

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.

• ## 2: Higher order linear ODEs

In this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different from those discussed earlier, and the solutions tend to involve trigonometric functions as well as exponential functions. Here we concentrate primarily on second-order equations with constant coefficients.

• ## 6: The Laplace Transform

The Laplace transform can also be used to solve differential equations and reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra.

• ## 8: Nonlinear Equations

Linear equations suffice in many applications, but in reality most phenomena require nonlinear equations. Nonlinear equations, however, are notoriously more difficult to understand than linear ones, and many strange new phenomena appear when we allow our equations to be nonlinear.