AMS 212A SYLLABUS, Winter 2009
General Information
Class and Exams Schedule
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General Information
Tentative schedule (this will be updated as the course proceeds)
Class and Exams Schedule
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General Information
- Textbook: An introduction to partial differential equations by Y. Pinchover and J. Rubinstein (Cambridge University Press; available on amazon.com)
- Supplemental material:
- Mathematical methods for
physics and engineering, Riley, Hobson & Bence (CUP)
- Partial differential equations of mathematical physics and integral equations by R. B. Guenther and J. W. Lee (Prentice Hall)
- Partial differential equations, sources and solutions by A. D. Snider (Prentice Hall)
- Introduction to partial
differential equations with applications by E. C. Zachmanoglou
and D. W. Thoe (William & Wilkins)
- Eligibility:
- Graduate Standing. This class assumes you master the concepts taught in AMS 211. Please check the AMS 211 Syllabus to make sure you do!
- Homework: Suggested homework will be given every week and
answers will be discussed in Section. You are strongly advised to
attempt and complete as much of the homework as possible and go to
section to find out the correct answers. Homework is not graded.
- Quizzes: Will be held approximately every two weeks and
will usually be based on one of the homework problems set during the
previous two weeks.
- Exams: There will be one mid-term exam and a final exam.
- Grading Policy:
- Quizzes: 20 % of total grade.
- Mid-term: 40 % of total grade.
- Final exam: 40 % of total grade.
Tentative schedule (this will be updated as the course proceeds)
- Week 1 (January):
- Jan 6: General introduction to PDEs. Famous PDEs and their behavior. The importance of scientific prejudice. The notion of covariance.
- Jan 8: First-order PDEs, introduction to the method of
characteristics.
- Week 2:
- Jan 13: Method of Characteristics for quasilinear equations. Examples. Existence & Uniqueness theorem.
- Jan 15: Conservations laws. Method for fully nonlinear equations; the Eikonal equation.
- Week 3:
- Jan 20: Weak solutions and shocks. Entropy condition.
- Jan 22: Examples. Traffic flow and others.
- Week 4:
- Jan 27: Second order linear equations in 2 variables; canonical form and classification.
- Jan 29: Method of separation of variables (1); Review on Fourier Series.
- Week 5 (February):
- Feb 3: Examples: the heat equation, the wave equation and Laplace's equation
- Feb 5: Non-Homogeneous equations.
- Week 6:
- Feb 10: Examples & Review
- Feb 12: Midterm
- Week 7:
- Feb 17: The need for generalized Fourier Series. Introduction to Sturm Liouville Theory (1)
- Feb 19: Sturm-Liouville Theory (2).
- Week 8:
- Feb 24: Sturm-Liouville Theory (3).
- Feb 26: Applications of Sturm-Liouville theory.
- Week 9 (March):
- Mar 3: The one-dimensional wave equation. Revisiting the problem with d'Alembert's solution.
- Mar 5: Introduction to Greens functions. Elliptic equations (1)
- Week 10:
- Mar 10: Elliptic
equations (2).
- Mar 12: Review
- Week 11:
- Tuesday, March 17th, 12:00-3:00PM, classroom.