Guide to Essential Math, 2nd Edition

Chapter 8

Differential Equations

To paraphrase the Greek philosopher Heraclitus,“The only thing constant is change.” Differential equations describe mathematically how things in the physical world change—both in time and in space. While the solution of an algebraic equation is usually a number, the solution of a differential equation gives a function.

In this chapter, we consider ordinary differential equations (ODEs), which involve just two variables, say, an independent variable and a dependent variable . Later we will take up partial differential ...