chap3_2.bas

介绍一些matlab在数学方面的应用

Attribute VB_Name = "chap3_2"
Public Sub PutOnClipboard(str As Variant)
    Dim MyDataObj As New DataObject
    MyDataObj.SetText Format(str)
    MyDataObj.PutInClipboard
End Sub
Sub c1()
CR = Chr(13) + Chr(10)
PutOnClipboard ("h=0.05; x=0:h:pi;" + CR + "syms x1; y=sin(x1)/(x1^2+4*x1+3);" + CR + "yy1=diff(y); f1=subs(yy1,x1,x);" + CR + "yy2=diff(yy1); f2=subs(yy2,x1,x);" + CR + "yy3=diff(yy2); f3=subs(yy3,x1,x);" + CR + "yy4=diff(yy3); f4=subs(yy4,x1,x);")
End Sub
Sub c2()
CR = Chr(13) + Chr(10)
PutOnClipboard ("y=sin(x)./(x.^2+4*x+3);" + CR + "[y1,dx1]=diff_ctr(y,h,1); subplot(221),plot(x,f1,dx1,y1,':');" + CR + "[y2,dx2]=diff_ctr(y,h,2); subplot(222),plot(x,f2,dx2,y2,':')")
End Sub
Sub c200()
CR = Chr(13) + Chr(10)
PutOnClipboard ("[y3,dx3]=diff_ctr(y,h,3); subplot(223),plot(x,f3,dx3,y3,':');" + CR + "[y4,dx4]=diff_ctr(y,h,4); subplot(224),plot(x,f4,dx4,y4,':')")
End Sub
Sub c3()
PutOnClipboard ("norm((y4-f4(4:60))./f4(4:60))")
End Sub
Sub c4()
CR = Chr(13) + Chr(10)
PutOnClipboard ("[x,y]=meshgrid(-3:.2:3,-2:.2:2);" + CR + "z=(x.^2-2*x).*exp(-x.^2-y.^2-x.*y);" + CR + "[fx,fy]=gradient(z); fx=fx/0.2; fy=fy/0.2;" + CR + "contour(x,y,z,30); hold on; quiver(x,y,fx,fy)")
End Sub
Sub c5()
CR = Chr(13) + Chr(10)
PutOnClipboard ("zx=-exp(-x.^2-y.^2-x.*y).*(-2*x+2+2*x.^3+x.^2.*y-4*x.^2-2*x.*y);" + CR + "zy=-x.*(x-2).*(2*y+x).*exp(-x.^2-y.^2-x.*y);" + CR + "surf(x,y,abs(fx-zx));" + CR + " axis([-3 3 -2 2 0,0.08])" + CR + "figure; surf(x,y,abs(fy-zy)); axis([-3 3 -2 2 0,0.11])")
End Sub
Sub c6()
CR = Chr(13) + Chr(10)
PutOnClipboard ("[x,y]=meshgrid(-3:.1:3,-2:.1:2);" + CR + "z=(x.^2-2*x).*exp(-x.^2-y.^2-x.*y);" + CR + "[fx,fy]=gradient(z); fx=fx/0.1; fy=fy/0.1;")
End Sub
Sub c60()
CR = Chr(13) + Chr(10)
PutOnClipboard ("zx=-exp(-x.^2-y.^2-x.*y).*(-2*x+2+2*x.^3+x.^2.*y-4*x.^2-2*x.*y);" + CR + "zy=-x.*(x-2).*(2*y+x).*exp(-x.^2-y.^2-x.*y);" + CR + "surf(x,y,abs(fx-zx)); axis([-3 3 -2 2 0,0.02])" + CR + "figure; surf(x,y,abs(fy-zy)); axis([-3 3 -2 2 0,0.06])")
End Sub
Sub c7()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x1=[0:pi/30:pi]';" + CR + "y=[sin(x1) cos(x1) sin(x1/2)];" + CR + "x=[x1 x1 x1];" + CR + " S=sum((2*y(1:end-1,:)+diff(y)).*diff(x))/2")
End Sub
Sub c8()
PutOnClipboard ("S1=trapz(x1,y)")
End Sub
Sub c9()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x=[0:0.01:3*pi/2, 3*pi/2];" + CR + "y=cos(15*x);" + CR + " plot(x,y)")
End Sub
Sub c10()
