Numerical methods: runge-kutta

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

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Optimal Control: KKT Conditions

Explores optimal control and KKT conditions for non-linear optimization with constraints.

Deep Neural Networks: Optimization and Approximation

Explores optimization and approximation in deep neural networks, including optimal control and numerical experiments.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Optimization with Constraints

Covers the optimization with constraints and the KKT theorem.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Ordinary Differential Equations: Methods and Applications

Explores ordinary differential equations and numerical integration methods for stability and accuracy.