Lectures in course PHYS-332: Computational physics III

Numerical Physics: Fourier Transforms and Linear Algebra

Covers advanced topics in computational physics, focusing on Fourier transforms and linear algebra.

Covers Fourier series, analysis, the heat equation, Gibbs phenomenon, and Fourier transform properties.

Covers the Fast Fourier Transform (FFT) algorithm, interpolation, filters, image processing, and experimental techniques in TEM and STM.

Signal Analysis and Filter Design

Explores signal analysis, FFT, filters, and power spectral density in signal processing.

Fourier Transform and Windowing

Explores spectral leakage, window functions, Fourier transforms, image processing, experimental techniques, and graphene materials.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions for solving linear systems and simulating dynamics.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions, algorithms, computational complexity, and predator-prey interactions in numerical linear algebra.

Floating Point Numbers: LU Decomposition and Errors

Explores floating point numbers, LU decomposition, errors, and matrix properties.

Eigenvalue Problems: Methods and Applications

Explores eigenvalue problems, iterative methods, convergence properties, and applications in computational physics.

Diagonalization Techniques: Jacobi Method

Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Conjugate Gradient Methods: Overview

Provides an overview of conjugate gradient methods, including preconditioning, nonlinear conjugate gradient, and singular value decomposition.

Singular Value Decomposition: Theory and Applications

Covers the theory and applications of Singular Value Decomposition in computational physics, including solving linear systems and polynomial fits.

Singular Value Decomposition: Theory and Applications

Explores Singular Value Decomposition theory, linear system solutions, least squares, and data fitting concepts.