Calculus of Residua Complex Functions Theory a-2 Leif Mejlbro Download free books at Leif Mejlbro Calculus of Residua Complex Functions Theory a-2 Download free eBooks at bookboon.com Calculus of Residua – Complex Functions Theory a-2 © 2010 Leif Mejlbro & Ventus Publishing ApS ISBN 978-87-7681-691-9 Download free eBooks at bookboon.com Contents Calculus of Residua Contents Introduction 1.1 1.2 1.3 9 11 22 24 29 29 1.5 1.6 1.7 Power Series Accumulations points and limes superior Power series Expansion of an analytic function in a power series Some basic power series Linear differential equations Existence and Uniqueness Theorems Practical procedures for solving a linear differential equations of analytical coeficients Zeros of analytical functions Simple Fourier series The maximum principle 2.1 2.2 2.3 2.4 Harmonic Functions Harmonic functions The maximum principle for harmonic functions The biharmonic equation Poisson’s Integral Formula 55 55 59 61 64 1.4 31 40 44 48 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges An environment in which your expertise is in high demand Enjoy the supportive working atmosphere within our global group and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Click on the ad to read more Download free eBooks at bookboon.com Contents Calculus of Residua 2.5 2.6 Electrostatic ields Static temperature ields 67 69 3.1 3.2 3.3 3.4 3.4.1 3.4.2 3.4.3 3.5 3.5.1 3.5.2 3.5.3 3.6 3.7 3.8 3.9 Laurent Series and Residua Laurent series Fourier series II Solution of a linear dierential equation by means of Laurent series Isolated boundary points Case I, where an = for all negative n Case II, where an ≠ 0 for a nite number of negative n Case III, where an ≠ 0 for innitely many negative n Innity ∞ as an isolated boundary point Case I*, where an = for all positive n Case II*, where an ≠ 0 for nitely many positive n Case III*, where an ≠ 0 for innitely many positive n Residua Simple rules of computation of the residuum at a (inite) pole The residuum at ∞ Summary of the Calculus of Residua 71 71 79 80 84 84 85 87 89 91 91 92 93 94 102 106 4.1 4.2 Applications of the Calculus of Residua Trigonometric integrals Improper integrals 111 111 113 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Click on the ad to read more Download free eBooks at bookboon.com ...Leif Mejlbro Calculus of Residua Complex Functions Theory a-2 Download free eBooks at bookboon.com Calculus of Residua – Complex Functions Theory a-2 © 2010 Leif Mejlbro & Ventus... n Residua Simple rules of computation of the residuum at a (inite) pole The residuum at ∞ Summary of the Calculus of Residua 71 71 79 80 84 84 85 87 89 91 91 92 93 94 102 106 4.1 4.2 Applications... OSRAM Click on the ad to read more Download free eBooks at bookboon.com Contents Calculus of Residua 2.5 2.6 Electrostatic ields Static temperature ields 67 69 3.1 3.2 3.3 3.4 3.4.1 3.4.2 3.4.3 3.5