Lectures related to Vibrating Plate: Stationary Wave Illustration

Square Potential Well

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

Spatial Base Solutions

Discusses spatial base solutions, boundary conditions, and the time-dependent diffusion equation.

Boundary Conditions and Basis Decomposition

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

Time-dependent Diffusion: Fourier Trick

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Poisson Problem: Periodic Boundary Conditions

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

Mechanics of Kirchhoff Rods II

Explores the mechanics of Kirchhoff rods, focusing on 3D kinematics and twisted solutions.

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.

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.

Computational Geomechanics: Unconfined Flow Analysis

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

Solute Transport in Porous Media

Explores solute transport in porous media, covering advection-diffusion equations, boundary conditions, reactions, and numerical modeling in PHREEQC.

Boundary Value Problems in 1D

Discusses boundary value problems in 1D and the mathematical principles involved.

Quantum Mechanics: Power Series Solutions

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

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

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

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.

Heterogeneous Reactions: Transport Effects

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

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.

Maxwell Equations: Green Functions for Electrostatic Problems

Explores the use of Green functions for solving electrostatic problems with different boundary conditions, emphasizing the importance of choosing the correct function.