This new book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. The world is changing. Because of the theory of wavelets, Fourier analysis is ever more important and central. And applications are a driving force behind much of mathematics.This text presents a more balanced picture. The text covers differential equations (both ordinary and partial), Fourier analysis and applications in equal measure and with equal weight.