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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2aVi a₁ a₂ sin 2x axis b₁ coefficients constant coördinates cos² cosh Crelle's Journal curve cylinder differential equation dx dx edition ellipsoid EXAMPLES external point finite formula Fourier's Series given function Green's Theorem Hence integral Jo(x Lamé's Laplace's Equation Legendre's Equation mth degree mx.dx obtained odd function P₁ P₁(cos P₂ P₂(cos particular solutions plane Pm(cos Pm(x potential function potential function due problem radius reduces required solution roots satisfy second member Sf(x sin x sin² sinh solution of Laplace's solution of Legendre's solve sphere Spherical Harmonic spheroid string substitute Surface Spherical Harmonic Surface Zonal Harmonic temperature zero term Unabridged republication V₁ vibration Zonal Harmonic αλ αμ λ² µ² Μπλ π π пу Пх