數應用P107 ex4.9 繪制(huzh)三維螺旋線 x=0:pi/50:10*pi; y=sin(x);z=cos(x); plot3(x,y,z) P107 ex 4.10 繪制參數(cnsh)為矩陣的三維圖 x,y=meshgrid(-2:0.1:2,-2:0.1:2); z=x.*exp(-x.2-y.2); plot3(x,y,z) P109 ex 4.11 使用mesh函數繪制三維面圖 x=-

14、8:0.5:8;y=x; a=ones(size(y)*x; b=y*ones(size(x); c=sqrt(a.2+b.2)+eps; z=sin(c)./c; mesh(z) P110 ex4.13 meshc函數繪制的三維面圖 X,Y=meshgrid(-4:0.5:4); Z=sqrt(X.2+Y.2); meshc(Z) P111 ex 4.16 繪制三維餅狀圖 clear x=2,4,6,8; pie(x) pie(x,0,0,1,0) pie3(x,0,0,1,0) pie3(x,0,0,1,1) P113 ex 4.19 繪制如圖柱面圖 x=0:pi/20:pi*3; r=5

15、+cos(x); a,b,c=cylinder(r,30); mesh(a,b,c) P113 ex 4.20 繪制(huzh)地球表面的氣溫分布示意圖 a,b,c=sphere(40); t=abs(c); surf(a,b,c,t); axis(equal) axis(square) colormap(hot) 5.圖形控制命令(mng lng)P118 ex 4.24 坐標標注(bio zh)函數應用 x=1:0.1*pi:2*pi; y=sin(x);plot(x,y) xlabel(x(0-2pi) ylabel(y=sin(x) title(正弦函數,FontSize)Error

16、using title (line 29)Incorrect number of input argumentsError in title (line 23) h = title(gca,varargin:); title(正弦函數,FontSize,12) title(正弦函數,FontSize,12,FontWeight,bold) %課本上不知由于版本問題還是什么，與2011b不同，最后嘗試用Bold成功解決 ADD 已解決，用單引號引起bold即可Undefined function or variable bold. title(正弦函數,FontSize,12,FontWeigh

17、t,Bold)Undefined function or variable Bold. title(正弦函數,FontSize,12,FontWeight,Bold) title(正弦函數,FontSize,12,FontWeight,Bold,FontName,隸書) P123 ex 4.30 在同一張途中繪制幾個三角函數圖 x=0:0.1*pi:2*pi; y=sin(x); z=cos(x); plot(x,y,-*) hold on plot (x,z,-o) plot(x,y+z,-+) legend(sin(x),cos(x),sin(x)+cos(x),0) P124 ex 4.

18、31 在4個子圖中繪制不同的三角函數 x=0:0.1*pi:2*pi; subplot(2,2,1); plot(x,sin(x),-*) title(sin(x) subplot(2,2,2) plot(x,cos(x),-o) title(cos(x) subplot(2,2,3) plot(x,sin(x).*cos(x),-x) title(sin(x)*cos(x) subplot(2,2,4) plot(x,sin(x)+cos(x),-h) title(sin(x)+cos() title(sin(x)+cos(x) % SUMMARY interp1:1-D data inte

19、rpolation (table lookup) % yi = interp1(x,Y,xi,method,extrap) method:nearest/linear/echip(hermite)/spline,etcP222 ex 7.3 正弦曲線的插值實例(shl) x=0:0.05:10; y=sin(x); xi=0:.125:10; yi=interp1(x,y,xi);%一維插值 plot(x,y,*,xi,yi)P227 例7.7二次擬合(n h) x=0.5:0.5:3.0; y=1.75 2.45 3.81 4.80 8.00 8.60; a=polyfit(x,y,2)%用

20、最小二乘法(chngf)擬合a = 0.4900 1.2501 0.8560 x1=0.5:0.05:3.0； y1=a(1)*x1.2+a(2)*x1+a(3);%擬合(n h)出的函數 plot(x1,y1,-or,x,y,-+b)P228 例7.8擬合(n h)，用求解(qi ji)矩陣的方法解，求解超定方程 xi=19:6:44xi = 19 25 31 37 43 yi=19.0 32.3 49.0 73.3 98.8; format short a=polyfit(xi,yi,2)a = 0.0635 -0.5932 7.2811 x1=19:.1:44; y1=a(1)*x1.2

