Variational Formulation: Finite Element Method

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Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Explores numerical methods for boundary value problems, including heat diffusion and fluid flow, using finite difference methods.

Explores transient stability in power systems dynamics, covering algebraic equations, generator models, and numerical integration techniques.

Covers numerical integration methods, focusing on the trapezoidal rule and iterative processes.

Focuses on Euler schemes for numerical approximation of forces and velocities.

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.