chap5.bas

介绍一些matlab在数学方面的应用

Attribute VB_Name = "chap5"
Public Sub PutOnClipboard(str As Variant)
    Dim MyDataObj As New DataObject
    MyDataObj.SetText Format(str)
    MyDataObj.PutInClipboard
End Sub
Sub e1()
PutOnClipboard ("syms t; f=t^2*exp(-2*t)*sin(t+pi); laplace(f)")
End Sub
Sub e2()
PutOnClipboard ("pretty(ans)")
End Sub
Sub e3()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x w; f=x^2*exp(-2*x)*sin(x+pi);" + CR + "F=laplace(f,x,w)")
End Sub
Sub e4()
PutOnClipboard ("ilaplace(F)")
End Sub
Sub e5()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x t;" + CR + "G=(-17*x^5-7*x^4+2*x^3+x^2-x+1)/(x^6+11*x^5+48*x^4+106*x^3+125*x^2+75*x+17);" + CR + "f=ilaplace(G,x,t)")
End Sub
Sub e6()
PutOnClipboard ("vpa(f,16)")
End Sub
Sub e7()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t s; " + CR + "f=t^2*exp(-2*t)*sin(t+pi);" + CR + "F=simple(laplace(diff(f,t,5)))")
End Sub
Sub e8()
PutOnClipboard ("F0=laplace(f); simple(F-s^5*F0)")
End Sub
Sub e9()
CR = Chr(13) + Chr(10)
PutOnClipboard ("ss=0; f1=f;" + CR + "for i=4:-1:0" + CR + "ss=ss-s^i*subs(f1,t,0); f1=diff(f1,t);" + CR + "end")
End Sub
Sub e10()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t; y=sym('f(t)')" + CR + "laplace(diff(y,t,2))")
End Sub
Sub e11()
PutOnClipboard ("laplace(diff(y,t,8))")
End Sub
Sub e12()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t; f=exp(-5*t)*cos(2*t+1)+5;" + CR + "F=laplace(diff(f,t,5));" + CR + " F=simple(F); latex(F)")
End Sub
Sub e13()
PutOnClipboard ("syms s; collect(F); latex(ans)")
End Sub
Sub e14()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a potitive" + CR + "f=1/(t^2+a^2); F=fourier(f,t,w)")
End Sub
Sub e15()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "f=pi*exp(-a*abs(w))/a; ifourier(f)")
End Sub
Sub e16()
PutOnClipboard ("ifourier(F)")
End Sub
Sub e17()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "f=sin(a*t)^2/t; fourier(f,t,w)")
End Sub
Sub e18()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms w t; syms a positive" + CR + "f=exp(-a*abs(t))/sqrt(abs(t)); " + CR + "F=fourier(f,t,w)")
End Sub
Sub e19()
CR = Chr(13) + Chr(10)
PutOnClipboard ("f1=exp(a*t)/sqrt(-t); f2=exp(-a*t)/sqrt(t);" + CR + " j=sym(sqrt(-1));" + CR + "F=int(f1*exp(-j*w*t),-inf,0)+int(f2*exp(-j*w*t),0,inf)")
End Sub
Sub e20()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "for i=1:8" + CR + "f=t^i*exp(-a*t); F=int(f*cos(w*t),t,0,inf); latex(simple(F))" + CR + "end")
End Sub
Sub e21()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "f=t^6*exp(-a*t);" + CR + " F=maple('fouriercos',f,t,w); latex(F)")
End Sub
Sub e22()
PutOnClipboard ("f1=maple('invfouriercos',F,w,t)")
End Sub
Sub e23()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "f=cos(t); F=simple(int(f*cos(w*t),t,0,a));" + CR + " latex(F)")
End Sub
Sub e24()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t k; syms a positive" + CR + "f1=t; f2=a-t;" + CR + "Fs=int(f1*sin(k*pi*t/a),t,0,a/2)+int(f2*sin(k*pi*t/a),t,a/2,a);" + CR + "simple(Fs)")
End Sub
Sub e25()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t z; syms z positive;" + CR + "f=log(t)/(t+a);" + CR + " M=simple(int(f*t^(z-1),t,0,inf)), latex(M)")
End Sub
Sub e26()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t z; syms a positive" + CR + "for i=1:8" + CR + "f=1/(t+a)^i; disp(int(f*t^(z-1),t,0,inf))" + CR + "end")
End Sub
Sub e27()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t z; syms a positive" + CR + "F=maple('mellin',1/(t+a)^8,t,z)")
End Sub
Sub e28()
PutOnClipboard ("f1=maple('invmellin',F,z,t)")
End Sub
