Differential equations: Here is a set

Here is a set of notes used by Paul Dawkins to teach his Differential Equations course at Lamar University. Included are most of the standard topics in 1st and 2nd order differential equations, Laplace transforms, systems of differential eqauations, series solutions as well as a brief introduction to boundary value problems, Fourier series and partial differntial equations. In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. What is a Differential Equation? A differential equation is an equation involving the derivatives of the dependent variable concerning the independent variable. For example. d 2 y d x + x = 0 dxd2y + x = 0. Here, x is the independent variable, and y is the dependent variable.