Lectures related to Resonators: Understanding Frequency Response and Eigenvalues

Exact Analytical Solution Methods: Matrix Method Linear ODEs

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

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

Quantum Mechanics: Power Series Solutions

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

Translation Groups on [0,1]

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Rayleigh Taylor: Normal Mode Expansion

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

Boundary Conditions and Basis Decomposition

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

Sturm-Liouville Problem: Legendre Equation

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

Green Functions in Electrostatics

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

Sturm-Liouville Problem: Introduction

Introduces the Sturm-Liouville problem, covering ODE solutions, boundary conditions, and eigenvalue problems.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Heterogeneous Reactions: Transport Effects

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

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Poincaré - Friedrichs: Theorem and Kernel Inequality

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

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Vibrating String: Mathematical Analysis

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

Existence of Minimizers: Direct Methods

Covers direct methods for finding minimizers in the Poisson equation, emphasizing the importance of convexity and boundary conditions.

Internal Heat Transfer Effects

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

Square Potential Well

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

Computational Geomechanics: Unconfined Flow

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

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

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