Lectures related to Bessel Equation: Introduction

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Fourier Transform and Differential Equations

Discusses the Fourier transform and its application to solving differential equations, focusing on the wave equation and its transformations.

Vibrating String: Mathematical Analysis

Covers the study of a vibrating string, wave equations, sinusoidal waves, and eigenvalue problems.

Wave Equation and Laplacian

Explores the wave equation, Laplacian properties, and non-dependent functions in neighborhoods.

Energy Conservation in Wave Equations

Explores energy conservation in wave equations, emphasizing uniqueness, existence of solutions, and stability.

Scalar Linear 2nd Order ODEs: Introduction

Explores solving scalar linear second order ODEs systematically and introduces special functions essential in physics.

Electronic Structure of Atoms: Hydrogen Atom

Explores the electronic structure of the hydrogen atom, covering radial wave functions, quantum numbers, and orbital sublayers.

Eigenvectors and 1D Wave Equation

Covers eigenvectors, eigenvalues, and the solution to the 1D wave equation on a bounded system.

Systems of n linear ODEs with constant coupling matrix A

Covers systems of n linear first-order ODEs with constant coupling matrix A and explores properties of solutions and the superposition principle.

Bessel Equation: Bessel Functions of the 2nd Kind

Explores the Bessel equation and its solutions, focusing on the Bessel functions of the 2nd kind and their properties.

Quantum Eigenfunctions

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Vibratory Mechanics: Continuous Systems

Explores vibratory mechanics in continuous systems, covering separation of variables, boundary conditions, and harmonic solutions.

Vibrating Strings: Mathematical Analysis and Fourier Series

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Linear Differential Equations

Covers second-order linear differential equations and their solutions, including the method of variation of constants.

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.

Linear Algebra: Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, diagonalization, and spectral theorem in linear algebra.

High Order Methods: Space Discretisation

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

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Eigenvalues and Optimization: Numerical Analysis Techniques

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

Wave Equation: Euler-Paissan-Doubana

Covers the wave equation and introduces the Euler-Paissan-Doubana formula, emphasizing key concepts.