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What is a good PDE book suitable for self study? I'm looking for a book that doesn't require much prerequisite knowledge beyond undergraduate-level analysis. My goal is to understand basic solutions techniques as well as some basic theory.

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Thanks for the advice. I purchased a 1st edition copy of Strauss for less than 10 USD. –  Digital Gal Aug 20 '10 at 18:19

7 Answers 7

up vote 12 down vote accepted

The book by Strauss is pretty good for a first course. For a second one the book by Evans is nice but it requires some knowledge of measure theory and functional analysis.

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Please include links, –  bobobobo Aug 19 '10 at 22:13
    
Consider it done. –  Jonas Teuwen Aug 19 '10 at 22:31
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+1 for Evans: great reference book- not a perfect first course, as you say, but brilliant to dip in and out of when you're reading around. Excellent if you are a graduate trying to tackle FA or PDE papers for the first time. Not that it answers the OP's question, mind, but +1 nonetheless... –  Tom Boardman Aug 20 '10 at 1:38
    
Evans came to my university someday before, a very nice man. –  eccstartup Aug 30 '13 at 5:08

I would recommend:

Fritz John, Partial Differential Equations (Applied Mathematical Sciences) ISBN: 0387906096. It is a classical Springer book that contains what you ask for.

Google Books might be a good start before you make your final decision.

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I think you cannot get anything better than Evans' book. Its size may be a little scaring, but it is the most clear and well written book on the subject I ever met.

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How difficult is this book? What are the prerequisites? –  Rafid Jun 22 '13 at 14:38
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I'd say the minimum prerequisites are a strong honors calculus course like Spivak or Lax/Terell (which I think will very quickly replace Spivak as the book of choice for such a course). That's really why I can't recommend Evans as a first course despite how good it is-it's too hard. –  Mathemagician1234 Oct 18 '13 at 17:53

Partial Differential Equations for Scientists and Engineers by Farlow. It's Dover, so it's cheap. And it's a great first intro - very applied. If you want to follow on with a more rigorous one, you can't beat Evans (Springer - ISBN13: 978-0821207729)

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I own this book, and I agree it is very applied. –  Digital Gal Aug 20 '10 at 19:23

I like Karl E. Gustafson's Introduction to Partial Differential Equations and Hilbert Space Methods. It was certainly readable after an advanced calc sequence. You will find a few short and worthwhile conversational paragraphs throughout the book. He also uses the technique of revisiting interesting concepts from different perspectives throughout the book. And it's a Dover paperback, so it's cheap.

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Logan's Applied Partial Differential Equations might be suitable for you if you want a (relatively) quick overview of the subject, since it's not very long (about 200 pages). It's aimed at undergraduates in math, engineering and the sciences.

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I haven't read a lot of PDE material, but I enjoyed Taylor's book. It's quite well-written, and also contains introductory material (like Lie derivatives), since it does things on manifolds.

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+1 for Taylor, but I seriously doubt any but a gifted undergraduate-which you clearly were, Akhil- could use it as a first course in PDE. Same problem as Evans. –  Mathemagician1234 Oct 18 '13 at 17:55

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