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.