113
$\begingroup$

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.

$\endgroup$
1
  • 5
    $\begingroup$ Thanks for the advice. I purchased a 1st edition copy of Strauss for less than 10 USD. $\endgroup$
    – Mykie
    Commented Aug 20, 2010 at 18:19

10 Answers 10

42
$\begingroup$

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.

$\endgroup$
4
  • $\begingroup$ Please include links, $\endgroup$
    – bobobobo
    Commented Aug 19, 2010 at 22:13
  • $\begingroup$ Consider it done. $\endgroup$
    – JT_NL
    Commented Aug 19, 2010 at 22:31
  • 12
    $\begingroup$ +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... $\endgroup$ Commented Aug 20, 2010 at 1:38
  • $\begingroup$ Evans came to my university someday before, a very nice man. $\endgroup$
    – eccstartup
    Commented Aug 30, 2013 at 5:08
15
$\begingroup$

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)

$\endgroup$
2
  • $\begingroup$ I own this book, and I agree it is very applied. $\endgroup$
    – Mykie
    Commented Aug 20, 2010 at 19:23
  • 2
    $\begingroup$ Correction: Evans' book is published by the AMS, not Springer. $\endgroup$ Commented Nov 16, 2015 at 20:45
12
$\begingroup$

Evans' book [1] is used in many curricula and is quite famous. It is easy to read for people with background in mathematics and analysis, it has many examples and exercises, and it covers quite diverse PDE topics. However, there are many alternatives if this book is not well-suited to the reader's background or objectives. Among others, one may prefer

  • the book by Strauss [2] -- one of my favorites -- which is very easy to read.

  • the book by Olver [3] -- one of my favorites -- is very easy to start with, since designed for undergraduate level.

  • the book by Arnold [4] for people interested in geometrical explanations, but not as easy for a first reading as the two previous books.

  • the book by Courant and Hilbert [5] is a classical reference in the spirit of mathematical physics, but it may not fit well for everybody.


[1] L.C. Evans, Partial Differential Equations, 2nd ed., American Mathematical Soc., 2010.

[2a] [2b] W. A. Strauss, Partial Differential Equations: An Introduction, 2nd ed., Wiley, 2008.

[3a] [3b] P.J. Olver, Introduction to Partial Differential Equations, Springer, 2014.

[4a] [4b] V.I. Arnold, Lectures on Partial Differential Equations, trad. R. Cooke, Springer, 2004.

[5] R. Courant, D. Hilbert, Methods of Mathematical Physics Vol. 2: Partial Differential Equations, Wiley-VCH, 1962.

$\endgroup$
1
  • 1
    $\begingroup$ Thanks for formatting the post so nicely. $\endgroup$
    – Naitree
    Commented Sep 17, 2023 at 7:13
11
$\begingroup$

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.

$\endgroup$
9
$\begingroup$

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.

$\endgroup$
1
  • 13
    $\begingroup$ you envision a very unique criminal element. $\endgroup$ Commented Jun 25, 2016 at 15:22
8
$\begingroup$

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.

$\endgroup$
8
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ I liked Logan's book on ODEs a lot, and think the PDE book is good too. It does not overwhelm the reader as many other books do. Because so many mathematical topics converge in ODEs and PDEs, it can be hard to find a good balance between clear explanation versus rigor. After reading Logan's books I definitely felt ready to engage more rigorous books on PDEs. $\endgroup$
    – krishnab
    Commented Jan 31, 2018 at 16:06
5
$\begingroup$

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.

$\endgroup$
1
  • 4
    $\begingroup$ +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. $\endgroup$ Commented Oct 18, 2013 at 17:55
5
$\begingroup$

I would also like to add Peter Olver's "Introduction to partial differential equations" to this growing list. It was published in 2014 and is very suitable for self-studying. The preface does a good job of explaining the various topics and prerequisites required to understand PDEs which I hadn't appreciated until I read it in the book-highly recommended. Solutions to about 20% of exercises are available on the author's website.

$\endgroup$
4
$\begingroup$

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.

$\endgroup$
3
  • 1
    $\begingroup$ How difficult is this book? What are the prerequisites? $\endgroup$
    – Rafid
    Commented Jun 22, 2013 at 14:38
  • 2
    $\begingroup$ 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. $\endgroup$ Commented Oct 18, 2013 at 17:53
  • 21
    $\begingroup$ Are you seriously recommending Evans' PDE as the first PDE book for self study? You have to be kidding. $\endgroup$
    – D1X
    Commented Feb 12, 2017 at 13:36

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .