数学实验课后习题解答王汝军编写实验一 曲线绘图【练习与思考】画出下列常见曲线的图形。以直角坐标方程表示的曲线：1 .立方曲线 y = X3clear;x=-2:0.1:2;y=x∙^3;plot(x,y)2.立方抛物线，=3χclear;y=-2:0.1:2;χ=y.^3;plot(x,y)grid on3 .高斯曲线 y = e T2clear;x=-3:0.1:3;y=exp(-x,^2);plot(x,y);grid on %axis equal以参数方程表示的曲线24. 奈尔抛物线 x=t3,y=t2 (y=x3)clear;t=-3:0.05:3;x=t.^3;y=t.^2;plot(x,y)axis equalgrid on5 . 半立方抛物线 x=t2,y=t3(y2=x3) clear;t=-3:0.05:3;x=t.^2;y=t.^3; plot(x,y) %axis equal grid on6 .迪卡尔曲线 X = H, y =把(X 3 + y 3 - 3 Oxy = 0)1 + 121 + 12clear;a=3;t=-6:0.1:6;x=3*a*t./(1+t.^2);y=3*a*t∙^2∙Z(1+t^2);plot(x,y)7 .蔓叶线 X =旦,y = 士 (y2 =旦) 1 + 21 + 2 a - Xclear;a=3;t=-6:0.1:6;x=3*a*t.^2.Z(1+t.^2);y=3*a*t.^3.Z(1+t.^2); plot(x,y)8 .摆线 X = a(t - sin t), y = b(1 - cost) clear;clc;a=1;b=1;t=0:pi/50:6*pi;x=a*(t-sin(t));y=b*(1-cos(t));plot(x,y);axis equalgrid on9 . 内摆线(星形线)clear;a=1;t=0:pi/50:2*pi;x=a*cos(t).^3;y=a*sin(t).^3;plot(x,y)222X = acos31, y = asin31 (X3 + y 3 = a3)10 .圆的渐伸线(渐开线)X = a(CoSt +1Sint),y = a(Sint clear;a=1;t=0:pi/50:6*pi;x=a*(cos(t)+t.*sin(t));y=a*(sin(t)+t.*cos(t));plot(x,y)grid on11 . 空间螺线 x =a cos t, y = b sin t, Z = Ctcleara=3;b=2;c=1;t=0:pi/50:6*pi;x=a*cos(t);y=b*sin(t);z=c*t;plot3(x,y,z)grid ontcost)以极坐标方程表示的曲线：12 .阿基米德线 r = aφ,r ≥ 0 clear;a=1;phy=0:pi/50:6*pi;rho=a*phy;polar(phy,rho,'r-*')13 .对数螺线 r = eaφclear;a=0.1;phy=0:pi/50:6*pi;rho=exp(a*phy);polar(phy,rho)14 .双纽线 r2 = a2 cos2φ ((X2 + y2)2 = a2(X2 - y2)) clear;a=1;phy=-pi/4:pi/50:pi/4;rho=a*sqrt(cos(2*phy));polar(phy,rho)hold onpolar(phy,-rho)15 .双纽线 r2 = a2 sin 2φ ((X2 + y2)2 = 2a2χy) clear;a=1;phy=0:pi/50:pi/2;rho=a*sqrt(sin(2*phy));polar(phy,rho)hold onpolar(phy,-rho)16 .四叶玫瑰线 r = asin2φ,r ≥ 0clear;closea=1;phy=0:pi/50:2*pi;rho=a*sin(2*phy);polar(phy,r...