PutOnClipboard ("syms x, A=int(cos(15*x),0,3*pi/2)")
End Sub
Sub c11()
CR = Chr(13) + Chr(10)
PutOnClipboard ("h0=[0.1,0.01,0.001,0.0001,0.00001,0.000001];" + CR + " v=[];" + CR + "for h=h0," + CR + "x=[0:h:3*pi/2, 3*pi/2];" + CR + " y=cos(15*x); I=trapz(x,y); " + CR + "v=[v; h,I,1/15-I];" + CR + "end")
End Sub
Sub c12()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f=inline('2/sqrt(pi)*exp(-x.^2)','x');" + CR + "y=quad(f,0,1.5)")
End Sub
Sub c13()
PutOnClipboard ("y=quad('c3ffun',0,1.5)")
End Sub
Sub c14()
PutOnClipboard ("syms x, y0=vpa(int(2/sqrt(pi)*exp(-x^2),0,1.5),60)")
End Sub
Sub c15()
PutOnClipboard ("y=quad(f,0,1.5,1e-20)")
End Sub
Sub c16()
PutOnClipboard ("y=quadl(f,0,1.5,1e-20)")
End Sub
Sub c17()
PutOnClipboard ("abs(y-y0)")
End Sub
Sub c18()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x=[0:0.01:2, 2+eps:0.01:4,4];" + CR + "y=exp(x.^2).*(x<=2)+80./(4-sin(16*pi*x)).*(x>2);" + CR + "y(end)=0; x=[eps, x]; y=[0,y]; fill(x,y,'g')")
End Sub
Sub c19()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f=inline('exp(x.^2).*(x<=2)+80*(x>2)./(4-sin(16*pi*x))','x');" + CR + "I1=quad(f,0,4)")
End Sub
Sub c20()
PutOnClipboard ("I2=quadl(f,0,4)")
End Sub
Sub c21()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x;" + CR + " I=vpa(int(exp(x^2),0,2)+int(80/(4-sin(16*pi*x)),2,4))")
End Sub
Sub c22()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f1=inline('exp(x.^2)','x');" + CR + " f2=inline('80./(4-sin(16*pi*x))','x');" + CR + "quad(f1,0,2)+quad(f2,2,4)")
End Sub
Sub c23()
PutOnClipboard ("quadl(f1,0,2)+quadl(f2,2,4)")
End Sub
Sub c24()
PutOnClipboard ("quadl(f1,0,2,1e-11)+quadl(f2,2,4,1e-11)")
End Sub
Sub c25()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f=inline('cos(15*x)','x');" + CR + "tic, S=quadl(f,0,3*pi/2,1e-15), toc")
End Sub
Sub c26()
PutOnClipboard ("S1=quad(f,0,3*pi/2)")
End Sub
Sub c27()
PutOnClipboard ("S1=quad(f,0,3*pi/2,1e-15)")
End Sub
Sub c28()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f=inline('exp(-x.^2/2).*sin(x.^2+y)','x','y');" + CR + "y=dblquad(f,-2,2,-1,1)")
End Sub
Sub c29()
CR = Chr(13) + Chr(10)
PutOnClipboard ("fh=inline('sqrt(1-x.^2/2)','x');" + CR + "fl=inline('-sqrt(1-x.^2/2)','x');" + CR + "f=inline('exp(-x.^2/2).*sin(x.^2+y)','y','x');" + CR + "y=quad2dggen(f,fl,fh,-1/2,1,eps),")
End Sub
Sub c30()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y " + CR + "i1=int(exp(-x^2/2)*sin(x^2+y),y,-sqrt(1-x^2/2),sqrt(1-x^2/2));" + CR + "int(i1,x,-1/2,1)" + CR + "vpa(ans)")