21、+a(2)*x1+a(2);%此處發生了一點錯誤，將a（3）誤輸為a(2),后面會有改正 plot(x1,y1,-x) plot(x1,y1,-) x2=xi.2;%采用(ciyng)求解矩陣的方法來求解此擬合(n h)問題(wnt) x2=ones(5,1),x2x2 = 1 361 1 625 1 961 1 1369 1 1849 ab=x2yiab = -1.3522 0.0540 y3=ab(1)+ab(2)*x1.2; hold on;plot(x1,y3,-g) y1=a(1)*x1.2+a(2)*x1+a(3); plot(x1,y1,-)%從圖中可以看出，兩種擬合方法較為吻合

22、P233 例7.10 分別用矩形和梯形公式求積分 y=inline(exp(-0.5*t).*sin(t+pi/6);%內聯函數 d=pi/1000; t=0:d:3*pi; nt=length(t)nt = 3001 y1=y(t); sc=cumsum(y1)*d; scf=sc(nt)scf = 0.9016 format long scfscf = 0.901618619310013%矩形(jxng)方法 z=trapz(y1)*dz = 0.900840276606885%梯形(txng)方法(fngf)P237 ex7.11 采用自適應Simpson公式求積分 f=inline(x

23、./(x.2+4); quad(f,0,1)ans = 0.111571765994935P237 ex 7.12 用quadl求積分 f=inline(exp(-x/2); f1=quadl(f,1,3)f1 = 0.7668 f2=quad(f,1,3,1e-10)f2 =0.7668 format long e f1f1 = 7.668009991284686e-001 f2f2 =7.668009991284349e-001P237 7.12 quadl gauss-labatto 求積分(jfn) quadl(exp(-x/2),1,3)ans = 0.7668%求線性方程組的方法(

24、fngf)一般有兩種：左除求法和linsolve求法P246 ex 7.17 求線性方程組 a=rand(4,4);%生成(shn chn)隨機矩陣 b=rand(4,1); x=abx = 1.728190838792039e+001 8.395388076704506e-001 -1.590669694986821e+0011.088276299038511e+000%此處與書上不同，為生成的隨機矩陣%SUMMARY矩陣左除 AB =A-1* B 等效于A*X=B求X inv(A) 注：.數組左除 A.B Bij/Aij ; /:矩陣右除 A/B =A*B-1 等效于X*B=A求X for

25、mat short x1=linsolve(a,b)%SUMMARY用linsolve求解線性方程；用solve use for linear function/fzero求解非線性方程；Dsolve Ordinary differential equation and system solver,用dsolve求解微分方程；fsolve Solve system of nonlinear equations, x,fval = fsolve(myfun,x0,options) % Call solverx1 = 17.2819 0.8395 -15.9067 1.0883P246 ex 7.

26、18 對矩陣(j zhn)進行(jnxng)LU分解(fnji) A=ones(4,4)A = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l,u=lu(A)l = 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1u = 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 l*uans = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1P265 ex 7.39 求方程組之符號解 x1,x2=solve(x1-0.7*sin(x1)-0.2*cos(x2)=0,x2-0.7*cos(x1)+0.2*sin(x2)=0) x1 = 0.

27、52652262191818418730769280519209 x2 = 0.50791971903684924497183722688768 x1=solve(x1-0.7*sin(x1)-0.2*cos(x2)=0,x2-0.7*cos(x1)+0.2*sin(x2)=0)x1 = x1: 1x1 sym x2: 1x1 sym x1.x1 ans = 0.52652262191818418730769280519209 x1.x2 ans = 0.50791971903684924497183722688768%方法(fngf)一：用solve求符號解，注意(zh y)使用x1,x2方

28、式(fngsh)調用才可求得具體數值 另有不動點迭代法和newton法，見課本p263editfc.mfunction f=fc(x)f(1)=x(1)-0.7*sin(x(1)-0.2*cos(x(2);f(2)=x(2)-0.7*cos(x(1)+0.2*sin(x(2);f=f(1) f(2);%編寫m文件 x0=0.5 0.5; fsolve(fc,x0)Equation solved.fsolve completed because the vector of function values is near zeroas measured by the default value o

29、f the function tolerance, andthe problem appears regular as measured by the gradient.ans = 0.5265 0.5079%用fsolve求解(qi ji)，顯然(xinrn)麻煩(m fan)很多P273 ex 7.42 微分方程數值解f=inline(-y+x+1); x,y=ode23(f,0,1,1)x = 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000y = 1.0000 1.0048 1.0187 1.

