數(shù)學(xué)實(shí)驗(yàn)作業(yè)

1、實(shí)驗(yàn)1 matlab矩陣命令的用法1生成 5 階的單位陣>> a=eye(5)2生產(chǎn)列向量 x=1, 3, 5, 7, 9, , 29>> a=1:2:29;x=a'3生成由 A 與 B 點(diǎn)乘得到的矩陣 DD=A*B4生成一個(gè)由 D 的第 8、4、10、13 行和第 7、1、6、9、2 列組成的子矩陣 EE=D(8 4 10 13,7 1 6 9 2)5求出矩陣 E 的最大元素A=max(max(E)畫圖練習(xí)1 作出函數(shù)和的圖形觀察其周期性和變化趨勢(shì)>> x=-2:0.05:2*pi;y1=tan(x);y2=cot(x);plot(x,y1,

2、9;r',x,y2,'b')2在區(qū)間畫出函數(shù)的圖形. >> x=-1:0.001:1;y=sin(1./x);plot(x,y)3畫出參數(shù)方程的圖形：>> t=linspace(0,2*pi,100);x=cos(t).*cos(5*t);y=sin(t).*cos(3*t);plot(x,y) 4 作出符號(hào)函數(shù)的圖形.>> x=linspace(-100,100,10000);y=sign(x);plot(x,y);axis(-100 100 -2 2)5作出函數(shù)的圖形.>> x=linspace(-5,5,500);x

3、,y=meshgrid(x);z=4./(1+x.2+y.2);mesh(x,y,z)6作出函數(shù)的圖形.>> x=-1:0.01:1;x,y=meshgrid(x);z=cos(4*x.2+9*y.2);mesh(x,y,z) 7作出單葉雙曲面的圖形.(曲面的參數(shù)方程為 () >> v=0:pi/100:2*pi;>> v=0:pi/100:2*pi;u=-pi/2:pi/100:pi/2;U,V=meshgrid(u,v);x=sec(U).*sin(V);y=2*sec(U).*cos(V);z=3*tan(U);surf(x,y,z) 8可以證明: 函

4、數(shù)的圖形是雙曲拋物面. 在區(qū)域上作出它的圖形.>> x=-2:0.01:2;x,y=meshgrid(x);z=x.*y;mesh(x,y,z)9畫出參數(shù)曲面 的圖形.>> v=0.001:0.001:2;u=0:pi/100:4*pi;U,V=meshgrid(u,v);x=cos(U).*sin(V);y=sin(U).*sin(V);z=cos(V)+log(tan(V/2)+U/5);mesh(x,y,z)10 作出空間曲線的圖形.>> syms t;ezplot3(t*cos(t),t*sin(t),2*t,0,6*pi)11繪制參數(shù)曲線 的圖形.

5、>> t=-2*pi:pi/100:2*pi;x=cos(t).*cos(t);y=1./(1+2*t);z=atan(t);plot3(x,y,z);grid;xlabel('x'),ylabel('y'),zlabel('z')12 一幅圖上同時(shí)畫上半球面 x2 + y2 + z2 = 4與柱面 (x1)2 +y2 =1(0z2);>> x,y,z=sphere(100);surf(2*x,2*y,2*abs(z);axis equal ;hold on ;X,Y,Z = cylinder(1,100);surf(X+

6、1,Y,2*Z) axis equal極限1分別畫出坐標(biāo)為的散點(diǎn)圖, 并畫出折線圖.散點(diǎn)圖：>> i=1:10;plot(i,i.2,'.')>> i=1:10;plot(i.2,4*(i.2)+i.3,'.')折線圖：>> i=1:10;plot(i,i.2,'-x')>> i=1:10;plot(i.2,4*(i.2)+i.3,'-x')2通過(guò)動(dòng)畫觀察當(dāng)時(shí)數(shù)列的變化趨勢(shì).>> n=1:100;an=(n.2);n=1:100;an=1./(n.2);n=1:

7、100;an=1./(n.2);for i=1:100;plot(n(1:i),an(1:i),axis(0,100,0,1);pause(0.1);end3在區(qū)間上作出函數(shù)的圖形, 并研究 和 >> x=-4:0.01:4;y=(x.3-9*x)./(x.3-x+eps);plot(x,y)從圖上看，在x1與x時(shí)極限為0.4計(jì)算極限 .(5) (1) >> syms x;limit(x*sin(1/x)+(1/x)*sin(x),x,inf)ans =1 (2) >> syms x;limit(x2/exp(x),inf) ans = 0(3) >&

8、gt; syms x;limit(tan(x)-sin(x)/x3,x,0)ans =1/2 (4) >> syms x; limit(xx,x,0,'right') ans =1 (5) >> syms x y;f=(log10(x+exp(y)/(x2+y2)(1/2);limit(limit(f,x,1),y,0) ans =log(2)/log(10)實(shí)驗(yàn)2.導(dǎo)數(shù)1. 作函數(shù)的圖形和在處的切線.>> syms x;y=2*x3+3*x2-12*x+7;diff(y)x=-1;f1=6*x2 + 6*x - 12x=-1; f2=2*x

