# Partial differential equations

Other Course , Prof. ChrisTisdell

240 students enrolled

# Overview

Contents:
how to solve PDE via method of characteristics - How to solve the transport equation (PDE) - How to solve basic transport PDE problems - The transport equation-How to solve PDE via directional derivatives - Solve PDE via an integrating factor - How to derive the more general transport equation - How to solve inhomogeneous transport PDE - How to solve PDE via change of co-ordinates - How to solve PDE via change of variables - Example of how to solve PDE via change of variables - Method of Characteristics: How to solve PDE - PDE and method of characteristics: a how to solve Burger's equation (PDE)-How to solve quasi linear PDE - Method of characteristics and PDE - How to factor and solve the wave equation (PDE) - How to solve second order PDE - How to classify second order PDE - How to solve the wave equation (PDE)

Solution to the wave equation + Duhamel's principle (PDE) - How to derive the wave equation (PDE) - How to solve the inhomogeneous wave equation (PDE) - 5 things you need to know: Heat equation - Heat equation: How to solve heat equation: example-How to solve heat equation on half line - Heat equation derivation - Turning PDE into ODE - Similarity solution method: PDE - Introduction to Laplace transforms - First shifting theorem: Laplace transforms - Second shifting theorem: Laplace transforms - Introduction to Heaviside step function - Laplace transform: square wave - Laplace transforms + ODEs -Solve PDE via Laplace transforms - How to solve PDE: Laplace transforms - Laplace transforms vs separation of variables - Intro to Fourier transforms: how to calculate them - Fourier transforms: Shifting theorem - How to apply Fourier transforms to solve differential equations - Intro to Partial Differential Equations (Revision Math Class)

### Lecture 1: How to solve PDE via method of characteristics

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# Lecture Details

Basic example showing how to solve PDE via method of characteristics. A general first order problem is solved with a concrete example discussed at the end. The ideas can be used to solve many kinds of first order partial differential equations.

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