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17Calculus Partial Differential Equations

Single Variable Calculus
Multi-Variable Calculus

Partial Differential Equations (PDE's)

On this page we get you started with partial differential equations.  First, we run through a review of partial derivatives and three important operations from vector calculus.  Do not skip the reviews even if you just finished the classes that covered that material.  Hearing another instructor explain it will expand and deepen your knowledge and may even raise your grade.  So don't miss this opportunity.

PDE Resources

Playlists and Videos

This first playlist is from Dr Chris Tisdell, who is one of our favorite instructors. The order of these videos seems to be mixed up but he always explains things very well.

Dr Chris Tisdell - PDE Playlist

video by Dr Chris Tisdell

This guy is another one of our favorites. He has an extensive library of mathematics, physics, engineering and chemistry videos. Here is his partial differential playlist. You won't find a better channel for learning math, science and engineering.

Michel vanBiezen - PDE Playlist

video by Michel vanBiezen

Here are a few more playlists that may help you.

Christopher Lum - Full PDE Course Playlist

video by Christopher Lum

MathTheBeautiful - PDEs Playlist

video by MathTheBeautiful

Recommended Books

Related Topics and Links

Pauls Online Math Notes - PDE

Partial Derivatives Review

Okay, at this point in your learning you already know what a partial derivative is.  However, even if you are absolutely convinced you completely understand everything there is to know about partial derivatives, this next video is a must watch.  It has a great explanation, using a graph, of what it means to hold one variable constant while taking the derivative of the other.  Even as an instructor I learned something from this video.  So I highly recommend it.

Michel vanBiezen - What is a Partial Differential Eqn?

video by Michel vanBiezen

Vector Calculus - Review of Three Important Operations

Before we get started with the details of partial differential equations, here is a great video to watch to remind us of the three basic operations from vector (multi-variable) calculus that we will be doing a lot when solving partial differential equations.  The three operations are divergence, gradient and curl.

Steve Brunton - Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs

video by Steve Brunton

What Is A Partial Differential Equation?

A partial differential equation (PDE) is an equation containing partial derivatives.  It works just like an ordinary differential equation (ODE) except that the solution is a function of more than one variable.  For example, you can verify a solution by taking partial derivatives and plugging them into the PDE just like you would with an ODE.
Here is a video with the big picture of where we are going.

Steve Brunton - Vector Calculus and Partial Differential Equations: Big Picture Overview

video by Steve Brunton

Really UNDERSTAND Differential Equations

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