SECTION: 59361, MWF 10:10-11:00, Ayres 118

ProfessorAlex Freire, Ayres 207 A (974-4313, freire@math.utk.edu)

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
*at
least 50 on the final are required

for a passing grade.

80% and above:A 68-79:
B 55-67:C

(no "curving")

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.

COURSE OUTLINE:

PART 1 : Systems of differential equations: examples, basic theory

PART 2 : Linear systems and linearization

PART 3: Periodic solutions of nonlinear systems; topological methods

PART
4:: Non-autonomous systems; forced oscillations