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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 CHAPTER V. Zonal Harmonics CHAPTER VI. Spherical Harmonics CHAPTER VII. Cylindrical Harmonics (Bessel's Functions) CHAPTER VIII. Laplace's Equation in Curvilinear Cöordinates. Ellipsoidal Harmonic CHAPTER IX. Historical Summary