Lectures related to Sturm-Liouville Problem: Legendre Equation

Quantum Mechanics: Power Series Solutions

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Numerical Methods for Boundary Value Problems

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

Explores the concept of separation of variables in quantum mechanics and its application in solving differential equations.

Exact Analytical Solution Methods: Matrix Method Linear ODEs

Covers the exact analytical solution methods for linear ODEs using matrices and eigenvalues.

Quantum Chemistry: Eigenfunctions and Hermitian Operators

Discusses eigenfunctions of Hermitian operators in quantum chemistry and the quantization of energy levels.

Vibratory Mechanics: Continuous Systems

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

Numerical Analysis: Stability in ODEs

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

Quantum Mechanics: Probability in Potential Wells

Delves into quantum mechanics, focusing on probability in potential wells and comparing classical and quantum predictions.

Boundary Conditions and Basis Decomposition

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

Inverse Monotonicity: Stability and Convergence

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Beam Deflection: Integrating Loads to Deformation

Explores integrating loads to deform beams, emphasizing boundary conditions and practical applications in stress analysis.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Numerical Groundwater Flow Resolution: Finite Elements

Covers the numerical resolution of groundwater flows using finite elements and emphasizes the importance of spatial and temporal discretization.

Quantum Chemistry

Covers eigenvalues, eigenfunctions, Hermitian operators, and the measurement of observables in quantum chemistry.

Fixed Energy Propagator: Density and Examples

Covers the fixed energy propagator, including its analytic structure and examples of free particle and barrier penetration.

Separation of Variables: Spatial Problems

Explores the method of separation of variables for solving spatial problems with second-order ODEs, emphasizing the significance of boundary conditions.

Quantum Chemistry: Schrödinger Equation Solutions

Explores the solutions to the Schrödinger Equation in Quantum Chemistry, emphasizing wavefunction properties and energy quantization.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Casting ODEs into Sturm-Liouville form

Explores casting ODEs into self-adjoint form and the role of boundary conditions in ensuring self-adjointness.

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.