Tung K.K. Partial Differential Equations and Fourier Analysis: A Short Introduction

Applied Mathematics University of Washington, 2005. — 195 pages.This short book is intended for a one-semester course for students in the sciences and engineering after they have taken one year of calculus and one term of ordinary differential equations. For universities on quarter systems, sections labelled "optional" can be omitted without loss of continuity. A course based on this book can be offered to sophomores and juniors.
Examples used in this book are drawn from traditional application areas such as physics and engineering, as well as from biology, music, finance and geophysics. I have tried, whenever appropriate, to emphasize physical motivation and have generally avoided theorems and proofs. I also have tried to teach solution techniques, which will be useful in a student's other courses, instead of the theory of partial differential equations.
I believe that the subjects of partial differential equations and Fourier analysis should be taught as early as feasible in an undergraduate's curriculum. Towards this end the book is written to present the subject matter as simply as possible. Ample worked examples are given at the end of the chapters as a further learning aid. Exercises are provided for the purpurpose of reinforcing standard techniques learned in class. Tricky problems, whose purpose is mainly to test the student's mental dexterity, are generally avoided.