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Applications of Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · dirichlet-problem-unit-disk
Problem Find the function ϕ ( x , y ) \phi(x,y) ϕ ( x , y ) ∣ z ∣ < 1 |z| < 1 ∣ z ∣ < 1 ϕ ( x , y ) = 1 for x + i y = z = e i θ , − π 2 < θ < π 2 ; \phi(x,y) = 1 \text{ for } x + iy = z = e^{i\theta},\; -\frac{\pi}{2} < \theta < \frac{\pi}{2}; ϕ ( x , y ) = 1 for x + i y = z = e i θ , − 2 π < θ < 2 π ; ϕ ( x , y ) = 0 for x + i y = z = e i θ , π 2 < θ < 3 π 2 . \phi(x,y) = 0 \text{ for } x + iy = z = e^{i\theta},\; \frac{\pi}{2} < \theta < \frac{3\pi}{2}. ϕ ( x , y ) = 0 for x + i y = z = e i θ , 2 π < θ < 2 3 π . Browse the problem library