Lectures related to Hyperbolic partial differential equation

Theoretical Study of Elliptic Partial Differential Equations

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

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

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

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 Differential Equations

Explores solving linear differential equations and the principle of superposition with illustrative examples.

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

Covers the basics of Partial Differential Equations, including well-posedness, operators, and classification of physical PDEs.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Distribution & Interpolation Spaces

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

Partial Differential Equations: Characteristics and Solutions

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

Density Results in Sobolev Spaces

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

Partial Differential Equations: Classification and Solutions

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

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.

Variational Methods in Mechanics

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

Fundamental Solutions

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

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Introduction to Ordinary Differential Equations

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

Partial Differential Equations: Solutions and Applications

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

Second Order Differential Equations: Solving Examples and Conditions

Focuses on solving second order differential equations with examples and conditions, including Fourier series and Sturm-Liouville theory.