Lectures related to Exponential of a Matrix

Path Integral and Gaussian Integrals

Covers the path integral representation of the propagator and Gaussian integrals in complex and multi-dimensional cases.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Matrix Equivalence Theorems

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

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.

Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.