Complex Analysis: The Hitchhiker's Guide to the Plane

Preface Acknowledgement 1. The origins of complex analysis and a modern viewpoint 2. Algebra of the complex plane 3. Topology of the complex plane 4. Power series 5. Differentiation 6. The exponential function 7. Integration 8. Angles, logarithms and the winding number 9. Cauchy's theorem 10. Homotopy versions of Cauchy's theorem 11. Taylor series 12. Laurent series 13. Residues 14. Conformal transformations 15. Analytic continuation Index.