These recommendation for PDE textbooks
are neither meant to be complete or definitive. They are only some books
that I have found useful recently while teaching at Harvey Mudd
College. Links are to amazon.com
which tends to have a great deal more information.
Introductory PDE's for Math Majors
Partial Differential Equations by David Logan -- A great
introductory textbook available in paperback for about $40.00; while
there are more complete texts, they are generally significantly more
Some texts more for the graduate level
On the Applied Side . . .
Partial Differential Equations by Richard Haberman -- Haberman
understands the importance of the applications of PDE without going over
to the rather "plug and chug" approach of the engineering texts. A good
choice for an introductory course aimed at applied matheticians,
physicists, or engineers.
For Engineers only . . .
These two textbooks are aimed at the undergraduate engineer; they tend
to cover the whole spectrum of engineering mathematics including an
introduction to complex variables, ODEs and some vector calculus.
Both have been widely adopted.
On the Reference Shelf
Analysis by T. W. Körner -- A beautiful, beautiful book with
numerous useful examples in Fourier Analysis and PDE, including a number
I hadn't seen before (my favorite being the isoperimetric theorem). The
writing is engaging and the historic anecdotes are priceless.
Analysis and Its Applications by Gerald B. Folland -- An advanced
undergraduate/introductory graduate text on Fourier analysis and
distributions with applications to functional analysis and PDE.
to Fourier Analysis by M. J. Lighthill -- A marvelous book
--while written in 1958, it has one of the most coherent introduction to
the theory of distributions from the applied viewpoint I have seen.
Physics by Eugene Butkov -- A great source for problems germane to
the physicist. While I tried this as a textbook and found it too terse
for undergraduate, it still has a place on my bookshelf as a reference
in the field.