Lectures related to Euler-Lagrange Equation

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Discusses optimization techniques, focusing on local and global extrema in functions.

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Covers the analysis of stationary points in functions, focusing on optimization methods.

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

Delves into the mechanics of slender structures, analyzing naturally curved hair in 2D under gravity.

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

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

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

Covers the analysis and solution of diffusion equations using Green's function approach and discusses boundary conditions and dimensional analysis.

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

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

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

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Discusses the numerical analysis of pollutant transport equations and their applications in environmental modeling.

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

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

Explores Magnetohydrodynamic equilibrium and stability, ideal MHD solutions, 'hairy ball' theorem, and boundary conditions.

Discusses local extrema of functions in two variables around the point (0,0).

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