chap3_1.bas

介绍一些matlab在数学方面的应用

Attribute VB_Name = "chap3_1"
Public Sub PutOnClipboard(str As Variant)
    Dim MyDataObj As New DataObject
    MyDataObj.SetText Format(str)
    MyDataObj.PutInClipboard
End Sub
Sub limit1()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x a b;" + CR + " f=x*(1+a/x)^x*sin(b/x);" + CR + " L=limit(f,x,inf)")

End Sub
Sub limit2()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x;" + CR + " limit((exp(x^3)-1)/(1-cos(sqrt(x-sin(x)))),x,0,'right')")

End Sub
Sub limit3()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x=-0.1:0.001:0.1;" + CR + " y=(exp(x.^3)-1)./(1-cos(sqrt(x-sin(x))));" + CR + "plot(x,y,'-',[0],[12],'o')")

End Sub
Sub limit4()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y a;" + CR + " f=exp(-1/(y^2+x^2))*sin(x)^2/x^2*(1+1/y^2)^(x+a^2*y^2);" + CR + "L=limit(limit(f,x,1/sqrt(y)),y,inf)")

End Sub
Sub limit5()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; f=sin(x)/(x^2+4*x+3);" + CR + " f1=diff(f); pretty(f1)")

End Sub
Sub limit50()
CR = Chr(13) + Chr(10)
PutOnClipboard ("x1=0:.01:5;" + CR + "y=subs(f,x,x1); y1=subs(f1,x,x1);" + CR + "plot(x1,y,x1,y1,':')")

End Sub
Sub limit6()
PutOnClipboard ("f4=diff(f,x,4); latex(f4)")

End Sub
Sub limit7()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y;" + CR + "z=(x^2-2*x)*exp(-x^2-y^2-x*y);" + CR + "zx=simple(diff(z,x))")
    
End Sub
Sub limit8()
PutOnClipboard ("zy=diff(z,y)")
    
End Sub
Sub limit9()
PutOnClipboard ("[x,y]=meshgrid(-3:.2:3,-2:.2:2);z=(x.^2-2*x).*exp(-x.^2-y.^2-x.*y);surf(x,y,z), axis([-3 3 -2 2 -0.7 1.5])")
    
End Sub

Sub limit10()
CR = Chr(13) + Chr(10)
PutOnClipboard ("contour(x,y,z,30), hold on" + CR + "zx=-exp(-x.^2-y.^2-x.*y).*(-2*x+2+2*x.^3+x.^2.*y-4*x.^2-2*x.*y);zy=-x.*(x-2).*(2*y+x).*exp(-x.^2-y.^2-x.*y);quiver(x,y,zx,zy)")
    
End Sub
Sub limit11()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y z; f=sin(x^2*y)*exp(-x^2*y-z^2);" + CR + "df=diff(diff(diff(f,x,2),y),z); df=simple(df); latex(df)")
    
End Sub
Sub limit12()
PutOnClipboard ("syms r theta phi; x=r*sin(theta)*cos(phi);y=r*sin(theta)*sin(phi); z=r*cos(theta);J=jacobian([x; y; z],[r theta phi])")
    
End Sub
Sub limit13()
PutOnClipboard ("syms x y; f=(x^2-2*x)*exp(-x^2-y^2-x*y);pretty(-simple(diff(f,x)/diff(f,y)))")
    
End Sub
Sub limit14()
PutOnClipboard ("syms x; y=sin(x)/(x^2+4*x+3); y1=diff(y);y0=int(y1); latex(y0)")
    
End Sub

Sub limit15()
PutOnClipboard ("y4=diff(y,4); y0=int(int(int(int(y4))));latex(simple(y0))")
    
End Sub
Sub limit16()
PutOnClipboard ("syms a x; f=simple(int(x^3*cos(a*x)^2,x))")
    
End Sub
Sub limit160()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f1=x^4/8+(x^3/(4*a)-3*x/(8*a^3))*sin(2*a*x)+(3*x^2/(8*a^2)-3/(16*a^4))*cos(2*a*x);" + CR + "simple(f-f1)")
    