30、0408 1.0703 1.1065 1.1488 1.1966 1.2493 1.3066 1.3679 plot(x,y)%ode、euler等方法都是數值法求解微分方程 x1,y1=ode45(f,0,1,1); plot(x,y,-*r,x1,y1,-o)P273 ex 7.45 R-K法求解(qi ji)微分方程(wi fn fn chn) f=inline(-2*y+2*x.2+2*x)f = Inline function: f(x,y) = -2*y+2*x.2+2*x x,y=ode23(f,0,.5,1);%此處定義域可再取大一些(yxi) plot(x,y)P274 ex

31、 7.46 求解剛性方程fgang.mfunction f=fgang(x,y)f=-2 0;998 -999*y+2*sin(x);999*(cos(x)-sin(x); ode23(fgang,0 10,2,3); %此題略神奇，記下吧%自己做的命令function f=rk15s(x,y)f=zeros(2,1);f(1)=-2*y(1)+y(2)+2*sin(x);f(2)=998*y(1)-999*y(2)+999*(cos(x)-sin(x); ode15s(rk15s,0 10,2,3)P275 ex 7.47 求常微分方程(wi fn fn chn)符號(fho)解 a=dso

32、lve(Dy=y+sin(t),y(pi/2)=0) a = exp(t)/(2*exp(pi/2) - sin(t)/2 - cos(t)/2%subs 代入數值(shz)至函數p307 ex 9.21 檢驗三臺機器生產的鋁合金報班有無顯著性差異（方差分析） x=.236 .238 .248 .245 .243;.257 .253 .255 .254 .261;.258 .264 .259 .267 .262; a=anova1(x)a = 1.3431e-005 %anova1為單因素試驗的方差分析，此處a的大小，是原假設均值相等的幾率P308 9.22 用三種(sn zhn)火箭推進器、

33、四種燃料(rnlio)做射程實驗，每種推進器和燃料(rnlio)的組合各發射火箭兩次，考察推進器和燃料對射程是否有顯著影響 A=58.2 56.2 65.3;52.6 41.2 60.8;49.1 54.1 51.6;42.8 50.5 48.4;60.1 70.9 39.2;58.3 73.2 40.7;75.8 58.2 48.7;.71.5 51 41.4; anova2(A,2)ans = 0.0035 0.0260 0.0001%見課本，課本中直接輸入為8x3的矩陣，使用anova2來求解，題目中的兩次發射表現在anova(a,2)中的數字2，意為：行列對所擁有的觀察點數，即題中所說

34、的發射幾次火箭。返回值有三個，老師講是：第一個：第一種影響因子的原假設均值相等的幾率；第二種同理；第三種是二者之乘積P309 ex 9.23 回歸分析，研究溫度對產品得率之影響，做y=a+bx型之回歸%其實就是擬合 x=100:10:190; y=45 51 54 61 66 70 74 78 85 89; a,b=polyfit(x,y,1)a = 0.4830 -2.7394b = R: 2x2 double df: 8 normr: 2.6878 f=a(1)*x+a(2); plot(x,y,or,x,f,-g)操作題 43 積分(jfn)的符號(fho)法和數值法 syms x in

35、t(log10(1+x),0,1) ans = (log(4) - 1)/log(10) double(ans)ans =0.1678%符號(fho)法，使用int語句積分，功能強大 f=inline(log10(x+1); quad(f,0,1)ans = 0.1678%用quad語句對于簡單的積分十分方便 x=0:.01:1; f=log10(x+1); ff=trapz(x,f)ff = 0.1678%用trapz梯形(txng)積分，用quad進行自適應(shyng)辛卜生法，用quad8進行(jnxng)Neton-cotes法，gauss-labatto:quadl,二重積分 I=

