Elliptic Partial Differential Equations

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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.