Lectures related to Elliptic Partial Differential Equations

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Linear Partial Differential Equations

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

Weak Solutions of Differential Equations

Explores weak solutions of differential equations and their properties.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Theoretical Study of Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including classical and weak solutions.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Variational Methods in Mechanics

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

Linear Algebra Basics

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Partial Differential Equations: Characteristics and Solutions

Explores characteristic curves and solutions in partial differential equations, emphasizing uniqueness and existence in various scenarios.

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Maximum Principle in Harmonic Functions

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Linear Equations: Introduction and Solutions

Covers the introduction and solutions of linear equations, including methods for solving systems and determining the number of solutions.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Direction Fields, Euler Methods, Differential Equations

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Linear Differential Equations

Covers linear differential equations of higher order, defining them as linear if they can be rewritten in a specific form.

Differential Equations Solutions

Covers solutions of differential equations with initial conditions and boundedness concepts.

Differential Equations: Solutions and Uniqueness

Explores differentiability, continuity, solutions, and uniqueness in differential equations, emphasizing well-posed problems and real-world applications.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.