36、dblquad(fname,xmin,xmax,ymin,ymax,tol ,trace)，三重積分：I = triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax,tol)操作題 44多階常微分 用ode23、ode45、ode113求y.mfunction y=y(x,y)dy=zeros(3,1)dy(1)=y(2)dy(2)=y(3)dy(3)=2*y(3)/x3+3*y(2)/x3+3*exp(2*x)/x3x23,y23=ode23(y,1,10,1 10 30);x45,y45=ode45(y,1,10,1 10 30);x113,y113=od

37、e113(y,1,10,1 10 30);plot(x23,y23,-xb,x45,y45,-+g,x113,y113,-or)操作題45 求方程的根 fzero(x.2+x-1,0.5)ans = 0.6180%fzero: Find root of continuous function of one variable. 格式(g shi)：x = fzero(fun,x0)；x0可以(ky)是某個數值(shz)，也可以是定義域；roots是求多項式的，也可以用來求本題 c=1 1 -1; roots(c)ans = -1.6180 0.6180操作題 46 求梯度和法向量%數值法求梯度，

38、使用Fx=gradient(F)只顯示FX/fx,fy=gradient(F) F=1 1.2 1.4 2.35;.06 3 4 2;-1 77.2 9 1.4; Fx,Fy=gradient(F)%二元多元函數求導一般用gradient和nx,ny,nz=surfnorm,gradient: Numerical gradient；surfnorm: Compute and display 3-D surface normal(法向量)Fx = 0.2000 0.2000 0.5750 0.9500 2.9400 1.9700 -0.5000 -2.0000 78.2000 5.0000 -3

39、7.9000 -7.6000Fy = -0.9400 1.8000 2.6000 -0.3500 -1.0000 38.0000 3.8000 -0.4750 -1.0600 74.2000 5.0000 -0.6000 Fx=gradient(F)Fx = 0.2000 0.2000 0.5750 0.9500 2.9400 1.9700 -0.5000 -2.0000 78.2000 5.0000 -37.9000 -7.6000 n=surfnorm(F)n = -0.1485 -0.0058 -0.3170 -0.7910 -0.9404 -0.0518 0.1262 0.9534 -

40、1.0000 -0.0452 0.9865 -0.9985%求法向量(xingling)用surfnorm操作題 47 add path,pathCan be used:1.addpath:Add folders to search path addpath(F:Download) Addmypath(1)F = -3ans = -32.pathtool: open Set Path dialog box to view and change search path3.genpath Generate path string p = genpath(fullfile(matlabroot,to

41、olbox,images)p =F:matric laboratarytoolboximages;F:matric laboratarytoolboximagescolorspaces;F:matric laboratarytoolboximagescolorspacesja;F:matric laboratarytoolboximagesicons;F:matric laboratarytoolboximagesimages;F:matric laboratarytoolboximagesimageseml;F:matric laboratarytoolboximagesimagesja;F

42、:matric laboratarytoolboximagesimdemos;F:matric laboratarytoolboximagesimdemosdemosearch;F:matric laboratarytoolboximagesimdemoshtml;F:matric laboratarytoolboximagesimdemoshtmlja;F:matric laboratarytoolboximagesimdemosja;F:matric laboratarytoolboximagesimdemosjademosearch;F:matric laboratarytoolboxi

43、magesimuitools;F:matric laboratarytoolboximagesimuitoolsja;F:matric laboratarytoolboximagesiptformats;F:matric laboratarytoolboximagesiptformatsja;F:matric laboratarytoolboximagesiptutils;F:matric laboratarytoolboximagesiptutilsja;操作題 48 求多項式的根并生成(shn chn)原多項式 p=1 21 20 0; roots(p)ans = 0 -20 -1%roo

44、ts: Polynomial roots, r = roots(c) returns a column vector whose elements are the roots of the polynomial c. f=poly2sym(p) f = x3 + 21*x2 + 20*x操作題 49 求極限(jxin)含參數(cnsh) syms x m n; a=limit(m./(1-x.m)-n./(1-x.n),x,1) a = (- n2/2 + n/2)/n - (- m2/2 + m/2)/m2.x=sym(x); a1=limit(x.3+x.2+x+1).3-sqrt(x.2

