Wright Math

Our last chapter is about Differential Equations (D.E.'s).  We're only going to look at the most basic D.E.'s (those of you who go on to Math 287 will see more advanced equations).  What's super cool, though, is that unlike some types of math, where it's hard to do anything meaningful until you get pretty deep into a topic, Differential Equations are immediately useful.  They really are an amazing tool for describing phenomena in the world!

As with any new topic, you'll need to build up some vocabulary and some idea about what the basic structures are.  This first video will provide that.

Video:  Differential Equations Introduction

This next video goes over an important concept that our textbook doesn't cover well, which is how to write a differential equation based on a description of rates and proportionality.  Watch the video then do the practice problems as part of your homework.

Video: Writing a Differential Equation

Practice:  Write Differential Equations

In the introductory video, we saw what the solution to a differential equation looks like...it's just a function that "satisfies" the equation.  This next video will show more examples on checking whether a given function is, in fact, a solution to a given differential equation.

Video:  Verifying solutions to DE's

The last part of the homework involves finding solutions to differential equations using just basic integration, so really just finding antiderivatives as we have in the past.  

The point to this is to show how that arbitrary constant ( + C) you get when you integrate creates a General Solution to the DE.  The General Solution is an entire family of functions.  The solution to an Initial Value Problem (IVP) is the one specific solution in the family that satisfies the Initial Condition.

 Here's a video, compliments of Krista King, that shows how this works.  You may also remember doing this in Calc 1.

Video:  Solving an IVP