Lectures related to Maximum Principle in Elliptic Problems

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

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

Vector Spaces and Scalar Products

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Finite Difference Method: Approximating Derivatives and Equations

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

Other Topics: Techniques for Fluid Interfaces

Explores numerical methods for fluid dynamics and techniques for handling fluid interfaces.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Excel Upgrade: Advanced Functions and Data Analysis

Covers advanced Excel functions and data analysis techniques, including automatic recording and using Solver.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Linear PDEs of Order 2

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

Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, covering gradient and Hessian checks, solver calls, and manual caching.

Waves in Inhomogeneous Medium

Explores waves in inhomogeneous media, covering initial and boundary conditions, numerical stability, eigen modes, and propagation principles.

Second Order Approximations: The Hessian Matrix

Explores second order approximations for twice differentiable functions using the Hessian matrix.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Renormalization of Gauge Theories

Covers the renormalization of gauge theories and composite operators.

Boundary Value Problems: Numerical Methods

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Transporters: a proxy for parallel transport

Explores transporters as a practical alternative to parallel transport, discussing minimal requirements, examples with matrices, pragmatic choices, and optimization algorithms.