- #1
Ask4material
- 18
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I couldn't find any book discussing all of this.
===================================================
U+jV=f(x+jy) W=f(z)
Ux=Vy
Uy= -Vx
jWx=Wy <--Cauchy-Riemann equation
Uxx+Uyy=0
Vxx+Vyy=0 <--harmonic condition
===================================================
U+jV=f(rcjsθ) W=f(z)
[itex]rU_r=V_θ[/itex]
[itex]rV_r=U_θ[/itex]
[itex]jrW_r=W_θ[/itex] <--Cauchy-Riemann equation[itex]U_{rr}[/itex]?? [itex]U_{θθ}[/itex]??
[itex]V_{rr}[/itex]?? [itex]V_{θθ}[/itex]?? <--harmonic condition??
===================================================
RcjsB=f(x+jy) W=f(z)
RBy = Rx
RBx= -Ry
jWx=Wy <--Cauchy-Riemann equation
Rxx?? Ryy??
Byy?? Bxx?? <--harmonic condition??
===================================================
RcjsB=f(rcjsθ) W=f(z)
[itex]rR_r=RB_θ[/itex]
[itex]rRB_r=-R_θ[/itex]
[itex]jrW_r=W_θ[/itex] <--Cauchy-Riemann equation
[itex]R_{rr}[/itex]?? [itex]R_{θθ}[/itex]??
[itex]B_{rr}[/itex]?? [itex]B_{θθ}[/itex]?? <--harmonic condition??
===================================================
U+jV=f(x+jy) W=f(z)
Ux=Vy
Uy= -Vx
jWx=Wy <--Cauchy-Riemann equation
Uxx+Uyy=0
Vxx+Vyy=0 <--harmonic condition
===================================================
U+jV=f(rcjsθ) W=f(z)
[itex]rU_r=V_θ[/itex]
[itex]rV_r=U_θ[/itex]
[itex]jrW_r=W_θ[/itex] <--Cauchy-Riemann equation[itex]U_{rr}[/itex]?? [itex]U_{θθ}[/itex]??
[itex]V_{rr}[/itex]?? [itex]V_{θθ}[/itex]?? <--harmonic condition??
===================================================
RcjsB=f(x+jy) W=f(z)
RBy = Rx
RBx= -Ry
jWx=Wy <--Cauchy-Riemann equation
Rxx?? Ryy??
Byy?? Bxx?? <--harmonic condition??
===================================================
RcjsB=f(rcjsθ) W=f(z)
[itex]rR_r=RB_θ[/itex]
[itex]rRB_r=-R_θ[/itex]
[itex]jrW_r=W_θ[/itex] <--Cauchy-Riemann equation
[itex]R_{rr}[/itex]?? [itex]R_{θθ}[/itex]??
[itex]B_{rr}[/itex]?? [itex]B_{θθ}[/itex]?? <--harmonic condition??
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