Last updated March 30, 2008
Spring 2008 CRN 33919
MWF 1500-1550 Kidder 356
Bent E. Petersen
Course Description
Systems of first-order differential equations. Recap of some linear
algebra and solutions of systems of first-order linear differential
equations with constant coefficients. Some discussion of linear systems with
periodic coefficients (Floquet theory). Linearization of a nonlinear
system at a solution, in particular at an equilibrium point or at a
periodic solution. Dynamical systems. Detailed discussion of nonlinear systems
in the case of two
equations - phase portraits, linearization and the stability of equilibria,
conservative systems, limit cycles and the
Poincare-Bendixson Theorem.
Some physical examples will be discussed or provided as assignments.
Mth 256 Applied Differential Equations or some equivalent course is a
prequisite. Mth 341 Linear Algebra is also required though you can probably
get by with the matrix part of Mth 306 or something equivalent. It would, in
any case, be convenient to know something about eigenvalues and eigenvectors,
but it is not necessary to be an expert.
Textbook
The textbook is not strictly required. We cover only a small portion of
it. You can probably get along without it. I have not orderd the text,
though the bookstore may still have some used copies available. You may
also be able to locate some copies on the web.
Lawrence Perko, Differential Equations and Dynamical Systems,
3rd ed., Springer-Verlag,
New York (1991 1996) 2001.
Note the 1st ed. may come in two versions,
the original edition (1991) and a corrected version (1993). New copies of edition 3 may
cost about $85. Used copies of the text run from $32 to $62 depending on the edition.
Additional (Optional) References
A book, more elementary than our text, which you may find useful as an additional text is
Steven H. Strogatz, Nonlinear Dynamics and Chaos With Applications
to Physics, Biology, Chemistry, and Engineering, Perseus Books, Reading, MA 1994
A recent Mth 256 text may be useful: for example, chapters 7 and 9 of
William E. Boyce and Richard C. DiPrima, Elementary Differential
Equations and Boundary Value Problems, 8th
ed., John Wiley & Sons, Inc., (1965) 2005
A book, more advanced than our text, which you may also find useful is
Stephen Wiggins, Introduction to Applied Nonlinear Dynamical
Systems and Chaos, 2nd ed., Springer-Verlag,
New York, (1990) 2003
A nice set of lecture notes by Gerald Teschl, a mathematical physicist at
the University of Vienna, is available on the web. The notes are available
in Postscript format (4 MB) and in PDF format (2.5 MB).
Gerald Teschl, Ordinary Differential Equations and
Dynamical Systems, 2000-2007 (current version March 9, 2007), 252 pages,
http://www.mat.univie.ac.at/~gerald/ftp/book-ode
Several classics (at the graduate level) are
Earl A. Coddington and Norman Levinson, Theory of Ordinary
Differential Equations, McGraw-Hill Book Co. Inc., New York 1955
V.V. Nemytskii and V.V. Stepanov, Qualitative Theory of
Differential Equations, Princeton Univ. Press, Princeton, NJ 1960
Grades
Grades will be based on homework assignments and zero, one or two tests. Each assignment
will be due approximately one week after it is set. Please turn in succint careful
solutions.
Homework assignments will be available only on the web. See
Mth 480 Documents.
Disclaimer
See Disclaimer for a list of everything I
could think of to disclaim.
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