Elliptic Partial Differential Equations

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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.