Fourier Series and Boundary Value Problems with Engineering Applications (Textbooks in Mathematics)

This book is a comprehensive and time-tested guide to the mathematical theory of Fourier series and boundary value problems, with a strong emphasis on engineering applications. Over the past two decades, Fourier Series and Boundary Value Problems with Engineering Applications has been rigorously refined and tested in classroom settings, ensuring its effectiveness as a teaching and learning resource.

The journey begins with a thorough development of Fourier series, a cornerstone of modern mathematics and engineering. The Fourier series provides a powerful framework for analyzing periodic functions and decomposing complex signals into simpler sinusoidal components. This foundational knowledge is then extended to boundary value problems, which arise naturally in the study of physical phenomena such as heat flow, vibrations, and wave propagation.

A distinctive feature of this book is its focus on applications in both rectangular and spherical coordinates. These coordinate systems are essential for modeling problems in diverse engineering contexts. Additionally, the book addresses partial differential equations on unbounded domains and ordinary differential equations.

Whether you are a student encountering Fourier series and boundary value problems for the first time, an educator seeking a reliable and classroom-tested resource, or a professional looking to refresh your knowledge, this book offers a clear exposition, practical focus, and extensive problem sets, making it an indispensable companion for mastering the mathematical tools that underpin modern engineering.

Youssef N. Raffoul is Professor and Graduate Program Director at the University of Dayton. He holds a Ph.D. from Southern Illinois University. He is the recipient of the University of Dayton College of Arts and Sciences’ Award for Outstanding Scholarship (twice), and the University of Dayton Alumni Award in Scholarship. Professor Raffoul has published over one hundred and sixty articles in prestigious journals in the area of functional differential equations, difference equations, and dynamical systems on time scales. He was honored by the Lebanese government with the Career in Science Award. The Archbishop of Lebanon awarded him the Lifetime Achievement Award. Most notably, and he is the recipient of the Order of Merit, Silver Medal with Distinction and awarded by the president of Lebanon, General Aoun.