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Syllabus of Math 611, Section 600
Introduction to Ordinary and Partial Differential Equations
Fall 2011, Instructor Peter Kuchment
Office Rm. Blocker 614A, Telephone (979)862-3257
Home Page: /~kuchment
Section: 600, Time: MWF 9:10 am - 10:00 am, Room: BLOC 164
Textbook: L. C. Evans, Partial Differential Equations: 2nd edition
, American Math. Society,
Office hours: MW 10:10-11:00, F 10:10-10:30, Blocker 614A
Additional office hours can
be arranged by appointment.
IntroductionThe class starts with a brief excursion into basic
facts concerning Ordinary Differential Equations and then shifts to the Partial
Besides numerous applications inside mathematics (e.g., to geometry), the
PDEs form the core part of our scientific understanding of the physical world:
from physics to chemistry, to biology, to meteorology, you name it.
The class (except the short initial ODE part) will be based on the well
respected textbook by L. Evans. It is planned to cover Part I
"Representation formulas for solutions" of the book. This includes a study of
the four major PDEs: transport, Laplace, heat, and wave equations, as well as analysis of
1st order non-linear PDEs and other methods of representing solutions (Fourier
transform, separation of variables, asymptotics, etc.).
This study will be continued in the next class Math 612 that will most probably cover the
Part II of the book "Theory of linear PDEs" (including more general initial value and
boundary value elliptic, hyperbolic, and parabolic problems, spectral theory, etc.).
Prerequisite:MATH 410 or equivalent or instructor's approval.
AssignmentsGrading will be based on home assignments and a
take-home final exam.
Tentative schedule of the course (watch for updates)
|Topics and sections
|Home assignments and recommended exercises
|8/29 - 9/02
|A survey of main
theorems on ODEs
|HW1, PDF file, due 9/07
|9/05 - 9/23
|Chapter 1 and Sections 2.1, 2.2 of Chapter 2
|HW2: PDF file , due 10/03. The problem #8 is moved to the extra credit part
|9/26 - 10/14
|Chapter 2, Sections 2.3, 2.4
|10/17 - 11/04
|11/07 - 12/02
|Final exam (take home)
|Percentage of points
|90% and higher
|80% and higher
|70% and higher
|60% and higher
|Less than 60%
Recommended additional reading:All of the books below are written by
great experts in differential equations, all are written well and provide
interesting and rewarding reading. This list is certainly far from being
comprehensive, it just contains some of the instructor's favorites. These books
approach the subject from different perspectives, and so reading (or at least
browsing through) all of them is a good idea for someone who wants to learn the
ODEs and PDEs. Do not try to do this in one semester, though :-).
Ordinary Differential Equations
- V. I. Arnold, Ordinary Differential Equations (any edition).
book that provides a contemporary geometric view of all the main issues of
ODEs. Requires a lot of work, but the reader gets rewarded for it with joy and
much deeper knowledge. Probably not suitable as the first ODE book.
- V. I. Arnold, Geometric Methods in the Theory of Ordinary Differential
Equations, Springer Verlag.
Can be considered as extension of the previous
book to cover important topics usually not in the standard ODE class.
- P. Hartman and P. Bates, Ordinary Differential Equations (Classics in
Applied Mathematics, 38), SIAM 2002 (older editions in '73 and '82 by other
A classical rather comprehensive book on ODEs.
- L. S. Pontryagin, Ordinary Differential Equations, Reading, Massachusetts:
Addison - Wesley Publishing.
A short and easy textbook that covers
introduction to ODEs with main theorems proven.
Partial Differential Equations
- Richard Courant and David Hilbert, Methods of Mathematical Physics, two
volume set (any edition).
This is an absolutely wonderful classics. In spite
of being 87 years old (starting with its 1st edition), it is still an extremely
important book, in many instances not surpassed by anything else. A must reading
for anyone using PDEs extensively.
- G. Eskin, Lectures on Linear Partial Differential Equations, AMS 2011.
From a review: This book is a reader-friendly, relatively short introduction to
the modern theory of linear partial differential equations. An effort has been
made to present complete proofs in an accessible and self-contained form. The
first three chapters are on elementary distribution theory and Sobolev spaces
with many examples and applications to equations with constant coefficients.
The following chapters study the Cauchy problem for parabolic and hyperbolic
equations, boundary value problems for elliptic equations, heat trace asymptotics,
and scattering theory. The book also covers microlocal analysis, including the
theory of pseudodifferential and Fourier integral operators, and the propagation
of singularities for operators of real principal type. Among the more advanced
topics are the global theory of Fourier integral operators and the geometric
optics construction in the large, the Atiyah-Singer index theorem in R^n,
and the oblique derivative problem.
- F. John, Partial Differential Equations, Springer Verlag.
outdated and more limited that Evans' book, this is still a very good introduction to
the mathematics of PDEs.
- I. G. Petrovsky, Lectures on Partial Differential Equations, Dover 1991.
good small textbook on basics of PDEs. Much more limited and outdated than
Evans, but still valuable.
- Y. Pinchover and J. Rubinstein, An Introduction to Partial Differential
Equations, Cambridge University Press, 2005.
A nice reading, probably at a somewhat
lover level than in the 611 class.
From a review: "This is an introductory book on the subject of partial
differential equations which is suitable for a large variety of basic courses
on this topic. In particular, it can be used as a textbook or self-study book
for large classes of readers with interests in mathematics, engineering, and
related fields. Its usefulness stems from its clarity, balance and conciseness,
achieved without compromising the mathematical rigor. One particularly attractive
feature is the way in which the authors managed to emphasize the relevance of
the theoretical tools in connection with practical applications."
- Michael E. Taylor, Partial Differential Equations: Basic Theory (Texts in
Applied Mathematics, 23), Springer Verlag, and its two consecutive volumes.
comprehensive set of books covering all major topics of PDEs from contemporary
points of view. Very geometric, in most cases equations are considered on
manifolds. This makes it a very good and important book, but probably not for
the first serious study of PDEs.
Make-up policy:Make-ups for missed quizzes, home assignments and
exams will only be allowed for a university approved excuse in writing. Wherever
possible, students should inform the instructor before an exam or quiz is
missed. Consistent with University
Student Rules , students are required to notify an instructor by the end of
the next working day after missing an exam or quiz. Otherwise, they forfeit
their rights to a make-up.
Grade complaints:Sometimes the instructor might make a mistake
grading your work. If you feel that this has happened, you have one week since
the graded work was handed back to you to talk to the instructor. If a mistake
is confirmed, the grade will be changed. No complaints after that deadline will
Scholastic dishonesty:Copying work done by others, either
in-class or out of class, is an act of scholastic dishonesty and will be
prosecuted to the full extent allowed by University policy. Collaboration on
assignments, either in-class or out-of-class, is forbidden unless permission to
do so is granted by your instructor. For more information on university policies
regarding scholastic dishonesty, see University Student Rules .
Students with Disabilities: The Americans with Disabilities Act
(ADA) is a federal anti-discrimination statute that provides comprehensive civil
rights protection for persons with disabilities. Among other things, this
legislation requires that all students with disabilities be guaranteed a
learning environment that provides for reasonable accommodation of their
disabilities. If you believe you have a disability requiring an accommodation,
please contact Services for Students with Disabilities, Koldus 126, 845-1637.
Copyright policy: All printed materials disseminated in class or
on the web are protected by Copyright laws. One xerox copy (or download from the
web) is allowed for personal use. Multiple copies or sale of any of these
materials is strictly prohibited.
GOOD LUCK IN YOUR STUDIES!!!
This syllabus is subject to change at the instructors'
Last revised August 28th, 2011