Contents Part I Angles Chapter 1 1.1 Sets 1.2 Complex numbers 1.3 Upper bounds 1.4 Square roots 1.5 Distance Chapter 2 2.1 Infinite series 2.2 Tests for convergence 2.

3 The Cauchy project Chapter 3 3.1 Continuity 3.2 Real continuous functions Chapter 4 4.1 The exponential function 4.2 The trigonometric functions 4.3 Periodicity 4.4 The hyperbolic functions Chapter 5 5.1 The argument of a complex number 5.

2 Logarithms 5.3 Exponents 5.4 Continuity of the logarithm Part II Basic Complex Analysis Chapter 6 6.1 Open and closed sets 6.2 Connected sets 6.3 Limits 6.4 Compact sets 6.5 Homeomorphisms 6.

6 Uniform convergence Chapter 7 7.1 Plane curves 7.2 The index of a curve 7.3 Properties of the index Chapter 8 8.1 Polynomials 8.2 Power series 8.3 Analytic functions 8.4 Inequalities 8.

5 The zeros of analytic functions Chapter 9 9.1 Derivatives 9.2 Line integrals 9.3 Inequalities 9.4 Chains and cycles 9.5 Evaluation of integrals 9.6 Cauchy's Theorem 9.7 Applications Chapter 10 10.

1 Conformal mapping 10.2 Stereographic projection 103. Mobius transformations Part III Interactions with Plane Topology Chapter 11 11.1 Simply connected domains 11.2 The Riemann Mapping Theorem 11.3 Branches of the argument 11.4 The Jordan Curve Theorem 11.5 Conformal mapping of a Jordan domain Appendix Bibliography Index.