45、+x+1).*(log(exp(x)+x)./x),inf) a1 = Inf3. syms x y; a2=limit(3.x+9.x).(1/x),x,1./y) a2 = 3*(3(1/y) + 1)y4. a3=limit(sqrt(1./x+sqrt(1./x+sqrt(1./x)-sqrt(1./x-sqrt(1./x+sqrt(1./x),x,0,right) a3 = 1%求極限(jxin)使用limit即可，調用(dioyng)格式：limit(1/x, x, 0, right)%求積分(jfn)SUMMARY 符號法求積分：int :int(expr,var,a,b,Nam

46、e,Value),求定積分、不定積分皆可 quad/quadl/quad8數值法求積分：Numerically evaluate integral, adaptive Simpson quadrature 調用q = quad(fun,a,b,tol,trace)；trapz:梯形積分：Trapezoidal numerical integration 調用：Z = trapz(X,Y),此處XY為數組操作題 50 求復雜函數的導數 diff(5*x3+3*x2-2*x+7)/(-4*x3+8*x+3),1) ans = (15*x2 + 6*x - 2)/(- 4*x3 + 8*x + 3)

47、 + (12*x2 - 8)*(5*x3 + 3*x2 - 2*x + 7)/(- 4*x3 + 8*x + 3)2%此式中不可有.等操作題 51 積分1. syms x f=(x+sin(x)/(1+cos(x) f = x + sin(x)/(cos(x) + 1) int(f) ans = x2/2 - log(cos(x) + 1)2. quad(sqrt(log(1./x),0,1)ans = 0.88623. syms x f=cos(x) x.2;2.x log(2+x); int(f) ans = sin(x), x3/3 2x/log(2), (log(x + 2) - 1)

48、*(x + 2)操作題52 taylor 冪級數展開(zhn ki)%taylor冪級數展開(zhn ki)：Taylor series expansion：taylor(f,n,a) taylor(sin(x),3,1) ans = sin(1) - (sin(1)*(x - 1)2)/2 + cos(1)*(x - 1) vpa(ans) ans = 0.54030230586813971740093660744298*x - 0.42073549240394825332625116081515*(x - 1.0)2 + 0.30116867893975678925156571418732

49、操作題 53 非線性方程(fngchng)、求偏導 syms u v x y;u,v=solve(x*u+y*v=0,y*u+x*v=1,u,v) u = -y/(x2 - y2) v = x/(x2 - y2) diff(u,x) ans = (2*x*y)/(x2 - y2)2 diff(ans,y) ans = (2*x)/(x2 - y2)2 + (8*x*y2)/(x2 - y2)3操作題 54 微分方程(wi fn fn chn)%符號(fho)法 dsolve dsolve(D2y=cos(2*x)-y,y(0)=1,Dy(0)=0,x) ans = (5*cos(x)/3 +

50、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) vpa(ans) ans = 1.6666666666666666666666666666667*cos(x) + sin(x)*(0.16666666666666666666666666666667*sin(3.0*x) + 0.5*sin(x) - (0.66666666666666666666666666666667*cos(x)*(6.0*tan(0.5*x)2 - 3.0*tan(0.5*x)4

51、 + 1.0)/(tan(0.5*x)2 + 1.0)3操作題 55 plotyy t=1:6t = 1 2 3 4 5 6 sr=2456 2032 1900 2450 2890 2280; ll=12.5 11.3 10.2 14.5 14.3 15.1; AX,H1,H2=plotyy(t,sr,t,ll)AX = 174.0037 190.0039H1 = 175.0079H2 = 191.0042 legend(銷售收入,邊際(binj)利潤率)操作題 56 圓錐螺線(lu xin)的繪制%office2013 抽風(chu fng)，把做的十多道題都搞沒了，怒罷工.不妨取v=2 a

52、=pi/6 w=3 syms t 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為t的取值范圍操作題 57 求函數的零點 f=inline(exp(x)-x-5)f = Inline function: f(x) = exp(x)-x-5 fzero(f,2) %初值點取在區間及區間附近都可以，據老師說最好取到區間內ans = 1.9368操作題 58 f=inline(1./(x-0.3).2+0.01)+1./(x-0.9).2+0