9、3+3*x2-12*x+7x=linspace(-10,10,1000);y1=2*x.3+3*x.2-12*x+7;y2=-12*(x+1)+20;plot(x,y1,'r',x,y2,'g')ans =6*x2 + 6*x 12f1 =-12f2 =202. 求函數(shù)的一階導(dǎo)數(shù). 并求>> syms a b x y;y= sin(a*x)*cos(b*x);D1=diff(y,x,1)x=1/(a+b);cos(a*x)*a*cos(b*x)-sin(a*x)*sin(b*x)*bD1 = a*cos(a*x)*cos(b*x) - b*sin(a

10、*x)*sin(b*x)ans = a*cos(a/(a + b)*cos(b/(a + b) - b*sin(a/(a + b)*sin(b/(a + b) 3.求下列函數(shù)的導(dǎo)數(shù): (1) ; (2) ;(3) ; (4) (1)>> syms x y;y=exp(x+1)(1/3);D1=diff(y,1) D1 =exp(x + 1)(1/3)/(3*(x + 1)(2/3)(2)>> syms x;y=log(tan(x/2+pi/4);D1=diff(y,1)D1 =(tan(pi/4 + x/2)2/2 + 1/2)/tan(pi/4 + x/2)(3) &

11、gt;> syms x;y=1/2*(cot(x)2+log10(sin(x);D1=diff(y,1) D1 =cos(x)/(log(10)*sin(x) - cot(x)*(cot(x)2 + 1) (4) >> syms x;y=(1/sqrt(2)*atan(sqrt(2)/x);D1=diff(y,1) D1 =-1/(x2*(2/x2 + 1)4. 設(shè)求>> syms x y;z=sin(x*y)+(cos(x*y)2;D1=diff(z,'x',1);D2=diff(z,'y',1);D3=diff(z,'x

12、',2);D4=diff(z,'y',2); D1,D2,D3,D4D1 =y*cos(x*y) - 2*y*cos(x*y)*sin(x*y)D2 = x*cos(x*y) - 2*x*cos(x*y)*sin(x*y)D3 =- 2*y2*cos(x*y)2 + 2*y2*sin(x*y)2 - y2*sin(x*y)D4 =- 2*x2*cos(x*y)2 + 2*x2*sin(x*y)2 - x2*sin(x*y)>> syms x y;z=(1+x*y)y;D1=diff(z,'x',1);D2=diff(z,'y'

13、,1);D1,D2x=1;y=1;D1=y2*(x*y + 1)(y - 1);D2 =log(x*y + 1)*(x*y + 1)y + x*y*(x*y + 1)(y - 1)D1,D2D1=y2*(x*y + 1)(y - 1)D2 =log(x*y + 1)*(x*y + 1)y + x*y*(x*y + 1)(y - 1)D1 =1D2 =2.3863一元函數(shù)積分學(xué)1. 求>> syms x y;y=x2*(1-x3)5;R=int(y,x)R = - x18/18 + x15/3 - (5*x12)/6 + (10*x9)/9 - (5*x6)/6 +x3/32.求&g

14、t;> syms x y;y=x2*atan(x);R=int(y,x) R = log(x2 + 1)/6 + (x3*atan(x)/3 - x2/63. 求>> syms x y;y=x-x2;R=int(y,x,0,1) R = 1/64 . 求變上限函數(shù)的導(dǎo)函數(shù).>> syms x y t;y=t*sin(t2);R=int(y,x,0,x)DR=diff(R,x,1)R =t*x*sin(t2)DR = t*sin(t2)多元函數(shù)積分學(xué)1. 計(jì)算 其中為由 所圍成的有界區(qū)域. >> syms x y;int(int(x*y2,x,2-y,s

15、qrt(y),y,1,2) ans = 193/120微分方程 1.求微分方程 的通解.>> y=dsolve('Dy+2*x*y=x*exp(-x2)','x')y = C2*exp(-x2) + (x2*exp(-x2)/ 2.求微分方程的通解.>> y=dsolve('D2y-2*Dy+5*y=exp(x)*cos(2*x)','x') y=(3*cos(2*x)*exp(x)/32+(cos(6*x)*exp(x)/32+sin(2*x)*exp(x)*(x/4 + sin(4*x)/16) + C

16、4*cos(2*x)*exp(x) + C5*sin(2*x)*exp(x)3.求微分方程組在初始條件下的特解.>> x,y=dsolve('Dx+x+2*y-exp(t)','Dy-x-y','x(0)=1','y(0)=0','t')x =cos(t)y =exp(t)/2 - cos(t)/2 + sin(t)/24.求解微分方程并作出積分曲線. >> syms x yy=dsolve('Dy-2*y/(x+1)-(x+1)(5/2)','x') y =(2*(x + 1)(7/2)/3 + C9*(x + 1)2>> syms x yx=linspace(-5,5,100);C=input('請(qǐng)輸入C的值:');y=(