Runge Kutta Method

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Euler Backward Method: ODEs

Explores the Euler backward method for ODEs, discussing stability, error reduction, and implicit vs explicit methods.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Runge-Kutta Methods: Approximating Differential Equations

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

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

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.

Optimization with Constraints: KKT Conditions

Covers optimization with constraints using KKT conditions and matrix invertibility in numerical analysis.

Neural Networks: Two-layer Networks and Backpropagation

Explores two-layer neural networks and backpropagation for learning feature spaces and approximating continuous functions.

Numerics: semester project

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

Ordinary Differential Equations: Methods and Applications

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

Numerical Methods for Schrödinger Equation

Explores numerical methods for solving the time-dependent Schrödinger equation using grid representation and split-operator algorithms.