The Composition of a Harmonic Function with A Holomorphic Function is Harmonic
We prove that if we compose a harmonic function with a holomorphic function that the result will be harmonic. The seemingly elementary result yields both beautiful results in the theory of partial differential equations and in differential geometry. We will se this result extensively in both fields!
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #harmonicfunction
Видео The Composition of a Harmonic Function with A Holomorphic Function is Harmonic канала Mike, the Mathematician
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #harmonicfunction
Видео The Composition of a Harmonic Function with A Holomorphic Function is Harmonic канала Mike, the Mathematician
mike the mathematician mike dabkowski math complex analysis complex analysis course complex analysis solutions holomorphic function Stein Shakarchi proofs Stein Shakarchi solutions harmonic functions harmonic functions and holomorphic functions harmonic composed with holomorphic harmonic and holomorphic still harmonic conformal factor real part harmonic imaginary part harmonic Chain Rule Chain Rule Calc 3 Applications of Chain Rule Cauchy-Riemann harmonic
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11 июня 2025 г. 9:00:38
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