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What you will learn

What are differential equations?

Why are differential equations important for linear circuits?

Why do all linear circuit differential equations behave the same way?

Description

Day 24 of Linear Circuits.  One of the biggest stumbling blocks for sophomore engineering and physics students is the use of differential equations in our daily homework problems and exam questions.  While an entire course on differential equations could last 30, 40, or 50 hours (or more!), we bring you the most important basics of what differential equations are, how they work, and why they are relevant to our linear circuit lessons.  Perhaps most importantly, however, we discover that differential equations don’t have to be that scary, and in fact, the solutions for all differential equations actually have a lot in common with each other.  Don’t be afraid – we’ll take it step-by-step.   : )

The material covers all of the lecture material from an twenty-fourth lecture in a traditional, sophomore-level linear circuits class.


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English
language

Content

Introduction

Agenda
Review
What If Resistance Changes Over Time?
The Different Parts of a Differential Equation
Writing a Second Order, Differential Equation
Setting Up the Simplest Differential Equation – The Zero Input Response
Finding the Characteristic Polynomial of a Differential Equation
Finding the General Solution for a Differential Equation
Example of Calculating the General Solution for a Differential Equation
Example of Calculating the Specific Solution Based Upon the Initial Conditions
What Does the Solution of a Differential Equation Mean???
Solving the Same Differential Equation for a Different Set of Initial Conditions
Special Cases of the Differential Equation General Solution
Summary
Solving a Linear Circuit with a Differential Equation, From Beginning to End