Harmonic Conjugate

159 days ago by TravisBarryDick

Computes a harmonic conjugate for u.
def harmonicConjugate(u): ux = diff(u, x) uy = diff(u, y) t = integrate(ux, y) return t + (diff(t, x) + uy) 
       
u(x,y) = exp(x) * (x * cos(y) - y * sin(y)) f(z) = u(real(z),imag(z)) + i*harmonicConjugate(u)(real(z),imag(z)) f.simplify() 
        
\newcommand{\Bold}[1]{\mathbf{#1}}z \ {\mapsto}\ z e^{z}
\newcommand{\Bold}[1]{\mathbf{#1}}z \ {\mapsto}\ z e^{z}