An introduction to the theory of complex variables

An introduction to the theory of complex variables R.S Johnson Download free books at R.S Johnson An introduction to the theory of complex variables Download free eBooks at bookboon.com An introduction to the theory of complex variables © 2012 R.S Johnson & bookboon.com ISBN 978-87-403-0162-5 Download free eBooks at bookboon.com An introduction to the theory of complex variables Contents Contents Preface to these two texts Part I: An introduction to complex variables Preface 10 Introduction 11 Complex Numbers 12 1.1 Elementary properties 12 1.2 Inequalities 15 1.3 Roots 16 Exercises 18 Functions 20 2.1 Elementary functions 21 Exercises 27 Diferentiability 29 3.1 Deinition 29 3.2 he derivative in detail 31 3.3 Analyticity 37 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 Download free eBooks at bookboon.com Click on the ad to read more An introduction to the theory of complex variables 3.4 Contents Harmonic functions 38 Exercises 41 Integration in the complex plane 42 4.1 he line integral 42 4.2 he fundamental theorem of calculus 45 4.3 Closed contours 46 Exercises 51 he Integral heorems 53 5.1 Cauchy’s Integral heorem (1825) 53 5.2 Cauchy’s Integral Formula (1831) 56 5.3 An integral inequality 63 5.4 An application to the evaluation of real integrals 66 Exercises 70 Power Series 71 6.1 he Laurent expansion (1843) 73 Exercises 78 he Residue heorem 80 7.1 he (Cauchy) Residue heorem (1846) 80 7.2 Application to real integrals 84 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Download free eBooks at bookboon.com Click on the ad to read more ...R.S Johnson An introduction to the theory of complex variables Download free eBooks at bookboon.com An introduction to the theory of complex variables © 2012 R.S Johnson &... bookboon.com An introduction to the theory of complex variables Contents Contents Preface to these two texts Part I: An introduction to complex variables Preface 10 Introduction 11 Complex Numbers... introduction to the theory of complex variables 3.4 Contents Harmonic functions 38 Exercises 41 Integration in the complex plane 42 4.1 he line integral 42 4.2 he fundamental theorem of calculus