Differential Equations explanations, examples, practice problems. Ready? Let's do this.
Differential Equations and Their Solutions
A differential equation (d.e.) is any equation that has one or more derivative in it. These can be first derivatives, second derivatives...whatever.Sample ProblemThe following are differential equa...
Word Problems
We can use differential equations to talk about things like how quickly a disease spreads, how fast a population grows, and how fast the temperature of cookies rises in an oven. Translating between...
Slope Fields
If you build it, they will come.Consider the first-order differential equationWe can't solve this d.e. by thinking backwards, but we can still think about how a solution to this d.e. would behave....
Euler's Method
Given an IVP, we can use Euler's (pronounced "Oiler's") method to find approximate values of the solution to the IVP (near the initial point). Before we fully explain what Euler's method is, we n...
Accuracy and Usefulness of Euler's Method
Things to remember about Euler's Method:Euler's Method gives only approximate values unless the function happens to be a straight line, in which case Euler's Method gives exact values of the functi...
In the Real World
Differential equations, believe it or not, show up everywhere.There are math departments studying how differential equations relate to biology using differential equations for the study of diseases...