Syllabus for MA 532, Fall 2001

Instructor: J. E. Franke
Office: HA 205
Office Hours: 10:15 - 11:15 MWF or by appointment
Phone Number: 515-2381
E-mail address: franke@math.ncsu.edu
Homepage: http://www.math.ncsu.edu/~franke

2. Goals and Objectives:

MA 532 is an introduction to the theory of ordinary differential equations. Students will

extend their understanding of ordinary differential equations.

develop their proof skills in the area of analysis as it applies to ordinary differential equations.

learn to build mathematical models involving ordinary differential equations and to solve problems in a variety of applications.

understand the concepts of existence and uniqueness, fundamental matrix, matrix exponential, and stability.

3. Textbook:

Differential Equations and Dynamical Systems, by Lawrence Perko. Springer 2000, Price 69.95
The Qualitative Theory of Ordinary Differential Equations An Introduction, by Fred Brauer and John A. Mohel. Dover 1969, Price $8.95

4. Topics and estimated days allocated to each topics:

Existence-Unigueness Theorem	1 weeks
x'= A(t)x+f(t): general theory, fundamental matrix solutions and variation of parameters.	3 weeks
x'= Ax, including e^Atand phase protraits	3 weeks
Equilibria of x' = f(x). Linearization, stability, Hartman's Theorem and Stable Manifold Theorem	3 weeks
Limit sets	1 week
One-dimensional autonomous systems: phase portaits	1 week
Two-dimensional autonomous sytems: phase portaris, Poincare-Bendixson Theorem	1 week
Liapunov theory, including LaSalle invariance principle	2 week

5. Tentative schedule of reading assignments

Read the sections to be covered for the week.

6. Tentative schedule of homework due dates, quizzes and tests

Homework is due a week after it is assigned.
The midterm will be in October.
The final is on Wednesday, December 12 at 8:00 am. It is a 3 hour test.

7. Determination of grades: + and - system

Homework: 25%

Midterm: 33%

Final: 42%

8. Policy on incomplete grades and late assignments: Late homework assignments will not be graded.

9. Policy on absences (excused and unexcused) and scheduling makeup work:

The attendance policy is consistent with the Academic Regulations which can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_regulations/attend/reg.htm (link)
In addition, the following clarifications are used in this course: Excused absences are required for making up a missed test.

10. Course Prerequisites / Restrictive Statements:

MA 341, MA 405 and Advanced Calculus.

More information is available at : http://www2.acs.ncsu.edu/reg_records/crs_cat/MA.html (link)

11. Academic Integrity Statement:

Students are expected to follow university guidelines available at http://www.ncsu.edu/provost/academic_regulations/integrity/reg.htm (link)

12. NC State policy on working with students with disabilities:

Information can be found at http://www2.ncsu.edu/ncsu/stud_affairs/counseling_center/dss/ (link)

13. Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips:

None

14. Statement on "pass-through" charges e.g. , lane rental at bowling alley, field trip costs, etc.:

None

Further Information:

NCSU Academic Regulations can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/ (link)