AMS 212A SYLLABUS, Winter 2012
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: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, fourth edition by Richard Haberman (Pearson - Prentice Hall; available on amazon.com)
- Supplemental material:
- An introduction to partial differential equations by Y. Pinchover and J. Rubinstein , Cambridge University Press
- 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: Homework will be given every week and
answers will be graded in Section. Section is mandatory.
- 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: 25 % of total grade.
- Mid-term: 35 % of total grade.
- Final exam: 40 % of total grade.
Tentative schedule (this will be updated as the course proceeds)
- Week 1 (January):
- Jan 10: General introduction to PDEs. Famous PDEs and their behavior. The importance of scientific prejudice. The notion of covariance.
- Jan 12: Chapter 2.1-2.4. Method of separation of variables. Application to the Heat equation.
- Week 2:
- Jan 17: Chapter 3, Chapter 2.5. Fourier Series. Application to Laplace's equation
- Jan 19: Chapter 4. The wave equation.
- Week 3:
- Jan 24: Chapter 5.1-5.4. Sturm-Liouville theory part 1, and examples.
- Jan 26: Chapter 5.5-5.9. Sturm-Liouville theory part 2, and more examples.
- Week 4:
- Jan 28: Chapter 7.1-7.6: Higher-dimensional problems part 1, and examples with Bessel functions.
- Jan 30: Chapter 7.7-7.10: Higher-dimensional problems part 2, and examples with Legendre functions.
- Week 5 (February):
- Feb 7: Chapter 8. Non-Homogeneous equations (forced systems) part 1, and examples
- Feb 9: Chapter 8. Non-Homogeneous equations (forced systems) part 2, and examples
- Week 6:
- Feb 14: Review and general questions
- Feb 16: Midterm
- Week 7:
- Feb 21: Chapter 9.1-9.3: Green's functions for ODEs.
- Feb 23: Chapter 9.4-9.5: Green's functions for PDEs.
- Week 8:
- Feb 28: Chapter 11: Green's functions for the wave and heat equations
- Mar 1: Chapter 12.1-12.5. First-order PDEs, introduction to the method of characteristics.
- Week 9 (March):
- Mar 6: Chapter 12.6. Method of Characteristics for semilinear and quasilinear equations. Examples.
- Mar 8: (Handout) Weak solutions and shocks. Entropy condition. Examples.
- Week 10 (March):
- Mar 13: (Handout) Canonical forms, part 1. Examples.
- Mar 15: (Handout) Canonical forms, part 1. Examples.
- Week 11:
- Monday, March 19th, 7:00 -- 10:30PM, classroom. (Note: this is the official date, I am looking to change it). Alternatively: take-home final.