End Sub
Sub c31()
PutOnClipboard ("vpa(ans,70)")
End Sub
Sub c32()
CR = Chr(13) + Chr(10)
PutOnClipboard ("fh=inline('sqrt(1-y.^2)','y');" + CR + "fl=inline('-sqrt(1-y.^2)','y');" + CR + "f=inline('exp(-x.^2/2).*sin(x.^2+y)','x','y');" + CR + "I=quad2dggen(f,fl,fh,-1,1,eps),")
End Sub
Sub c33()
CR = Chr(13) + Chr(10)
PutOnClipboard ("triplequad(inline('4*x.*z.*exp(-x.*x.*y-z.*z)','x','y','z')," + CR + "0, 2, 0, pi, 0, pi,1e-7,@quadl)")
End Sub
Sub c34()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t; syms a positive" + CR + "x=a*cos(t); y=a*sin(t); z=a*t;" + CR + "I=int(z^2/(x^2+y^2)*sqrt(diff(x,t)^2+diff(y,t)^2+diff(z,t)^2),t,0,2*pi)")
End Sub
Sub c35()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x=0:.001:1.2;" + CR + " y1=x; y2=x.^2; plot(x,y1,x,y2)")
End Sub
Sub c36()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; y1=x; y2=x^2;" + CR + "I1=int((x^2+y2^2)*sqrt(1+diff(y2,x)^2),x,0,1);" + CR + "I2=int((x^2+y1^2)*sqrt(1+diff(y1,x)^2),x,1,0);" + CR + " I=I1+I2")
End Sub
Sub c37()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t; syms a positive;" + CR + "x=a*cos(t); y=a*sin(t);" + CR + "F=[(x+y)/(x^2+y^2),-(x-y)/(x^2+y^2)]; " + CR + "ds=[diff(x,t);diff(y,t)];" + CR + "I=int(F*ds,t,2*pi,0)")
End Sub
Sub c38()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; y=x^2;" + CR + "F=[x^2-2*x*y,x^2-2*x*y];" + CR + " ds=[1; diff(y,x)];" + CR + "I=int(F*ds,x,-1,1)")
End Sub
Sub c39()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y; syms a positive;" + CR + " z=a-x-y;" + CR + "I=int(int(x*y*z*sqrt(1+diff(z,x)^2+diff(z,y)^2),y,0,a-x),x,0,a)")
End Sub
Sub c40()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms u v; syms a positive;" + CR + "x=u*cos(v); y=u*sin(v); z=v; f=x^2*y+z*y^2;")
End Sub
Sub c401()
CR = Chr(13) + Chr(10)
PutOnClipboard ("E=simple(diff(x,u)^2+diff(y,u)^2+diff(z,u)^2);" + CR + "F=diff(x,u)*diff(x,v)+diff(y,u)*diff(y,v)+diff(z,u)*diff(z,v);" + CR + "G=simple(diff(x,v)^2+diff(y,v)^2+diff(z,v)^2);" + CR + "I=int(int(f*sqrt(E*G-F^2),u,0,a),v,0,2*pi)")
End Sub
Sub c41()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms u v; syms a b c positive;" + CR + "x=a*sin(u)*cos(v); y=b*sin(u)*sin(v); z=c*cos(u);" + CR + "A=diff(y,u)*diff(z,v)-diff(z,u)*diff(y,v);" + CR + "I=int(int(x^3*A,u,0,pi/2),v,0,2*pi)")
End Sub
Sub c42()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t; y=sin(t)/(t+1)^3; x=cos(t)/(t+1)^3;" + CR + "latex(diff(y,t,4)/diff(x,t,4))")
End Sub