Bessel Equation: Introduction

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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.