53、.04)-6)f = Inline function: f(x) = 1./(x-0.3).2+0.01)+1./(x-0.9).2+0.04)-6 fzero(f,1)ans =1.2995操作題 59.插值法求點 t=0:0.125:0.5; i=0 6.24 7.75 4.85 0; k=0:50; t1=0.01*k; i1=interp1(t,i,t1)i1 = Columns 1 through 10 0 0.4992 0.9984 1.4976 1.9968 2.4960 2.9952 3.4944 3.9936 4.4928 Columns 11 through 20 4.99

54、20 5.4912 5.9904 6.3004 6.4212 6.5420 6.6628 6.7836 6.9044 7.0252 Columns 21 through 30 7.1460 7.2668 7.3876 7.5084 7.6292 7.7500 7.5180 7.2860 7.0540 6.8220 Columns 31 through 40 6.5900 6.3580 6.1260 5.8940 5.6620 5.4300 5.1980 4.9660 4.6560 4.2680 Columns 41 through 50 3.8800 3.4920 3.1040 2.7160

55、2.3280 1.9400 1.5520 1.1640 0.7760 0.3880 Column 51 0操作題 60. 三次(sn c)hermite插值 x=-1:0.5:1; y=1./(1+25.*x.2); x1=-1:0.1:1; pchip(x,y,x1)ans = Columns 1 through 10 0.0385 0.0431 0.0564 0.0772 0.1048 0.1379 0.2504 0.4671 0.7137 0.9161 Columns 11 through 20 1.0000 0.9161 0.7137 0.4671 0.2504 0.1379 0.10

56、48 0.0772 0.0564 0.0431 Column 210.0385%此題用interp1(x,y,xi,p)亦可操作題 61. x=-1:0.5:1; %初值取步長多少不影響(yngxing)差值結果 y=1./(1+25.*x.2); x1=-1:0.1:1; spline(x,y,x1) %或者(huzh)interp1(x,y,x1,spline)ans = Columns 1 through 10 0.0385 -0.1817 -0.2520 -0.2023 -0.0623 0.1379 0.3687 0.6001 0.8024 0.9456 Columns 11 thro

57、ugh 20 1.0000 0.9456 0.8024 0.6001 0.3687 0.1379 -0.0623 -0.2023 -0.2520 -0.1817 Column 210.0385操作題 62. 線性插值 t=0 20 40 56 68 80 84 96 104 110; v=1 20 20 38 80 80 100 100 125 125; t1=0:5:110; interp1(t,v,t1)ans = Columns 1 through 10 1.0000 5.7500 10.5000 15.2500 20.0000 20.0000 20.0000 20.0000 20.00

58、00 25.6250 Columns 11 through 20 31.2500 36.8750 52.0000 69.5000 80.0000 80.0000 80.0000 100.0000 100.0000 100.0000 Columns 21 through 23 112.5000 125.0000 125.0000plot(t,v,+,t1,ans,o)操作題63. 插值SUMMARY x=0:0.5:5; x1=0:0.1:5; y=x.2; interp1(x,y,x1); %線性插值 interp1(x,y,x1,spline); %三次(sn c)樣條插值 interp1(

59、x,y,x1,cubic); %三次(sn c)插值 interp1(x,y,x1,pchip); %hermit插值操作題 64 線性插值求點 D=18:2:30; S=9.9617724 9.9543645 9.9468069 9.9390950 9.9312245 9.9231915 9.9149925; interp1(S,D,9.935799)ans = 24.837557969633686%此種方法(fngf)可求某點處的數值，還有種實現方法見help example 3操作題 65 m=1:12; t=80.9 67.2 67.1 50.5 32 33.6 36.6 46.8 5

60、2.3 62 64.1 71.2; mi=1:.2:12; ti=interp1(m,t,mi,p); plot(m,t,-ok,mi,ti,-r)%使用(shyng)hermite插值，得到(d do)其圖像可知該地在一年的五月份左右(zuyu)日照時間最短，到了十二月份到一月份，日照時間最長操作題 67 二維插值 x=1:4;y=1:4; h=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; xi=1:.1:4;yi=1:.1:4; hi=interp2(x,y,h,xi,yi,