How Complex Analysis Models Fluid Flow
Автор: TPSA Ireland
Загружено: 2025-08-31
Просмотров: 11104
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Ever wondered how mathematicians and engineers model the flow of water around obstacles, air over airplane wings, or currents in the ocean? The answer lies in the elegant world of complex analysis, where imaginary numbers become real tools for understanding fluid motion.
Video by Ameilia Ryan
Concept by Casey Farren-Colloty
0:00 Intro
0:37 Holomorphicity and The Cauchy Riemann Equations
1:12 Harmonic Functions
1:25 All Holomorphic Functions Are Harmonic
3:03 The Continuity Equation
3:38 The Divergence of the Curl is Zero
4:35 Conformal Mapping
5:27 The Maximum Principle
7:11 Water Flow Around a Cylinder
8:23 Non-Rigorous Proof of Maximum Principle for Harmonic Functions
9:09 Tying it all Together
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