Syllabus MATH 3511 Fall 97

Applied Mathematics (81052) - Fall 97

The Theory of Ordinary Differential Equations

MW 1:30-2:50 in CLRB 404 (and CLRB 402)

Instructor. Dr. H. Knaust, Bell Hall 219, tel. 747-7002,
e-mail: helmut@math.utep.edu
Office Hours. MW 3:00-4:30, or by appointment.
Other Help.
- Club Zero will sponsor an Analysis Workshop on the 4th floor of the classroom building Mondays, Wednesdays and Thursdays from 5:00-8:00 p.m.
Textbook. Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd edition, Springer-Verlag, 1996.
The textbook is not easy to read; so our pace will be somewhat slow.
Prerequisites. The course material is accessible to beginning graduate students and advanced undergraduate students, who have taken an introductory differential equations course (Math 3226), know some linear algebra (Math 3323 or Math 3426), and have a strong background in real analysis (at least Math 3341).
Contents. The course will "uncover" the first eight chapters of the textbook. If time permits, we will also explore selected topics from Chapters 12-14.
Homework. The most important part of the course is your homework. I will regularly assign homework, which will be collected and graded. Some of the assignments will be individual assignments, while others will be group projects.
Tests etc. The course will have a mid-term exam and a comprehensive final. Part of the final examination will be a take-home project.
Software. You will make some use of computer software (Mathematica et al.) to visualize the results presented. Knowledge of Mathematica is not a prerequisite; instead, you are expected to aquire some basic knowledge during the course.

References.

V. I. Arnold
Ordinary Differential Equations.
Springer-Verlag 1996. Features nice explanations from a geometric point of view, lots of physics.
P. Blanchard, R. Devaney & G. Hall
Differential Equations.
PWS 1996. The undergraduate textbook used at UTEP.
E. A. Coddington & N. Levinson
Theory of Ordinary Differential Equations.
Krieger 1984. Very precise and well-written.
J. Hale & H. Koçak
Dynamics and Bifurcations.
Springer-Verlag 1991. A different approach: the book is organized by dimension of the differential system, including dimensions 1.5 and 2.5.
J. Hale
Ordinary Differential Equations.
J. Wiley 1969. Verhulst follows Hale's treatment of the Poincare-Bendixson Theorem.
M. Hirsch & S. Smale
Differential Equations, Dynamical Systems, and Linear Algebra.
Academic Press, 1974. Lots of applications.
J. H. Hubbard & B. H. West
Differential Equations: A Dynamical Systems Approach (2 vols.).
Springer-Verlag 1991 and 1995. The first two installments of a planned series of four books. Not too hard to read, with lots of examples.
J. La Salle & S. Lefschetz
Stability by Liapunov's Direct Method, with Applications.
Academic Press, 1961. One of the classic textbooks for stability!
D. Schwalbe & S. Wagon
VisualDSolve. Visualizing Differential Equations with Mathematica.
Springer-Verlag 1997. The VisualDSolve package makes it easy to produce high quality graphs of phase planes, Poincare maps, etc.
Ferdinand Verhulst
Nonlinear Differential Equations and Dynamical Systems.
Springer-Verlag 1996. A good reference book; the style is quite dense.

October 21, 1997

V. I. Arnold Ordinary Differential Equations. Springer-Verlag 1996.	Features nice explanations from a geometric point of view, lots of physics.
P. Blanchard, R. Devaney & G. Hall Differential Equations. PWS 1996.	The undergraduate textbook used at UTEP.
E. A. Coddington & N. Levinson Theory of Ordinary Differential Equations. Krieger 1984.	Very precise and well-written.
J. Hale & H. Koçak Dynamics and Bifurcations. Springer-Verlag 1991.	A different approach: the book is organized by dimension of the differential system, including dimensions 1.5 and 2.5.
J. Hale Ordinary Differential Equations. J. Wiley 1969.	Verhulst follows Hale's treatment of the Poincare-Bendixson Theorem.
M. Hirsch & S. Smale Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, 1974.	Lots of applications.
J. H. Hubbard & B. H. West Differential Equations: A Dynamical Systems Approach (2 vols.). Springer-Verlag 1991 and 1995.	The first two installments of a planned series of four books. Not too hard to read, with lots of examples.
J. La Salle & S. Lefschetz Stability by Liapunov's Direct Method, with Applications. Academic Press, 1961.	One of the classic textbooks for stability!
D. Schwalbe & S. Wagon VisualDSolve. Visualizing Differential Equations with Mathematica. Springer-Verlag 1997.	The VisualDSolve package makes it easy to produce high quality graphs of phase planes, Poincare maps, etc.
Ferdinand Verhulst Nonlinear Differential Equations and Dynamical Systems. Springer-Verlag 1996.	A good reference book; the style is quite dense.