Transcription of INTRODUCTION TO THE SPECIAL FUNCTIONS OF ... - Physics
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INTRODUCTION TO THE SPECIAL FUNCTIONS OF ... - Physics
INTRODUCTION TO THE SPECIAL FUNCTIONS OF MATHEMATICAL Physics with applications to the physical and applied sciences John Michael Finn April 13, 2005 CONTENTS Contents iii Preface xi Dedication xvii 1. Infinite Series 1 1 cautionary tale 2 series 6 Proof by mathematical induction 6 of an infinite series 7 Convergence of the chessboard problem 8 Distance traveled by A bouncing ball 9 remainder of a series 11 about series 12 Formal definition of convergence 13 series 13 Alternating Harmonic Series 14 Convergence 16 Distributive Law for scalar multiplication 18 Scalar multiplication 18 Addition of seri
The course begins with review of infinite series and complex analysis, then covers Gamma and Elliptic functions in some de-tail, before turning to the main theme of the course: the unified study of the most ubiquitous scalar partial differential equations of physics, namely the wave, diffusion, Laplace, Poisson, and Schrödinger equations.
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