Linear Circuits 1 - 24 - Differential Equations

Name: Linear Circuits 1 - 24 - Differential Equations
Rating: 4.7 (50 reviews)

Using Differential Equations to Solve Circuits with Inductors and Capacitors

Created byMark Budnik, Mark M. Budnik

Last updated 6/2020

English

What you'll learn

What are differential equations?
Why are differential equations important for linear circuits?
Why do all linear circuit differential equations behave the same way?

Course content

1 section • 15 lectures • 1h 10m total length

Agenda0:27
Review2:19
What If Resistance Changes Over Time?2:14
The Different Parts of a Differential Equation4:17
Writing a Second Order, Differential Equation4:57
This lecture introduces integral differential equations and demonstrates turning them into purely differential equations by differentiation, using the capital D operator to write derivatives and highlighting easier solving for engineers.
Setting Up the Simplest Differential Equation - The Zero Input Response5:36
Learn to solve differential equations via zero input response, using D operator notation with Q(D) and P(D), illustrated by a circuit with a zero voltage source and an inductor.
Finding the Characteristic Polynomial of a Differential Equation8:13
Finding the General Solution for a Differential Equation4:17
Example of Calculating the General Solution for a Differential Equation7:00
Example of Calculating the Specific Solution Based Upon the Initial Conditions4:40
What Does the Solution of a Differential Equation Mean???7:11
Solving the Same Differential Equation for a Different Set of Initial Conditions4:25
Special Cases of the Differential Equation General Solution5:18
Summary2:16
Read the polynomial Q(D) from the differential equation, form the characteristic equation, and solve for eigenvalues; distinct, repeated, or complex conjugate values govern zero input response with decay and oscillation.
Solving a Linear Circuit with a Differential Equation, From Beginning to End7:04

Requirements

High School or College Physics
Calculus 1 Would Be Extremely Helpful

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.

Who this course is for:

Beginner Engineering and Physics Students