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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
up vote 18 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
+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

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
Correction: Evans' book is published by the AMS, not Springer. – Mathemagician1234 Nov 16 '15 at 20:45

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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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
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

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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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

My favorite undergraduate texts on PDEs are the older ones-I don't like more recent undergraduate texts because they either require too much prerequisites or they're just not very well organized. An undergraduate text on PDE's is really a course on the classical theory that doesn't use graduate level analysis-when you look at it from that point of view, it makes sense to use the older books for a first course.

The book I first learned PDEs from was Elementary Partial Differential Equations by Paul W. Berg and James. L. McGregor. It is extremely clear, very gentle and covers all the basic with just a background in calculus needed. It also has many wonderful problems. Somewhat more sophisticated but equally good is Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou and Dale W. Thoe.It's a bit more rigorous, but it covers a great deal more, including the geometry of PDE's in R^3 and many of the basic equations of mathematical physics. It requires a bit more in the way of prerequisites: some advanced calculus of functions of several variables, some linear algebra and basic differential equations. But it's beautifully written and covers a lot more-and it's available in Dover paperback. If I had a gun to my head and could only use one book, that's the one I'd use.

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