Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Complex Analysis: Theory and Applications · Problem 10.2.8
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 ) = 8 for x + i y = z = e i θ , 0 < θ < π ; \phi(x,y) = 8 \text{ for } x + iy = z = e^{i\theta},\; 0 < \theta < \pi; ϕ ( x , y ) = 8 for x + i y = z = e i θ , 0 < θ < π ; ϕ ( x , y ) = 4 for x + i y = z = e i θ , π < θ < 2 π . \phi(x,y) = 4 \text{ for } x + iy = z = e^{i\theta},\; \pi < \theta < 2\pi. ϕ ( x , y ) = 4 for x + i y = z = e i θ , π < θ < 2 π . Browse the problem library