Fourier's Series & Harmonics in Mathematical Physics by William Byerly
Fourier's Series & Harmonics in Mathematical Physics - Table of Contents
1. Introduction
2. Development in Trigonometric Series
3. Convergence of Fourier’s Series
4. Solution of Problems in Physics by the Aid of Fourier’s Integrals and Fourier’s Series
5. Zonal Harmonics
6. Spherical Harmonics
7. Cylindrical Harmonics (including Bessel’s Functions)
8. Laplace’s Equation in Curvilinear Coordinates; Ellipsoidal Harmonics
9. Historical Summary
10. Tables
What You Will Learn in Fourier's Series & Harmonics in Mathematical Physics
"An elementary treatise on Fourier's series and Spherical, Cylindrical, and Ellipsoidal Harmonics with Applications to Problems in Mathematical physics" by William Byerly is a foundational text that introduces the principles of "Fourier series" and their applications in mathematical physics. The book explains how periodic functions can be expressed as sums of sines and cosines, enabling precise analysis of vibrations, heat conduction, and wave phenomena. Byerly combines rigorous theory with practical examples, making complex concepts accessible to students and practitioners alike.
The book systematically develops the theory of harmonics, covering orthogonal functions, convergence, and boundary value problems. It provides detailed methods for solving physical problems using Fourier expansions, helping readers understand both the underlying mathematics and its real-world applications. The text emphasizes clarity, with step-by-step derivations and illustrative examples that reinforce key ideas.
Rich in exercises and applications, Byerly’s work bridges pure and applied mathematics. It is widely regarded as an essential reference for students, engineers, and physicists seeking to master Fourier analysis and its role in mathematical modeling. Whether for academic study or practical problem-solving, this book remains a timeless guide to understanding and applying "Fourier series" in science and engineering.
Book Details & Specifications
Title:
Fourier's Series & Harmonics in Mathematical Physics by William Byerly
Publisher:
Ginn & Company
Year:
1893
Pages:
316
Type:
PDF
Language:
English
ISBN-10 #:
1289509271
ISBN-13 #:
978-1289509279
License:
Public Domain Work
Amazon:
Amazon
About the Author: William Elwood Byerly
The author William Elwood Byerly
(1820–1906) was a prominent American mathematician and educator, known for his work in applied mathematics and mathematical physics. He served as a professor at Harvard University, teaching advanced mathematics and mechanics with clarity and rigor. Byerly is especially recognized for his contributions to "Fourier series" and harmonics. His book "Fourier’s Series and Harmonics in Mathematical Physics" became a key reference for students and engineers, blending theoretical concepts with practical applications in vibrations, waves, and heat conduction. His work continues to influence the study and teaching of applied mathematics today.
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