Course Objectives: The course covers mathematical analysis of partial differential equations, with emphasis on analytical solutions of first-order and second-order linear equations. Lectures contain both the results and the derivations, while assignments include analytical problems of different levels. Computer demonstrations of solutions of partial differential equations are accessed via links to web-enabled interactive software. The course can be continued with next-level courses: advanced analysis of PDEs (Math4GG3), numerical methods for PDEs (Math4Q03) and applied nonlinear PDEs (Math742).
Topics: first-order equations, second-order wave, heat and Laplace equations, Fourier solutions on finite intervals, fundamental solutions in infinite intervals, Green's functions for non-homogeneous equations, and Fourier solutions in two and three dimensions.
Instructor:
Dr. Dmitry Pelinovsky, BSB-204, ext.23424,
e-mail: dmpeli@math.mcmaster.ca
Teaching Assistant:
Zhenbin Yan, BSB-233E, ext. 27112,
e-mail: yanz@math.mcmaster.ca
Hours:
Lectures: Tuesday, Thursday, Friday (8:30-9:20); BSB/B116
Office hours: Tuesday, Thursday (9:30-10:30), or by appointment
Main textbooks:
"Elementary Applied Partial Differential Equations"
by R. Haberman (Prentice Hall, 1998)
"Partial Differential Equations: an introduction"
by W.A. Strauss, (John Wiley, 1992)
Optional textbooks:
"Partial Differential Equations and Boundary-Value Problems"
by N. Asmar (PH, 2000)
"A Very Applied First Course in Partial Differential Equations"
by M. Keane (PH, 2002)
Assignments: Six home assignments will be handed out in class on Tuesdays every second week, starting the week of January 13. The assignments are due at 9:20 on Tuesdays in the following week. The texts for assignments and solutions will be posted on the course webpage.
Class Test: There will be one class test on Thursday: February 13. Only the McMaster standard calculator Casio fx-991 is allowed on the test and exam.
Final Exam: The course is completed by a three-hour final examination. The date and location of the final exam will be announced by the registrar's office in mid-term.
Marking scheme:
Final exam (3 hrs) - 30%
Class test (50 min) - 20%
Six homework assignments - 50%
Senate Policy Statement: The course is regulated under the following documents: Statement on Academic Ethics and Senate Resolutions on Avademic Dishonesty. Any student who infringes one of these resolutions will be treated according to the published policy.