An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics: With Applications to Problems in Mathematical Physics

Cosimo, Inc., 2007 - Science - 300 pages
First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on Fourier's series . solution of problems in physics by the aid of Fourier's integrals and Fourier's series . zonal harmonics . spherical harmonics . cylindrical harmonics (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).

What people are saying -Write a review

We haven't found any reviews in the usual places.

Contents

 CHAPTER 1 Zonal Harmonics lM194 11 Somjtioh of Problems i Physics sr the Aid op Fouriers Integrals 30 Development is Trigonometric Series 3064 48 Arts 4448 Logarithmic Potential Flow of electricity in an infinite plane 53 4 Temperatures due to instantaneous and to permanent heat sources and sinks 60 Arts 8890 Daetopment in Zonal Harmonic Series Integral of the product of 174
 CHAPTER VI 195 CHAPTER VII 219 CHAPTER IX 235 Historical Srauumr 267276 267 Tables 277287 277 Laplaces Equation is Cvbvimhsar Coordinates Ellipsoidal Harmonics 588286 286 Copyright

Popular passages

Page 19 - Let these roots be called a and /S, then is a solution, and since it contains two arbitrary constants it is the general solution.
Page 12 - ... about an axis through the centre perpendicular to the plane of the figure.
Page 9 - As (5) must be true no matter what the value of x, the coefficient of any given power of x, as for instance a;*, must vanish. Hence (k + 2) (A + 1K+, - k(k + l)at + m(m + !)лл— 0 (6) m...