Lectures related to Image Method: Charge Configuration and Potential Calculation

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.

Computational Geomechanics: Unconfined Flow

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

Poincaré - Friedrichs: Theorem and Kernel Inequality

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

Structural Mechanics Fundamentals

Introduces the fundamentals of structural mechanics, covering equilibrium, boundary conditions, free-body diagrams, and constraints.

Quantum Mechanics: Power Series Solutions

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

Computational Geomechanics: Unconfined Flow Analysis

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

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

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

Boundary Conditions and Basis Decomposition

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

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.

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.

Poisson Problem: Fourier Transform Approach

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

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Square Potential Well

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

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.

Solute Transport in Porous Media

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

Poisson Problem with Neumann Boundary Conditions

Explores the Poisson problem with Neumann boundary conditions and periodic boundary conditions in mathematical modeling and fluid dynamics.

Thermal Diffusion: Conservation and Fourier Law

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

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.