Complex Analysis/Harmonic function: Revision history

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8 January 2025

  • curprev 23:0323:03, 8 January 2025 imported>Eshaa2024 3,215 bytes +3,215 New resource with "==Definition== Let <math>U \subseteq \mathbb{C}</math> be an open set. A function <math>u \colon U \to \mathbb{R}</math> is called ''harmonic'' if it is twice differentiable and satisfies <center><math> \Delta u := \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0 </math></center> have. The real part of a holomorphic function is harmonic, as follows from the Cauchy-Riemann-Differential equation. Interestingly, the conv..."
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