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I am an engineering student trying to study mathematical analysis because it will help me in my post graduate studies.

My problem is that when I searched the internet I found that some university sites recommend topology class while others do not. Also, some recommend a "mathematical analysis" text before going into real and complex analysis. The problem is in the diversity of titles.

So my question is, if I want to study real and complex analysis, what topics do I need and under what book titles are those topics given?

I want to emphasis that am searching in English so I ask that all book titles are according to an American or English syllabus. If you are of a different nationality, please tell me the order of studying real and complex analysis in your country.

P.S. The particular topics I want to study are functions of complex variables, integration in the complex plane, series and residues, and conformal mapping.

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  • $\begingroup$ What topics are you aiming for in your studies? $\endgroup$ – Chris C Dec 29 '14 at 17:09
  • $\begingroup$ @ChrisC Real analysis and Complex analysis $\endgroup$ – Eng_Boody Dec 29 '14 at 17:37
  • $\begingroup$ I mean which part of the subject will help your studies (probability measures, Lp-spaces,...)? Many graduate courses are somewhat aligned with the interests of the instructor and/or department which explains the variability. $\endgroup$ – Chris C Dec 29 '14 at 19:35
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    $\begingroup$ From what you said, I think Marsden/Hoffman's Elementary Classical Analysis (for real analysis) and Marsden/Hoffman's Basic Complex Analysis might be a good fit for you. $\endgroup$ – Dave L Renfro Dec 30 '14 at 17:34
  • $\begingroup$ @ChrisC , I want to study : - functions of complex variables , - integration in complex plan , -series and residues, - conformal mapping ...... sorry for being late in responce $\endgroup$ – Eng_Boody Jan 1 '15 at 17:10
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If you want to study real and complex analysis, a classic text is W. Rudin's "Real and complex analysis". In fact pretty much anything by Rudin is excellent.

A more accessible title of Rudin is "Principles of Mathematical Analysis".

Another classic complex analysis book is by Alfors, although the title by Stewart and Tall, both called "Complex analysis", might be more accessible (and slightly more modern in its approach).

These are all introductory (1st year mathematics undergraduate) texts - for UK universities.

Rudin's "Real and complex analysis" does contain advanced material, and is probably not suitable as an introductory text for an engineering student. Worth a look, just in case.

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  • $\begingroup$ I would not say those are freshman undergraduate texts but first year graduate that require much knowledge of how to prove things that an engineer might not be familiar with. $\endgroup$ – Chris C Jan 1 '15 at 23:36
  • $\begingroup$ @ChrisC I meant to include Rudin's "Principles of Mathematical Analysis". The OP does state "Post graduate studies". I am answering from a UK university perspective. $\endgroup$ – Rusan Kax Jan 2 '15 at 1:10
  • $\begingroup$ the problem for me in studying from applied approach is the epsilon-delta definitions and the definition of neighborhoods which is defined in topology .. which pulls downward toward purism $\endgroup$ – Eng_Boody Jan 2 '15 at 1:21
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    $\begingroup$ @Eng_Boody OK, I'm not sure what you mean, exactly. But it sounds like you need to start right at the basics of real analysis. Try "Introduction to Analysis" by Gaughan: amazon.com/Introduction-Analysis-Applied-Undergraduate-Texts/dp/… $\endgroup$ – Rusan Kax Jan 2 '15 at 2:03
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    $\begingroup$ @Eng_Boody: As I suggested in my answer to another question of yours (matheducators.stackexchange.com/a/5856/376), you may wish to try Alcock's new book How to Think about Analysis to help you with the epsilon-delta definitions. However, perhaps I have misunderstood what you are looking for. $\endgroup$ – J W Jan 2 '15 at 14:10
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A would agree with Rusan Kax but like to add that another good introductory analysis book is by Tom Apsotol. Also, for beginners in analysis, I would say either start with Rudin's baby analysis or Apsotol. As for Complex analysis, you may want to learn some abstract algebra and/or number theory since many texts incorporate the use of Algebra. Books in complex analysis that I think are good for beginners are Graduate Text in Complex Analysis by Serge Lang and Complex Analysis by Alfors as well. If you are keen to learning some Algebra, I would suggest Dummit and Foote; however, it is not a small text.

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