2
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ I would argue that Needham's book is not too broad. It is maybe voluminous, but it is such an easy and pleasant reading that really, size does not matter. Of course, it is not a proof-based book in the classical sense of the term, which is an aspect that may or may not be important to you. $\endgroup$ – An aedonist Aug 30 '17 at 9:29
  • 1
    $\begingroup$ I'm surprised by the claim that Conway has no exercises nor examples, as it has many of both. $\endgroup$ – Martin Argerami Aug 30 '17 at 13:58
  • $\begingroup$ @MartinArgerami;I didn't say that ;I said I want a book with lots of examples as examples help to do self-study $\endgroup$ – Learnmore Aug 30 '17 at 14:30
4
$\begingroup$

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

$\endgroup$
2
$\begingroup$

My favorite:

Robert B. Burckel: An introduction to classical complex analysis, Vol.1 (Birkhäuser).

$\endgroup$
1
$\begingroup$

A first course in complex analysis with application by Dennis G.Zill. this book covers all topics that you mentioned above.

$\endgroup$
1
$\begingroup$

Complex Analysis-Bak, Neumann should suit you.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.