Lectures related to Numerical Methods for Physics: Iterative Solutions and Mesh Convergence

Numerical Methods for Boundary Value Problems

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

Numerical Methods: Differential Equations

Covers the application of numerical methods to solve differential equations using MATLAB.

Numerical Methods: Boundary Value Problems

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

Finite Element Method: Applications and Formulations

Explores the application and formulation of the finite element method in solving various engineering problems.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Matlab: 3D Surface Plotting

Covers logical arrays, 3D surface plotting, parametric curves, interpolation, and fitting in Matlab.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Matlab Programming: Script and Function

Explores Matlab programming with scripts and functions, vectorization, and 2D graphics.

Matrix Construction and Function Manipulation

Covers tips on matrix construction and function manipulation using MATLAB.

Numerical Integration Methods

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Finite Element Method Basics

Covers the basics of the Finite Element Method (FEM) for linear and nonlinear partial differential equations.

Numerical Approximation of Partial Differential Equations

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.

High Order Methods: Space Discretisation

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

Complex Analysis: Residue Theorem and Fourier Transforms

Discusses complex analysis, focusing on the residue theorem and Fourier transforms, with practical exercises and applications in solving differential equations.

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

MATLAB Essentials: Functions and Variables

Covers essential MATLAB functions, variables, loops, and debugging tools.

Statistical Signal Processing

Covers Gaussian Mixture Models, Denoising, Data Classification, and Spike Sorting using Principal Component Analysis.

Macrofinance Models Analysis

Covers macroeconomic models incorporating financial markets, analyzing financial decisions, macroeconomic events, and policy responses.