End Sub
Sub limit17()
PutOnClipboard ("syms x; int(exp(-x^2/2))")
    
End Sub
Sub limit18()
PutOnClipboard ("syms a x; int(x*sin(a*x^4)*exp(x^2/2))")
    
End Sub
Sub limit19()
PutOnClipboard ("syms x; I1=int(exp(-x^2/2),x,0,1.5)")
    
End Sub
Sub limit20()
PutOnClipboard ("vpa(I1,70)")
End Sub
Sub limit21()
PutOnClipboard ("I2=int(exp(-x^2/2),x,0,inf)")
End Sub
Sub limit22()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x t; f=(-2*x^2+1)/(2*x^2-3*x+1)^2;" + CR + "I=simple(int(f,x,cos(t),exp(-2*t))), latex(I)")
End Sub
Sub limit23()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y z; f0=-4*z*exp(-x^2*y-z^2)*(cos(x^2*y)-10*cos(x^2*y)*y*x^2+4*sin(x^2*y)*x^4*y^2+4*cos(x^2*y)*x^4*y^2-sin(x^2*y));" + CR + "f1=int(f0,z); f1=int(f1,y); f1=int(f1,x); f1=simple(int(f1,x))")
End Sub
Sub limit24()
PutOnClipboard ("f2=int(f0,z); f2=int(f2,x); f2=int(f2,x); f2=simple(int(f2,y))")
End Sub
Sub limit25()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y z;" + CR + "int(int(int(4*x*z*exp(-x^2*y-z^2),x,0,2),y,0,pi),z,0,pi)")
End Sub
Sub limit26()
PutOnClipboard ("vpa(ans,60)")
End Sub
Sub limit27()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x;" + CR + "f=sin(x)/(x^2+4*x+3);" + CR + "y1=taylor(f,x,9); latex(y1)")
End Sub
Sub limit28()
PutOnClipboard ("taylor(y,x,9,2)")
End Sub
Sub limit29()
PutOnClipboard ("syms a; taylor(y,x,5,a)")
End Sub
Sub limit30()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x y;" + CR + " f=(x^2-2*x)*exp(-x^2-y^2-x*y);" + CR + "F=maple('mtaylor',f,'[x,y]',8)" + CR + "latex(collect(F,x))")
End Sub
Sub limit31()
PutOnClipboard ("syms a; F=maple('mtaylor',f,'[x=1,y=a]',3);")
End Sub
Sub limit32()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; f=x*(x-pi)*(x-2*pi);" + CR + "[A,B,F]=fseries(f,x,12,0,2*pi); latex(F)")
End Sub
Sub limit33()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; f=abs(x)/x;" + CR + "xx=[-pi:pi/200:pi]; xx=xx(xx~=0);" + CR + " xx=sort([xx,-eps,eps]);yy=subs(f,x,xx);" + CR + " plot(xx,yy), hold on " + CR + "for n=1:20" + CR + "[a,b,f1]=fseries(f,x,n); y1=subs(f1,x,xx); plot(xx,y1)" + CR + "end")
End Sub
Sub limit34()
PutOnClipboard ("[a,b,f1]=fseries(f,x,14); latex(f1)")
End Sub
Sub limit35()
PutOnClipboard ("format long; sum(2.^[0:63])")
End Sub
Sub limit36()
PutOnClipboard ("sum(sym(2).^[0:200])")
End Sub
Sub limit37()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms n;" + CR + " s=symsum(1/((3*n-2)*(3*n+1)),n,1,inf)")
End Sub
Sub limit38()
CR = Chr(13) + Chr(10)
PutOnClipboard ("m=1:10000000;" + CR + "s1=sum(1./((3*m-2).*(3*m+1)));" + CR + "format long;")
End Sub
Sub limit39()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms n x;" + CR + "s1=symsum(2/((2*n+1)*(2*x+1)^(2*n+1)),n,0,inf);" + CR + "simple(s1)")
End Sub
Sub limit40()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms m n;" + CR + " limit(symsum(1/m,m,1,n)-log(n),n,inf)")
End Sub
Sub limit41()
PutOnClipboard ("vpa(ans, 70)")
End Sub