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Exercises

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....

Slopes (Again)

We know that the slope of a line is given byor bySince y is usually the dependent variable and x is usually the independent variable, you may also seeorThe symbol Δ is the Greek capital letter "De...

Tangent Line Approximations (Again)

Tangent line approximation can also be called local linearization, linear approximation, and probably a bunch of other names. The important thing is that you're using a line to approximate a curve....

The Scoop on Euler

Euler's Method is a bunch of tangent line approximations stuck together. The basic idea is that you start with a differential equation and a point. You do a tangent line approximation to get a new...

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...
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