Lectures related to Exact Analytical Solution Methods: Matrix Method Linear ODEs

Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Quantum Mechanics: Power Series Solutions

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

Resonators: Understanding Frequency Response and Eigenvalues

Covers resonators, Eigenvalue problem for flexural resonators, and normalization importance.

Inverse Monotonicity: Stability and Convergence

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

Numerical Methods for Boundary Value Problems

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

Finite Difference Method: Approximating Derivatives and Equations

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

Beam Deflection: Integrating Loads to Deformation

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

Complex Reactions: Kinetics and Approximations

Covers complex reactions, rate laws, differential equations, and steady-state approximation for parallel reactions.

Numerical Analysis: Stability in ODEs

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

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.

Vibratory Mechanics: Continuous Systems

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

Waves in Inhomogeneous Medium

Explores waves in inhomogeneous media, covering initial and boundary conditions, numerical stability, eigen modes, and propagation principles.

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.

Boundary Conditions and Basis Decomposition

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

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Fixed Energy Propagator: Density and Examples

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

Poisson Problem: Fourier Transform Approach

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

Differential Relations for Internal Forces

Explains the differential method for calculating internal forces in beams and handling discontinuities at point loads.

Heterogeneous Reactions: Transport Effects

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

Law of Hooke Applications: Spring Problems

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.