Lectures related to Poincaré - Friedrichs: Theorem and Kernel Inequality

Discusses equilibrium, extension analysis, stress distribution, and strain components' compatibility for a valid solution.

Covers the verification of equilibrium equations and compatibility in tension scenarios, ensuring uniform stress distribution.

Explores stress and strain compatibility, closed-form expressions, and constant strain components.

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

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

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

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

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

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

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

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

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

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

Covers boundary conditions for heat diffusion in 1D systems.

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

Covers diffusion on an infinite domain using Green's method and emphasizes finding steady-state solutions and conservation of material.

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

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

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

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