Partial Differential Equations: Solutions and Applications

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Related lectures (28)

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Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Taylor Polynomials: Correction Exam 2018

Covers the correction of an exam from 2018, focusing on Taylor polynomials and Jacobian matrices.

Setting up Experiments: Compactness, Isometries, Quasi-Isometry

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Introduction to Ordinary Differential Equations

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Differential Equations: Part 2

Explores Peano's existence theorem, compactness properties, uniqueness of solutions, Ascoli-Arzela theorem, and ripeness in differential equations.

Fundamental Solutions

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

Partial Differential Equations: Characteristics and Solutions

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

Heat and Wave Equations: Analysis IV

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Partial Differential Equations and Hessians

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.