Another beautiful branch of mathematics. While you're in high school, you may wonder what's the point of introducing imaginary number i, does it really exists? Is it really useful? In an introductory complex analysis course, you will see the beauty of this construction. Gauss, Riemann, Weierstrass and Cauchy are key figures in this area. Key concepts to learn are: analytic functions, Cauchy-Riemann equations, contour integral, Cauchy-Goursat theorem, residues and poles.
- Ablowitz M.J. and Fokas A.S. Complex Variables: Introduction and Applications
- Bass R.F. Complex Analysis [.pdf] (FREE!)
- Beck M., Marchesi G. and Pixton D. A First Course in Complex Analysis (FREE!)
- Brown J.W. and Churchill R.V. Complex Variables and Applications - Study up to chapter 7.
- Cain G. Complex Analysis (FREE!)
- Carne T.K. Complex Analysis [.pdf] (FREE!)
- Chen W.W.L. Introduction to Complex Analysis (FREE!)
- Kuttler K. Complex Analysis [.pdf] (FREE!)
- Marsden J.E. and Hoffman M.J. Basic Complex Analysis - See Marsden's page for errata.
- Ponnusamy S. and Silverman H. Complex Variables with Applications
- Saff E.B. and Snider A.D. Fundamentals of Complex Analysis
- Spiegel M.R. Schaum's Outline of Complex Variables
- Tao T. Complex Analysis for Applications (FREE!)
- Wilkins D.R. Functions of a Complex Variable (FREE!)
- Wunsch D.A. Complex Variables with Applications
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