An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics
Originally 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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CONVERGENCE OF FOURIER SERIES 6668
HISTORIcAL SDMMARY 267276
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a2 sin 2x abscissas approaches axis becomes Bessel's Equation circles of latitude coefficients convergent corresponding cosh cosines curvilinear coordinates cylinder derivative differential equation edition ellipsoid Ellipsoidal Harmonics equal to zero EXAMPLES expressed external point finite flow of heat formula Fourier's Equation Fourier's Series given function Hence homogeneous homogeneous function indefinitely increased initially distorted integer Jm(x Laplace's Equation Laplacian Legendre's Equation limiting value linear ma.da membrane mth degree multiply mx.dx obtained odd function particular solution plane positive integer potential function potential function due radius reduces required solution roots second member Show sin x sin2 sine sinh slab solid solution of Bessel's solution of Laplace's solution of Legendre's solution of vm solve spherical coordinates spheroid string substitute Surface Spherical Harmonic Surface Zonal Harmonic tion Trigonometric Series Unabridged republication unit sphere vibration whence whole number Zonal Harmonic