AMS 212A SYLLABUS, Winter 2010
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)
- IMPORTANT: Students are expected to master selected chapters in this book, see Lectures page for details of when the material from RHB will be used.
- 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 10 days and
will be based on one of the recently assigned homework problems.
- 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 5: General introduction to PDEs. Famous PDEs and their behavior. The importance of scientific prejudice. The notion of covariance.
- Jan 7: First-order PDEs, introduction to the method of characteristics.
- Week 2:
- Jan 12: Method of Characteristics for semilinear and quasilinear equations. Examples.
- Jan 14: Conservations laws, examples of traffic flow and phone lines.
- Week 3:
- Jan 19: Weak solutions and shocks. Entropy condition. Examples.
- Jan 21: Fully nonlinear equations. Examples.
- Week 4:
- Jan 26: Second order linear equations. Canonical form and classification.
- Jan 28: Canonical forms (continued)
- Week 5 (February):
- Feb 2: Fundamental second-order linear equations. Separation of variables. the heat equation, the wave equation and Laplace's equation
- Feb 4: Fundamental second-order linear equations (continued)
- Week 6:
- Feb 9: Non-Homogeneous equations (forced systems).
- Feb 11: Midterm
- Week 7:
- Feb 16: The need for generalized Fourier Series. Introduction to Sturm Liouville Theory (1)
- Feb 18: Sturm-Liouville Theory (2).
- Week 8:
- Feb 23: Sturm-Liouville Theory (3).
- Feb 25: Applications of Sturm-Liouville theory and forced problems
- Week 9 (March):
- Mar 2: Applications of Sturm-Liouville theory and forced problems (2)
- Mar 4: The one-dimensional wave equation. Revisiting the problem with d'Alembert's solution.
- Week 10:
- Mar 9: Introduction to Greens functions. Elliptic equations (1)
- Mar 11: Elliptic equations (2).
- Week 11:
- Tuesday, March 16th, 4:00-7:00PM, classroom.