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Applications of Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · dirichlet-problem-half-disk
Problem Find the function ϕ ( x , y ) \phi(x,y) ϕ ( x , y ) y > 0 y > 0 y > 0 ∣ z ∣ < 1 |z| < 1 ∣ z ∣ < 1 ϕ ( x , y ) = 5 for x + i y = z = e i θ , 0 < θ < π ; \phi(x,y) = 5 \text{ for } x + iy = z = e^{i\theta},\; 0 < \theta < \pi; ϕ ( x , y ) = 5 for x + i y = z = e i θ , 0 < θ < π ; ϕ ( x , 0 ) = − 5 for − 1 < x < 1. \phi(x,0) = -5 \text{ for } -1 < x < 1. ϕ ( x , 0 ) = − 5 for − 1 < x < 1. Browse the problem library