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Hi,

Please recommend a good book on wave equations and fourier series / transforms at 3rd year undergraduate level.

Our course text is a bit dense and can be hard to follow - see the course text at http://www.ouw.co.uk/bin/ouwsdll.dll?COURSEMS324_Mathematics_-_Pure_and_Applied# - Block 1 - Waves.

As mentioned below normally the OU texts are very readable but I'm having a bit of trouble with this one.

Thanks!

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    $\begingroup$ What is your course text? It will help to determine what an appropriate level is. $\endgroup$
    – Willie Wong
    May 26, 2010 at 14:23
  • $\begingroup$ Rather an obscure one as it's a proprietary text from the UK's Open University. Normally the texts are very straightforward to follow, but I'm finding this one a bit heavy. See: ouw.co.uk/bin/… It's the book on waves: Block 1. Any recommendations? $\endgroup$
    – Ben Collier
    May 26, 2010 at 14:32
  • $\begingroup$ I second the request that you list your current course book - it would be no good if someone posted it as a suggestion (I hope I have not done this). Also, you should probably edit your post and click "community wiki", which is the appropriate mode for questions without a definite answer. $\endgroup$
    – Steven Gubkin
    May 26, 2010 at 15:53

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Hum, unfortunately I am not familiar with the Open University course, so I am just making a guess based on the course description you linked to.

Insofar as Fourier Analysis is concerned, a decent text is Stein and Shakarchi's Fourier Analysis: an introduction. ( http://press.princeton.edu/titles/7562.html ) You will most likely only need chapters 1, 2, 4, and 5, with a bit of knowledge of 3. One thing good about the book is that it was written as a first course in an analysis sequence, so doesn't assume too much knowledge about real and complex analysis.

Once you have a bit of Fourier analysis under your belt, reading Korner's Fourier Analysis ( http://books.google.com/books?id=OcZ5iKsGrmoC&lpg=PP1&dq=korner%20fourier%20analysis&pg=PR8#v=onepage&q=korner%20fourier%20analysis&f=false ) can be enlightening and give you some feel about what one can do using the machinery.

For the applications to wave equations as mentioned in the course description, somehow I feel that a textbook in electromagnetism (Jackson or Griffiths) may contain more practical material (look at the sections on standing waves and wave-guides).

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  • $\begingroup$ Was thinking of Stein and Shakarchi, +1 $\endgroup$
    – Michael Hoffman
    May 26, 2010 at 17:39
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    $\begingroup$ Although SS's book was written for a first course in analysis, keep in mind who the target audience was for the course in which it was developed: Princeton's freshman honors analysis students. So it is not so clear that it will be at the right level for random students studying analysis. To be specific, I know someone who used Stein/Shakarchi's complex analysis book as a class text a few years ago because he thought it looked like an awesome book, but it turned out the students thought it left out too much detail in the proofs for them to learn well from it. $\endgroup$
    – KConrad
    May 28, 2010 at 1:10
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    $\begingroup$ A small correction: it was aimed I think at Princeton's spring-term sophomore honors analysis students. Which would peg it at even one level higher in terms of difficulty. But considering that the OP is studying at third year undergraduate level at UK (which as I understand it is more-or-less senior level in US), I should hope it is not too much of a stretch to recommend SS's book. $\endgroup$
    – Willie Wong
    May 31, 2010 at 17:57
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    $\begingroup$ also, of the three books in the series, Complex Analysis is the one I would recommend against using. In hindsight (from studying for general exams in graduate school) the material in that course is a bit too classical and lacking in some breadth typically required for complex analysis. I had to spend some sit-down time with Alfors to catch-up on equicontinuous families and whatnots. The treatment in "Real Analysis" (really measure theory) is also from a classical POV, but useful and comprehensive enough. The Fourier Analysis course, I think, is very good. $\endgroup$
    – Willie Wong
    May 31, 2010 at 18:02
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I have found Folland's Fourier analysis and its applications to be very enjoyable and well-motivated reading.

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  • $\begingroup$ All of Folland's texts are top notch. $\endgroup$
    – The Mathemagician
    May 27, 2010 at 2:54
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Fourier Series and Integrals by Dym and McKean.

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  • $\begingroup$ I think we can stop this thread right here if we just mention the equally wonderous Fourier Analysis by Tom Korner.You really need no other introductory text on the subjects.Despite the enormous number of good texts on these subjects,you really won't find one better then these 2. $\endgroup$
    – The Mathemagician
    May 26, 2010 at 20:57

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