You CAN Ace Differential Equations

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Single Variable Calculus

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Differential Equations

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This page contains several differential equations topics that are not discussed in detail but we provide some overview information and maybe a video or two, as well as links to other pages with more in-depth information, if we have any. We may expand these topics as a later date but, for now, this will get you started.

Existence and Uniqueness

Here is a discussion of the Lipschitz condition, which is related to whether a differential equation has a solution and, if so, whether the solution is unique.

Dr Chris Tisdell - Lipschitz Condition

video by Dr Chris Tisdell

Boundary Value Problems

Here are three videos related to boundary value problems.

Dr Chris Tisdell - advanced differential equations and boundary value problems

video by Dr Chris Tisdell

Dr Chris Tisdell - how to determine eigenvalues of a boundary value problem

video by Dr Chris Tisdell

Dr Chris Tisdell - D'alembert's approach for boundary value problems

video by Dr Chris Tisdell

Euler's Method

MIT OCW - Euler's Numerical Method for y'=f(x,y) and its Generalizations

video by MIT OCW

Inhomogeneous ODEs

MIT OCW - Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials

video by MIT OCW

Vibration

Dr Chris Tisdell - Vibrating systems + differential equations

video by Dr Chris Tisdell

Resonance

MIT OCW - Interpretation of the Exceptional Case: Resonance

video by MIT OCW

Partial Differential Equations

Here are two videos related to pde's using the method of characteristics. We highly recommend this guys' videos.
This first video introduces the topic and gives some examples.

Dr Chris Tisdell - How to solve PDE via method of characteristics

video by Dr Chris Tisdell

This second video gives more detail and another example.

Dr Chris Tisdell - PDE and method of characteristics: a how to

video by Dr Chris Tisdell

Linear Systems

Dr Chris Tisdell - How to solve systems of ODEs without matrices

video by Dr Chris Tisdell

Dr Chris Tisdell - Basic solution form to systems of differential equations

video by Dr Chris Tisdell

Dr Chris Tisdell - How to solve systems of differential equations

video by Dr Chris Tisdell

PatrickJMT - Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1

video by PatrickJMT

PatrickJMT - Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2

video by PatrickJMT

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