Lectures related to Extension Theorems: Sobolev Spaces and Poincaré Inequality

Explores density results in Sobolev spaces, emphasizing their applications and proof techniques.

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

Variational Methods in Mechanics

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

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving 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.

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.

Partial Differential Equations: Characteristics and Solutions

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

Introduction to Ordinary Differential Equations

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

Direction Fields, Euler Methods, Differential Equations

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

Biomechanics Modeling: Musculoskeletal System

Explores biomechanical modeling of the musculoskeletal system using differential equations and finite element modeling.

Elliptic Partial Differential Equations

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Partial Differential Equations: Classification and Solutions

Covers the classification and solutions of partial differential equations, including Laplace transform and separation of variables techniques.

Distribution & Interpolation Spaces

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

Theoretical Study of Elliptic Partial Differential Equations

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

Nonlinear PDE Models with Stochastic Fractional Perturbation

Explores nonlinear PDE models with stochastic fractional perturbation, focusing on regularity identification and space-time noise interpretation.

Partial Differential Equations: Basics and Classification

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.

Elliptic Partial Differential Equations

Covers the theoretical study of Elliptic Partial Differential Equations, including electrostatics and advection-diffusion-reaction equations.

Partial Differential Equations: Solutions and Applications

Explores solutions to partial differential equations and their applications in various scenarios.

Numerical Methods for Physics: Iterative Solutions and Mesh Convergence

Explores finite differences for solving linear systems from PDEs iteratively, emphasizing convergence criteria and exercises on singularities.