Fourier Analysis by Eric Stade

Book Preface

This book is aimed primarily at upper level undergraduate and early graduate students in mathematics. I hope and believe, though, that it will also be of value to engineering students (particularly those studying electrical engineering, signal processing, and the like); to students in physics and other sciences; to scientists and technicians who use Fourier analysis “in real life”; and to anyone fostering an appreciation of the beauty and power of Fourier analysis, or a desire to acquire such an appreciation.

The prerequisites are few: A good grasp of calculus in one and several variables will suffice. A number of more advanced concepts are encountered in the course of the text – complex numbers, linear algebra, differential equations, and a good truckload or two of ideas from real analysis. But familiarity with these concepts is not required; in fact, I hope that the reader who has not encountered them previously will find
herein a good introduction to them.

I’ve strived for relatively high degrees of mathematical rigor and completeness. But at the same time, I’ve tried to place the math in scientific and technological (and historical) context and to infuse due detail into discussions of specific applications. (The detail is, though, for the most part limited to that which relates to Fourier analysis. Real-world applications necessarily entail myriad other considerations; I’ve avoided reflection on these in order to stay on point, and because I understand them only marginally.)