## An Elementary Treatise on Fourier's Series: and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in MathematicalOriginally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is assumed in many other studies but seldom available in such concise form. The development of functions, series, and their differential equations receives detailed explanations, and throughout the text, theory is applied to practical problems, with the solutions fully worked out. In addition, 190 problems, many with hints, are included. 1893 edition. Appendix of 6 tables. |

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absolutely convergent axis Bessel’s Function coefficients coeﬂicient convergent convergent series coordinates cosh curve curvilinear coordinates cylinder differential equation doublet of strength edition ellipsoid Ellipsoidal Harmonics equal to zero EXAMPLES external point f(ac ff(A ﬁgures ﬁnd ﬁnite ﬁrst member ﬂow of heat formula Fourier’s Series given function Hence homogeneous homogeneous function indeﬁnitely increased inﬁnite initial temperature initially distorted integer Lamé Lamé’s Laplace’s Equation Laplacian Legendre’s Equation limiting value lines of ﬂow membrane method mth degree multiply obtained odd function parallelopiped particular solutions plane positive integer potential function due radius rectangular reduces required solution roots satisﬁes satisfy second member Show sin2 sinh slab solid solution of Laplace’s solution of Legendre’s solve spherical coordinates spheroid string substitute Surface Spherical Harmonic symmetrical temperature zero theory Trigonometric Trigonometric Series Unabridged republication unit sphere vibration whence whole number Zonal Harmonic