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.