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Real and complex Analysis

  1. Jul 4, 2011 #1
    I have never studied analysis as i am graduate student in engineering. Can any one point me the elementary book on real and complex analysis preferably junior, undergraduate level book. I found this 2. Can any one math graduate student comment or put some advice onto it.

    1. Elementary Real and Complex Analysis by Georgi E. Shilov
    2. Real and Complex Analysis by Walter Rudin.

    I am trying to do self study in math preferably undergraduate level math. Also for topology I found this book.
    1. Topology without tears.
    Are there basic books for the first time like mild treatment for the materials.I don't prefer bulky book.
     
  2. jcsd
  3. Jul 4, 2011 #2
    Rudin's Real and Complex Analysis is absolutely not an introductory textbook; it's something you would read after having had a very solid introduction to the field (and there are better books out there anyway, in my opinion). I'm a big fan of Shilov's book, and if you have any experience at all with proof based mathematics it would work very well as an introduction. If you're less comfortable with writing proofs, there are some analysis texts out there designed for students with little or no experience in abstract math. A few good ones...

    Understanding Analysis - Abbot
    Elementary Analysis: The theory of calculus - Ross

    The above two are very gentle introductions and very well written, but you'd probably want to move on to something a little more substantial afterwards (like Shilov).

    For topology (which I applaud you for studying, since it's one of the most interesting areas in mathematics), I would probably wait until you've studied some analysis (and algebra, if you haven't already), since analysis will motivate a lot of the topics in topology. I haven't read Topology without tears myself, but I've heard good things. Munkres' Topology is pretty standard, and is generally considered to be fantastic. If you're looking for a bit of a different perspective, Lee's "Introduction to topological manifolds" is a good introduction (though it assumes a working knowledge of group theory and comfort with analysis), but it's very nonstandard (written from the perspective of a differential geometer).
     
    Last edited: Jul 4, 2011
  4. Jul 4, 2011 #3
    for an engineer this book is about as good as it gets. the last third has a bunch of applications, from fluids, E&M, etc:

    414GMxWpCXL._SS500_.jpg
    https://www.amazon.com/Complex-Vari...=sr_1_1?s=books&ie=UTF8&qid=1309810861&sr=1-1

    ...& if you want to save your $150
    http://www.abebooks.com/servlet/Sea...hurchill&sts=t&tn=complex+variables&x=66&y=15
     
  5. Jul 4, 2011 #4

    micromass

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    One of the best complex analysis books is the ine by Bak and Newman. See https://www.amazon.com/Complex-Analysis-Joseph-Bak/dp/0387947566

    As for Real analysis, I've heard good things of Berberian's books. So it's worth to check out. If you want to go for Rudin, then start of with "Principles of Real analysis" and not with "Real analysis and Complex Analysis".
     
  6. Jul 4, 2011 #5
    If you're not too experienced with proof writing, I recommend Elementary Analysis by Ross. It's a very gentle introduction to analysis. This book solely deals with analysis on the real numbers, and does not concern itself with metric spaces or anything. The problems are very friendly and I think it has hints in the back. A great self study and first analysis book.

    https://www.amazon.com/Elementary-A...8111/ref=sr_1_1?ie=UTF8&qid=1309818784&sr=8-1

    If you want something tougher which does more abstract work, I'd recommend my favorite undergraduate real analysis book is by N. L. Carothers:

    https://www.amazon.com/Real-Analysi...=sr_1_1?ie=UTF8&s=books&qid=1309818972&sr=1-1

    Both of these books are fairly priced (about 50 bucks) and very readable. The exercises are also very helpful and the books are great choices for self-study.
     
  7. Jul 4, 2011 #6
    Are these subjects really useful to an engineering student?
     
  8. Jul 4, 2011 #7
    Depends on what you intend to specialize in. If, for example, you want to be really strong in theoretical foundation in system/control/signal, knowledge in real analysis (and math in general) is extremely useful.
     
  9. Jul 4, 2011 #8
    How about aerospace propulsion (chemical rocket and experimental) and computational fluid dynamics?
     
  10. Jul 4, 2011 #9
    I believe micromass meant "Principles of Mathematical Analysis" by Rudin, which is a great book for introduction to real analysis (if you are comfortable with proof already). To study topology, you need to get some exposure to open sets and continuity in analysis first IMO, or you will just see a lot of abstract definitions. Munkres' book is very good as #9 already pointed out.
     
  11. Jul 5, 2011 #10
    Thankyou Number9 and others. Could you also share your thoughts for linear algebra and abstract algebra? And last one for statistics(not probability & Random variable) topics includes the basic theory of statistical inference for instance classical theory of estimation & hypothesis testing, linear models & least squares etc.
     
  12. Jul 5, 2011 #11
    the first 2nd one is more advanced than the 1st one
    https://www.amazon.com/Introduction...=sr_1_2?s=books&ie=UTF8&qid=1309899553&sr=1-2
    https://www.amazon.com/Linear-Algebra-Applications-Gilbert-Strang/dp/0030105676/ref=pd_sim_b_4

    hard to think of an abstract algebra book that would be good for an engineer.... reviews say gallian has lots of examples but I haven't looked at it myself. I liked herstein.
     
    Last edited by a moderator: Apr 26, 2017
  13. Jul 5, 2011 #12

    micromass

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    For abstract algebra, check out "a book on abstract algebra" by Pinter. A very good introduction to the topic.
     
  14. Jul 5, 2011 #13
    For detection and estimation theory, try "Fundamentals of Statistical Signal Processing" Vol 1 & 2 by Steven Kay.
     
  15. Jul 5, 2011 #14

    jasonRF

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    I took complex analysis as an engineering student and must say that it is very useful. Some EE departments require their students to learn this stuff. My department taught us just a little in a required course - just the minimum to get us through basic applications of the residue theorem, but I later took it from the math department and got a much better understanding. Here is my recommendation for an ee, as it discusses integral (and Z) transforms, which Churchill&Brown leave out:

    https://www.amazon.com/Fundamentals...tmm_hrd_title_1?ie=UTF8&qid=1309911700&sr=8-1

    Most EE PhDs I know who specialized in signal processing, communications, or other more mathy fields of EE took at least one semester of undergrad real analysis, and many took an abstract algebra course as well. So for cutting edge research it is required, but not for the daily jobs of most employed EEs. I wish I had taken a real analysis course, as it would make the literature easier to read - I taught myself really basic analysis, which has helped quite a bit (I used Lay - analysis with an introduction to proof.).

    I also second the recommendation on the statistical signal processing books by Kay, as they are really well written. The downside: they are really expensive!

    good luck,

    jason
     
    Last edited by a moderator: Apr 26, 2017
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