Lectures related to Partial Differential Equations: Solutions and Applications

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.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Numerical Analysis: Implicit Schemes

Covers implicit schemes in numerical analysis for solving partial differential equations.

Partial Differential Equations

Introduces partial differential equations, covering derivatives, special cases, transformations, and the Jacobian matrix.

Variational Methods in Mechanics

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

Continuum Mechanics: Conservation Laws and Kinematics

Introduces continuum mechanics, focusing on conservation laws and kinematics for continuous media.

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.

Mathematical Methods for Physicists: Differential Equations and Special Functions

Covers solving differential equations and special functions essential for physicists, emphasizing practical problem-solving skills.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Direction Fields, Euler Methods, Differential Equations

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