This page will contain some information about the Fall 2009 APM 346 course on PDEs.
Course outline:
This is a short half year introductory course in partial differential equations for mathematics students. The course will focus on the classical PDEs of mathematical physics: the wave equation, the diffusion equation and Laplace’s equation with some variations. We will develop important techniques of finding general solutions for the classical PDEs in explicit form. When an explicit form of the solution is unavailable (and this is almost always the case in the real life 🙁 ) we will apply qualitative analysis to study existence, uniqueness, and stability of the solutions of the equations.
Course coordinator:
Marina Chugunova, HU 1025, (416) 946-3769, chugunom@math.utoronto.ca
Lectures: Monday, Wednesday, Friday (9:10 – 10:00) room SS 2110
Office hours: Friday (16:00 – 18:00) HU 1025
Instructor:
Victor Ivrii, HU 1008, (416) 978-4031, ivrii@math.utoronto.ca
Lectures: Monday, Wednesday, Friday (9:10 – 10:00) room MP 134
Office hours: Wednesday (1:00-3:00) HU 1008
Link to the web page
Teaching assistants:
Mircea Voda, SS 622, 416-978-2967, mircea.voda@utoronto.ca
Office hours: Monday (16:00-17:30) BA 6283
Ioannis Anapolitanos, HU 1026, 416-978-3646, ioanap@math.utoronto.ca
Office hours: Wednesday (16:00-17:30) HU 1026
Format:
This is a lecture course meeting 3 times per week on MWF9. The lectures form the essential content of the course, and you are responsible for all material covered in lectures (unless otherwise indicated.) Most of the material can be found in the textbook, but the lectures may deviate from the book in content or ordering of material. If you miss a lecture, it is your responsibility to find out (from a classmate) what has been covered in your absence. A table containing the titles of the topics covered (and a reference to the textbook if appropriate) in each previous lecture will be posted on this web page.
Recommended reading:
“ Partial Differential Equations. Analytical and Numerical Methods. “, (Chapters 1-6)
by Mark S. Gockenbach, SIAM, ISBN 0-89871-518-0
“ Partial Differential Equations. “, (Chapters 1-5)
by Walter A. Strauss, John Wiley & Sons, ISBN-13 978-0470-05456-7
Textbook:
“ Beginning Partial Differential Equations “,
Second Edition, by Peter V. O’Neil, John Wiley & Sons (publishers), ISBN 978-0-470-13390-3.
The text is viewed as a learning resource for the students (a supplement to the lectures), and a source of homework and practice problems. You are strongly recommended to obtain a copy of the book or to make systematic use of a borrowed copy.
Topics:
We will cover Chapters 1 – 5, with supplemental material provided in the lectures. After that, if time permits, we will cover selected topics from Chapters 6, 7, 8
Homework:
Exercises from the Peter V. O’Neil textbook will be assigned weekly with some exceptions. The homework will be posted on Monday and will be due in 10 days on Wednesday at the beginning of class.
Marking Scheme:
There will be two tests and a final exam. The tests will occur in mid-October and mid-November and time will be scheduled for the final exam. The final grade will be determined by the scale:
Max([25% Test 1, 25% Test 2, 40% Final exam and 10% homework]; [90% Final exam and 10% homework]) ( To resolve dog-ate-my-homework-like situations only 7 the best homeworks out of 8 will be counted. )
Note:
If you miss a test, an exam or homework due date due to illness or other emergency, you must obtain a medical certificate from Student Health Services or a doctor. For more information please consult the document: http://www.utoronto.ca/health/forms/forms.htm
Warning!:
Be aware of the University policies on Academic Dishonesty: You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity. Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour 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 types of academic dishonesty please refer to the Academic Integrity Policy, located at:
http://www.utoronto.ca/academicintegrity