I am an undergrad student and this semester I took a complex analysis course. can anyone recommend $\mathbf {a \ complex\ analysis\ book\ with\ a\ lot\ of\ exercises?}$ I read Ahlfors's and Joseph Back's books but they only have a little number of exercises.

Course Content:

  1. The Complex Plane: Complex Numbers, Topology of the Complex Plane.

  2. Complex Functions: Limits and Continuity, Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Elementary Transcendental Functions.

  3. Complex Integration: Complex-valued functions of real variables, Complex Line Integrals, Cauchy-Goursat Theorem, Cauchy Integral Formula, The Mean Value Property and the Maximum Modulus Principle.

  4. Power Series: Series of Complex Numbers, Uniform Convergence, Power Series, Power Series Expansion of an Analytic Function, The Zeros of an Analytic Function.

  5. Laurent Series and Isolated Singularities: Laurent Series, Isolated Singularities of Analytic Functions

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    $\begingroup$ Maybe you can read E.M.Stein's book: complex analysis. $\endgroup$ – LoveQYG Sep 6 '18 at 5:14
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    $\begingroup$ I have used Daniel Alpay's A complex Analysis Problem Book. Maybe you could take a look at it. $\endgroup$ – xbh Sep 6 '18 at 5:18
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    $\begingroup$ Hi - as an undergrad Priestley was standard (at several unis in the uk e.g. Cambridge). Has lots of exercises though in some sense presentation perhaps slightly more elementary. I read Ahlfors too at the time for another perspective and the two worked well together. Covers most - actually probably all of the above (been a while!) as well as some topics like Fourier / Laplace transforms. $\endgroup$ – Mehness Sep 6 '18 at 5:28
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    $\begingroup$ I seem to remember that Churchill (now Brown and Churchill) has lots of exercises. Maybe you can take a look inside it on amazon. But buy a cheap used copy. The text material will be pretty simple for someone who's read Alfors. $\endgroup$ – saulspatz Sep 6 '18 at 5:28
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    $\begingroup$ Brown and Churchill is the best one. $\endgroup$ – Emma Sep 6 '18 at 5:29


1) Complex variables and applications by J.W.Brown and R.V.Churchill

2) Foundations of complex analysis by S.Ponnusamy

Both book contains a lot of good exercise problems for grow up the knowledge!


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