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

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Cosimo, Inc., 2007 - Science - 300 pages
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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).
 

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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
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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.
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