Lectures related to Elliptic Equations: Linear and Order

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

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

Linear Partial Differential Equations

Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Diffusion in Concentration Coordinates

Explores diffusion in concentration coordinates and boundary conditions in different systems.

Biomechanical Tissues: Non-linear Constitutive Laws

Explores ligamentoplasty outcomes, biomechanical analysis, finite element analysis, and tissue characterization through constitutive laws.

Computational Geomechanics: Unconfined Flow

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

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.

Linear 2nd Order ODEs: Boundary Value Problems

Explores linear 2nd order ODEs as boundary value problems with various types of conditions, ensuring unique solutions.

Computational Geomechanics: Unconfined Flow Analysis

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

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.

Boundary Conditions and Basis Decomposition

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

Internal Heat Transfer Effects

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

Partial Differential Equations: Viscoelastic Materials

Explores the application of PDEs in viscoelastic materials and materials science.

Thermal Diffusion: Conservation and Fourier Law

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

Elastic Membrane Boundary Problem 2D

Covers the elastic membrane boundary problem in 2D, exploring mathematical formulation and solution methods.

Finite Element Method: Weak Formulation and Applications

Explores integral and weak formulations in Finite Element Method applications.

Finite Difference Method: Approximating Derivatives and Equations

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

Poincaré - Friedrichs: Theorem and Kernel Inequality

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

Easing Model Conformal Theory: Scaling Limits and Correlations

Covers the Easing model conformal theory, focusing on scaling limits and correlation functions.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.