An Elementary Treatise on Fourier’s Series and Spherical, Cylindrical, and Ellipsoidal Harmonics With Applications to Problems in Mathematical Physics

Written by: William Elwood Byerly (Harvard University)

Another great vintage math textbook from Gutenberg. This math text by William Elwood Byerly, a professor at Harvard University, is full of well-explained examples. Despite the age, this text uses plain language to explain terms and would probably make a great supplement to a more modern text on the same subject.

Students will need to be familiar with differential and integral calculus.

Table of Contents

Chapter I: Introduction
Chapter II: Development in Trigonometric Series
Chapter III: Convergence of Fourier’s Series
Chapter IV: Solution of Problems in Physics by the Aid of Fourier’s Integrals and Fourier’s Series
Miscellaneous Problems
I. Logarithmic Potential. Polar Coordinates
II. Potential Function in Space
III. Conduction of Heat in a Plane
IV. Conduction of Heat in Space
Chapter V: Zonal Harmonics
Chapter VI: Spherical Harmonics
Chapter VII: Cylindrical Harmonics (Bessel’s Functions)
Chapter VIII: Laplace’s Equation in Curvilinear Coordinates. Ellipsoidal Harmonics
Chapter IX: Historical Summary
Appendix
   

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An Elementary Treatise on Fourier’s Series and Spherical, Cylindrical, and Ellipsoidal Harmonics With Applications to Problems in Mathematical Physics


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