Lectures related to Sturm-Liouville Problem: Introduction

Resonators: Understanding Frequency Response and Eigenvalues

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

Boundary Conditions and Basis Decomposition

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

Explores methods to construct Green functions in electrostatics, including image charge and eigenfunction expansion, under different boundary conditions.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Quantum Mechanics: Power Series Solutions

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

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Internal Heat Transfer Effects

Covers internal heat transfer effects in heterogeneous reactions, emphasizing dimensionless numbers and transport effects.

Poincaré - Friedrichs: Theorem and Kernel Inequality

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Finite Difference Method: Approximating Derivatives and Equations

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

Sturm-Liouville Problem: Legendre Equation

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

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Exact Analytical Solution Methods: Matrix Method Linear ODEs

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

Electric Displacement in Dielectrics: Gauss's Law and Boundary Conditions

Introduces the concept of electric displacement vector D and explores boundary conditions in dielectrics.

Thermal Diffusion: Conservation and Fourier Law

Explains conservation of energy and Fourier's law in thermal diffusion.

Recent Advances in the Dimer Model and Its Applications

Covers recent advancements in the dimer model, emphasizing its applications in probability and conformal field theory.

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Boundary Conditions in Harmonic Functions

Explains harmonic functions and their boundary conditions, including Dirichlet and Robin conditions.

Square Potential Well

Covers the concept of a square potential well and the search for solutions using trigonometric functions.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Structural Mechanics Part 2: FEM & Scaling Laws

Explores Finite Element Modeling in Structural Mechanics, covering convergence, nonlinear displacement, and scaling laws in micro and nanosystems.