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Applications of Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · dirichlet-problem-harmonic-functions
Problem Find the function ϕ ( x , y ) \phi(x,y) ϕ ( x , y ) Im ( z ) > 0 \operatorname{Im}(z) > 0 Im ( z ) > 0 ϕ ( x , 0 ) = 3 for x < − 3 , ϕ ( x , 0 ) = 7 for − 3 < x < − 1 ; \phi(x,0) = 3 \text{ for } x < -3, \quad \phi(x,0) = 7 \text{ for } -3 < x < -1; ϕ ( x , 0 ) = 3 for x < − 3 , ϕ ( x , 0 ) = 7 for − 3 < x < − 1 ; ϕ ( x , 0 ) = 1 for − 1 < x < 2 , ϕ ( x , 0 ) = 4 for x > 2. \phi(x,0) = 1 \text{ for } -1 < x < 2, \quad \phi(x,0) = 4 \text{ for } x > 2. ϕ ( x , 0 ) = 1 for − 1 < x < 2 , ϕ ( x , 0 ) = 4 for x > 2. Browse the problem library