Math 553 Partial Differential Equations
Reading Sources on Partial Differential Equations
Required Text
Partial Differential Equations, Methods and Applications ,
second edition, by R. McOwen; Prentice Hall, New Jersey, 2003 (MCOWEN)
(On reserve at Math Library.)
An excellent presentation of the theoretical side of the subject with
an interspersing of examples and methods. For this course, only Chapters 1-5
are covered. The remainder of the book
is an introduction to research methods in PDEs and would be excellent
for a second course in the subject, one emphasizing the functional
analytic side of the discipline.
Supplementary Texts (not required)
Theoretical Treatments
Partial Differential Equations by L. C. Evans; American Math.
Society, Providence, RI, 1998 (EVANS)
(On reserve at Math Library.)
This superb and very readable text is used in Math 554 and 555
(where Parts II and III of the book are covered). If you are planning to take
Math 554, I recommend buying EVANS now, as it will be helpful for
Math 553 also.
Part I of the book covers a good deal of the material in Chapters 1-5 of
MCOWEN, and has
many additional topics on first order PDE, similarity solutions, transform
methods, asymptotics, ... . We will cover a few sections of
this additional material during the semester. However, MCOWEN has several
advantages for our purposes: early in the book it treats weak solutions and
distributions for second order
equations, and it gives more discussion of the physical meaning of
the PDEs. Also,
EVANS approaches first order equations from a level of generality that
might seem
bewildering unless you had first absorbed the more elementary approach
in MCOWEN (though
the approach in EVANS will seem natural and powerful after you understand
MCOWEN).
Partial Differential Equations by F. John; Springer-Verlag,
New York,
1982 (4th Edition) (JOHN)
(On reserve at Math Library.)
This classic text gives a more detailed and comprehensive treatment than
Chapters 1-5 of MCOWEN, but it does not go very far into functional analytic
methods. It is an excellent place to go for an additional treatment of
a subject presented in MCOWEN.
Introduction to Partial Differential Equations with
Applications by E. C. Zachmanoglou and D. W. Thoe; Dover, New York,
1986 (Z & T)
(On reserve at Math Library.)
Slightly less sophisticated (and much less expensive) than JOHN, but still
covering
most of what we need for Math 553. It's a good place to go for an
elementary introduction to
a subject, before turning to MCOWEN or EVANS for the fuller story.
Partial Differential Equations, An Introduction by B. Epstein;
R. E. Kreiger Co., Malabar, Florida 1983 (3rd Edition)
(EPSTEIN)
Another excellent theoretical treatment of the subject, especially
with extended discussions of rigorous arguments. Covers the classical material
corresponding to Chapters 1 - 5 of MCOWEN (plus basic functional analysis
of Banach and Hilbert spaces), but covers that material in more depth.
Terribly short on practical exercises.
Treatments of Methods and Applications
Partial Differential Equations, Theory and Technique by G.
Carrier and
C. Pearson; Academic Press, New York, 1988 (2nd Edition)
(CARRIER & PEARSON)
(On reserve at Math Library.)
The hallmark applications and methods text. Excellent source for worked
examples, extra problems and extended discussions of techniques. Also covers
several advanced techniques such as perturbation methods and numerical
methods.
Elementary Applied Partial Differential Equations, with Fourier
Series and Boundary Value Problems by R. Haberman; Prentice-Hall,
New Jersey, 1983 (HABERMAN)
If you would like a book with a modern presentation but which concentrates
on methods and calculations, this is the one for you. The presentation is
thin on general
principles, concepts and proofs, but it does a good job of discussing methods,
especially if they relate to Fourier type analysis.
Partial Differential Equations of Mathematical Physics by
T. Myint-U; North Holland, New York, 1980 (MYINT-U)
An excellent overall treatment of classical PDEs together with practical
examples. Might be used as an alternate text for a course such as ours,
but MCOWEN gives a slightly more general and rigorous discussion. There
are a good number of problems to test one's skills.
(Thanks to Professor Robert Muncaster for most of the above commentary.)