Sub e29()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms t w; syms a positive" + CR + "f=t^a; F=maple('hankel',f,t,w,0)")
End Sub
Sub e30()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms a T k" + CR + "f=a*k*T-2+(a*k*T+2)*exp(-a*k*T); " + CR + "F=ztrans(f); latex(F)")
End Sub
Sub e31()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms p q z" + CR + "for i=1:8" + CR + "disp (simple(iztrans(q / (1 / z - p) ^ i)))" + CR + "end")
End Sub
Sub e32()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms z" + CR + "f = sin(z + pi / 3) * exp(-2 * z) / (z ^ 3 * (z - 1))" + CR + "limit(diff(f*z^3,z,2)/prod(1:2),z,0)")
End Sub
Sub e33()
PutOnClipboard ("limit(f*(z-1),z,1)")
End Sub
Sub e34()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms z; f=(sin(z)-z)/z^6;" + CR + "limit(diff(f*z^2,z,1)/prod(1:1),z,0)")
End Sub
Sub e35()
PutOnClipboard ("limit(diff(f*z^3,z,2)/prod(1:2),z,0)")
End Sub
Sub e36()
PutOnClipboard ("limit(diff(f*z^20,z,19)/prod(1:19),z,0)")
End Sub
Sub e37()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms z; f=(sin(z)-z)/z^6;" + CR + "limit(diff(f*z^6,z,5)/prod(1:5),z,0)")
End Sub
Sub e38()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms z; f=1/(z*sin(z));" + CR + "c0=limit(f*z^2,z,0)")
End Sub
Sub e39()
CR = Chr(13) + Chr(10)
PutOnClipboard ("k=[-4 4 -3 3 -2 2 -1 1]; c=[];" + CR + "for kk=k; c=[c,limit(f*(z-kk*pi),z,kk*pi)]; end; c")
End Sub
Sub e40()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; A=x^4+7*x^3+13*x^2+19*x+20;" + CR + "B=x^7+16*x^6+103*x^5+346*x^4+655*x^3+700*x^2+393*x+90;" + CR + "d=gcd(A,B)")
End Sub
Sub e41()
PutOnClipboard ("simple(A/d)")
End Sub
Sub e42()
PutOnClipboard ("simple(B/d)")
End Sub
Sub e43()
CR = Chr(13) + Chr(10)
PutOnClipboard ("n=[1,2,3,4]; d=[1,11,48,106,125,75,18];" + CR + " format long" + CR + "[r,p,k]=residue(n,d); [n,d1]=rat(r); " + CR + "[n,d1,p]")
End Sub
Sub e44()
CR = Chr(13) + Chr(10)
PutOnClipboard ("n=[2,0,0,0,2,0,0,8];" + CR + "d=[1,30,386,2772,12093,32598,52520,45600,16000];" + CR + "[r,p]=residue(n,d)")
End Sub
Sub e45()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms s;" + CR + "G=(s^3+2*s^2+3*s+4)/(s^6+11*s^5+48*s^4+106*s^3+125*s^2+75*s+18);" + CR + "G1=residue1(G,s)")
End Sub
Sub e46()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms s" + CR + "G=(2*s^7+2*s^3+8)/(s^8+30*s^7+386*s^6+2772*s^5+12093*s^4+32598*s^3+52520*s^2+45600*s+16000);" + CR + "f=residue1(G); latex(f)")
End Sub
Sub e47()
PutOnClipboard ("simple(f-G)")
End Sub
Sub e48()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x; A=x^4+7*x^3+13*x^2+19*x+20;" + CR + "B=x^7+16*x^6+103*x^5+346*x^4+655*x^3+700*x^2+393*x+90;" + CR + "n=sym2poly(A); d=sym2poly(B);" + CR + "[r,p,k]=residue(n,d); [n1,d1]=rat(r); [n1,d1,p]")
End Sub
Sub e49()
PutOnClipboard ("r(1)")
End Sub
Sub e50()
PutOnClipboard ("residue1(A/B,x)")
End Sub
Sub e51()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms x;" + CR + " G=(-17*x^5-7*x^4+2*x^3+x^2-x+1)/(x^6+11*x^5+48*x^4+106*x^3+125*x^2+75*x+17);" + CR + "G1=latex(residue1(G,x))")
End Sub
Sub e52()
PutOnClipboard ("G1=latex(residue(G,x)),")
End Sub
Sub e53()
CR = Chr(13) + Chr(10)
PutOnClipboard ("num=[-17,-7,2,1,-1,1];" + CR + " den=[1,11,48,106,125,75,17];" + CR + "[r,p,k]=pfrac(num,den); format long e; [r,p]")
End Sub
Sub e54()
CR = Chr(13) + Chr(10)
PutOnClipboard ("i=sym(sqrt(-1)); syms z" + CR + "f=1/((z+i)^10*(z-1)*(z-3));" + CR + " r1=limit(diff(f*(z+i)^10,z,9)/prod(1:9),z,-i);" + CR + "r2=limit(f*(z-1),z,1); a=2*pi*i*(r1+r2)")
End Sub
Sub e55()
PutOnClipboard ("a+pi*i/(3+i)^10")
End Sub