Need a good PDE text 4 the hard times...

February 12, 2008 12:23 PM

Anyone know a good introductory text to partial differential equations?

I'm taking a course in partial differential equations and we're using Fritz John's book, which I'm finding hard to learn from. It's written in a very dense, compact style, and he doesn't slow down to explain anything. It doesn't have very many pictures or graphs either, and it's hard for me to visualize all this stuff.

Can anyone recommend a good introductory text to partial differential equations with lots of hand-holding, graphs, and the like? I've seen a few at my library, but they seem to stress Fourier series, whereas our course (judging by the book) will only be touching on them. I've seen other, "cookbook"-like textbooks that show how to solve various PDEs that crop up in physics and engineering, but our course is more theory-based.

Bonus points if the book is commonly available in university libraries or can be found used.

posted by pravit to education (8 comments total)

Did you try Boyce & DiPrima?
posted by swordfishtrombones at 12:28 PM on February 12, 2008

I adore my Farlow PDE book - it's by Dover, so it's cheap, lots of really good examples. It's geared towards scientists and engineers, so it's probably not terribly rigorous, but i use it far more than Boyce/DiPrima or anything else I had in college.
posted by universal_qlc at 12:57 PM on February 12, 2008

Seconding Boyce and DiPrima. It's a very easy book to follow.
posted by Loto at 1:01 PM on February 12, 2008

Hi pravit, my Applied Mathematics department uses Haberman to teach PDEs, mostly to students with engineering backgrounds. Haberman is definitely a cookbook guy, but he does a good job of explaining WHY the standard recipes for the heat and wave equations work. His book has plenty of picture examples, and it's my recommendation for you, but here are a couple other books to be aware of:

MIT appears to use Strauss for their introductory PDE class, which is available on Open Courseware. I have no experience with this book.

I would stay away from Evans, a solid PDE textbook, but probably not what you're looking for. I took a graduate level class with Evans, and it is extremely well-written, but low on examples and pictures.

Also, just out of curiosity, what concepts are giving you the most difficulty? It's possible that what you really need is a good linear algebra, multivariate calculus, or ODE book (like Boyce & DiPrima) to fill you in on what your current book considers a pre-requisite.
posted by onalark at 1:17 PM on February 12, 2008

Strauss is what I had. I don't think it's what you're looking for. It is more theory based, but I wouldn't describe it as doing any hand-holding-- I certainly could've used a better hand-holder when I was first doing PDEs.

If it's the proofs that are giving you issues, a good real analysis book might actually be of more use; I know I understood the proofs behind PDEs tons better after my analysis course.
posted by nat at 1:35 PM on February 12, 2008

I feel you. I took a graduate level PDE class last semester and was woefully unprepared (as a physicist by training). We used lecture notes culled from the professor's own PDE textbook (see DiBenedetto). You may be able to find that in your university library.

A list of PDE books can be found here. Throughout the course I recall referencing Sommerfeld, Garabedian, Epstein, and a few others (Harrison comes to mind, but I can't seem to find that book).

There doesn't really seem to be a good, rigorous treatment of PDEs at a moderate level of difficulty. The books seem divided between elementary, "cookbook" presentations, and advanced texts designed for upper level graduate students. I think the best thing to do is try and pinpoint your weaknesses are and find a text suitable to them - I spent a lot of time just reviewing basic analysis, ala Rudin.
posted by casaubon at 1:39 PM on February 12, 2008

Thanks for the responses!

Just back from the library. I looked at the Boyce & DiPrima book, but it didn't seem to have very much about partial differential equations. They didn't have the Strauss book and somebody already got the Haberman book, but here's what I found:

Basic Partial Differential Equations by David Bleecker and George Csordas. It seems to explain a lot more and goes at a slower pace, along with lots of pictures, so I hope it will help.

Thanks for the Farlow recommendation - I might just snag it off Amazon since it's quite cheap.
posted by pravit at 5:12 PM on February 12, 2008

Hey, I found another good introductory PDE book, in case anyone later on finds this thread!

The book is "Partial Differential Equations" by Phoolan Prasad and Renuka Ravindran. It might be kind of hard to find (try checking the library). I'm finding it more clear and easier to follow.
posted by pravit at 2:35 PM on February 19, 2008