Math 741 FALL 2019 Course Outline

Math 741
Methods of Applied Math I

FALL 2019 Course Outline

Instructor:	Gail Wolkowicz
Office:	Hamilton Hall, Room 318
Office Hours:	Wednesdays 11:00-12:00 and Fridays 2:00-3:00 or by appointment
Telephone:	(905) 525-9140, Extension 24808
Email:	wolkowic@mcmaster.ca
Home Page:	http://www.math.mcmaster.ca/wolkowic/wolkowic.html
Course Home Page:	https://ms.mcmaster.ca/wolkowic/Courses/M741/Math741_2019.html

Lecture Times and Location: Tuesday 11:00-12:30 & Friday 11:00-12:30 in HH/312.

Brief Course Description: The course covers in detail the theory of Ordinary Differential Equations and is very proof intensive, i.e., almost all theorems discussed will be proved and you will also be expected to provide proofs on assignments and the take home exam.

Topics selected from: well-posed initial value problems (i. e. existence, uniqueness, continuation and continuous dependence); general non-autonomous linear systems; special linear systems (autonomous, periodic including Floquet theory, the Poincaré map); classical stability theory for nonlinear systems (i. e. Lyapunov functions, linearization, invariance theory, comparison theorems); hyperbolicity and topological congugacies; planar systems including index theory, and Poincaré-Bendixson theory; an introduction to bifurcation theory, centre manifolds, normal forms and use of simulation software such as XPPAUT (downloadable free on the web at: http://www.math.pitt.edu/~bard/xpp/xpp.html.)

Prerequisite: Registration as a graduate student in the Department of Mathematics and Statistics, MATH 3F03, or permission of the instructor. Comfort with real analysis is highly recommended as the course is proof intensive.

Tentative Grading Scheme: Component Weight

Assignments 40%

Final Take Home Exam 60%

Tentative Grading Scheme:	Component	Weight
	Assignments	40%
	Final Take Home Exam	60%

The tentative post and due dates of the assigments are indicated in the Table below:

#	Post Date	Due Date
Assignment 1	Tuesday, September 24	Tuesday, October 8
Assignment 2	Tuesday, October 8	Tuesday, October 29
Assignment 3	Tuesday, October 29	Tuesday, November 12
Assignment 4	Tuesday, November 19	Tuesday, December 3

These dates are only tentative. Actual due dates will be announced in class and on the assignment sheets. In most circumstances, late assignments will not be accepted. The instructor reserves the right to alter your final grade. However, the grade may only be increased.

Academic Intgrity

Academic dishonesty consists of misrepresentation by deception or by other fraudulent means and can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various kinds of a academic dishonesty please refer to the Academic Integrity Policy, specifically Appendix 3, located at http://www.mcmaster.ca/policy/Students-AcademicStudies/AcademicIntegrity.pdf

In particular, in this course:

On assignments, you are encouraged to discuss the assigned problems with other students in your class. However, you must write the solutions in your own words without referring to any other students' work. The copying or even paraphrasing of other students' solutions will be considered academic dishonesty.

On the take home exam, you are NOT allowed to discuss the problems with anyone but this course instructor, nor consult anyone else's notes but your own. However, you may consult published books (e.g. books on the reference list). If you do so, you must cite the sources and you must still write up your solutions in your own words using the notation used in class.

ACADEMIC ACCOMMODATION OF STUDENTS WITH DISABILITIES Students with disabilities who require academic accommodation must contact Student Accessibility Services (SAS) to make arrangements with a Program Coordinator. Student Accessibility Services can be contacted by phone 905-525-9140 ext. 28652 or e-mail sas@mcmaster.ca For further information, consult McMaster University’s Academic Accommodation of Students with Disabilities policy.

http://www.mcmaster.ca/policy/Students-AcademicStudies/AcademicAccommodation-StudentsWithDisabilities.pdf
ACADEMIC ACCOMMODATION FOR RELIGIOUS, INDIGENOUS OR SPIRITUAL OBSERVANCES (RISO) Students requiring academic accommodation based on religious, indigenous or spiritual observances should follow the procedures set out in the RISO policy. Students requiring a RISO accommodation should submit their request to their Faculty Office normally within 10 working days of the beginning of term in which they anticipate a need for accommodation or to the Registrar's Office prior to their examinations. Students should also contact their instructors as soon as possible to make alternative arrangements for classes, assignments, and tests.

Important Notice:

The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.