title: Complex Functions: An Algebraic and Geometric Viewpoint
author:  Gareth A. Jones 
description: "...a very nice treatment which emphasizes the unity of mathematics...Several years ago the reviewer wanted to teach an undergraduate course that gave an introduction to hyperbolic geometry, Mbius transformations and discrete groups. There was no suitable undergraduate text. This book fills that void," Mathematical Reviews<br /><br />"Well motivated with good selection of problems at the end of each chapter." American Mathematical Monthly<br /><br />"...clear and well written...Its message, admirably conveyed, is that mathematics is not a collection of neat parcels, the contents of one being blind to the contents of another." Times Higher Education Supplement<br /><br />"...clearly presented...a delightful book..." American Scientist
zlib_text: 2 
  Leif Mejlbro
  Elementary Analytic Functions 
  Complex Functions Theory a-1
  Download free eBooks at bookboon.com
  
  3 
  Elementary Analytic Functions – Complex Functions Theory a-1
  © 2010 Leif Mejlbro & Ventus Publishing ApS
  ISBN 978-87-7681-690-2
  Download free eBooks at bookboon.com
  
  Elementary Analytic Functions
  4 
  Contents
  Contents
   
  Introduction  
  7
  1  
  The Complex Numbers  
  9
  1.1  
  Rectangular form of complex numbers 
  10
  1.2  
  Polar form of complex numbers 
  13
  1.3  
  The binomial equation 
  20
  1.4  
  The general equation Az2 + Bz + C = 0 of second degree  
  26
  1.5  
  The equations of third and fourth degree  
  27
   
  The equation of third degree 
  28
   
  The equation of fourth degree 
  31
  1.6  
  Rational roots and multiple roots of a polynomial 
  32
   
  Procedure of nding rational roots  
  33
   
  Procedure of nding multiple roots  
  35
  1.7  
  Symbolic currents and voltages. Time vectors 
  37
  2  
  Basic Topology and Complex Functions  
  40
  2.1  
  Basic Topology 
  40
   
  Topology of open sets 
  42
   
  Compact sets 
  