SECTION: 59361, MWF 10:10-11:00, Ayres 118
ProfessorAlex Freire, Ayres 207 A (974-4313, email@example.com)
Office Hours: M,W 11-12 or by appointment (questions by e-mail also OK)
TEXT: J.Hubbard, B.West: Differential Equations:
a dynamical systems approach-
Higher dimensional Systems, Texts in Applied Mathematics vol. 18, Springer-Verlag 1995
Important remark: some of the topics to be covered
in the course are not found in the
textbook; your class notes (and eventual handouts) are an integral part of the course. In
general, attendance to every class meeting is expected.
GOAL: Second course in ordinary differential equations,
including linear and
non-linear systems. The emphasis is on the geometric/qualitative approach to DEs.
Proofs of the main theorems will be presented, but not emphasized. The intended
audience includes advanced mathematics majors and graduate students in
engineering, the physical sciences and ecology. PREREQUISITES: Multivariable
calculus (M241), introductory differential equations (M231), linear algebra (M200 or M251).
Important remark: a working knowledge of the material
in the above-mentioned courses
will be assumed.
GRADING: Based on 3 in-class exams (15% each),
homework (25%) and a comprehensive
final exam (30%). Exam dates are given in the calendar
Important remark: There will be no make-up
exams: students with justified time conflicts should
warn me well before the exam date.
EXPECTED GRADING SCALE: Average of at least 50 and
least 50 on the final are required
for a passing grade.
80% and above:A 68-79: B 55-67:C
HOMEWORK: will consist of 5-7 problems due each Friday
(starting 1/19). The homework
problems (from the text) are given in the links below.
MATHEMATICS SOFTWARE: Some of the homework problems will
require use of software
such as Maple, Matlab or Mathematica. I'll use Maple, but students are free to use any software
they are familiar with. A tutorial session on Maple V will be scheduled early in the semester.
PART 1 : Systems of differential equations: examples, basic theory
PART 2 : Linear systems and linearization
PART 3: Periodic solutions of nonlinear systems; topological methods
4:: Non-autonomous systems; forced oscillations