Bessel Functions & Their Applications to Physics by Andrew Gray
Bessel Functions & Their Applications to Physics - Table of Contents
1. Introductory — Bernoulli’s Problem, Fourier’s Problem, Bessel’s Problem, Laplace’s Equation, Cylindrical Harmonics
2. Solution of the Differential Equation — Method of Frobenius, Definition of Neumann’s Bessel Function, Recurrence Relations, Special Values for Half-Odd-Integer Orders
3. Functions of Integral Order; Series Expansions — Bessel Coefficients, Expansion of (x^n), Addition Theorem, Schlömilch’s Expansion
4. Semiconvergent Expansions
5. The Zeros of the Bessel Functions
6. Fourier–Bessel Expansions
7. Complex Theory
8. Definite Integrals Involving Bessel Functions
9. The Relation of the Bessel Functions to Spherical Harmonics
10. Vibrations of Membranes (Applications)
11. Hydrodynamics — Stokes’ Current Function, Cylindrical Vortex Oscillations, Wave Motion in a Cylindrical Tank, Rotating Liquid, Viscous Fluid Motion
12. Steady Flow of Electricity or Heat in Uniform Isotropic Media — Potentials, Circular Disk, Conductors, etc.
13. Propagation of Electromagnetic Waves Along Wires — Field Equations, Guided Waves, Diffusion, etc.
14. Diffraction of Light — Axisymmetric Case, Intensity Expressed by Bessel Functions, Maxima and Minima, Graphical Analysis, Struve’s Function
15. Miscellaneous Applications
What You Will Learn in Bessel Functions & Their Applications to Physics
"A Treatise on Bessel Functions and Their Applications to Physics" by "Andrew Gray" is a detailed text on "Bessel functions", a class of "special functions" that play a crucial role in "mathematical physics" and applied mathematics. The book systematically explores their properties, differential equations, series expansions, and integral representations, offering a thorough theoretical foundation.
Gray emphasizes the practical use of "Bessel functions" in solving physical problems, including heat conduction, wave propagation, vibrations in circular membranes, and cylindrical systems. The book provides worked examples, tables, and exercises that illustrate both the computational techniques and theoretical principles, bridging the gap between abstract theory and real-world applications.
Renowned for clarity and depth, Gray’s text remains an essential reference in "function theory" and applied mathematics. Its rigorous treatment of Bessel functions, combined with numerous examples from physics, makes it invaluable for students, researchers, and engineers. By connecting classical mathematical theory with practical physical problems, the book continues to be a key resource for understanding and applying "Bessel functions" in both theoretical and applied contexts.
Book Details & Specifications
Title:
Bessel Functions & Their Applications to Physics by Andrew Gray
Publisher:
Macmillan
Year:
1895
Pages:
314
Type:
PDF
Language:
English
ISBN-10 #:
1528160398
ISBN-13 #:
978-1528160391
License:
Public Domain Work
Amazon:
Amazon
About the Author: Andrew Gray
The author Andrew Gray
(1847–1925) was a Scottish mathematician and physicist known for his work on "Bessel functions", "special functions", "mathematical physics", and "function theory". He taught at University College, Dundee, and focused on making advanced mathematical concepts accessible through clear explanations and practical examples. Gray authored "Bessel Functions & Their Applications to Physics", a seminal text combining rigorous proofs with real-world applications. His work remains influential in "applied mathematics", physics, and engineering, providing students and researchers with a strong foundation in both theoretical and practical aspects of Bessel functions.
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