Saturday, 7 February 2015

reference request - Book for complex analysis covering specific requirements



I want a book on Complex Analysis for self-study which covers the following syllabus in detail.





  • Algebra of complex numbers, the complex plane, polynomials, power series,
    transcendental functions such as exponential, trigonometric and hyperbolic functions.


  • Analytic functions, Cauchy-Riemann equations.
    Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum
    modulus principle, Schwarz lemma, Open mapping theorem.


  • Taylor series, Laurent series, calculus of residues.
    Conformal mappings, Mobius transformations.





I searched for various books here which mostly included




  • Functions of one complex variable by J.B.Conway.

  • Visual complex analysis-Needham

  • Stein Shakarchi.



The two of them Conway and Stein don't contain examples and exercises for self -study.




Needham is too broad to be used as a text.



I want to get a book which will cover the syllabus in detail and give handsome exercises and examples and hints to the exercises(if possible).



Please suggest a text accordingly as it is not possible for me to find atext on my own.


Answer



My favorite: L. V. Ahlfors: Complex Analysis. Also includes many examples and exercises.


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