General Information
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:
- 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. Some familiarity with ODEs, Complex
Analysis, Linear Algebra will be useful.
- 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.
- Presentation: 10% of total grade.
- Mid-term: 30 % of total grade.
- Final exam: 40 % of total grade.
(very) Tentative Schedule: (this will be
updated as
the
course progresses)
- Week 1 (September):
- Sep 22: General introduction. Test of general mathematical
background.
- Week 2:
- Sep 27: Introduction to PDEs. Elements of vector calculus.
General concepts and definitions.
Examples.
- Sep 29: Examples (2). First Order PDEs. Linear PDEs.
- Week 3:
- Oct
4: Quasilinear equations; Method of
Characteristics for quasilinear equations. Examples.
- Oct
6: Special cases of quasilinear equations. Conservations laws, and probability
generating functions.
- Week 4:
- Oct 11: (Quiz 1). Conservations
laws, and probability
generating functions (2). Existence and uniqueness
theorem.
- Oct 13: Method for fully nonlinear equations; the Eikonal
equation. Weak
solutions and shocks (1)
- Week 5:
- Oct 18: Weak
solutions and shocks (2)
- Oct 20: Second order linear equations in 2 variables;
canonical form and classification.
- Week 6: Transform methods
- Oct 25: The one-dimensional wave equation.
- Oct 27: Method of separation of variables (1); Fourier Series.
- Week 7: (November)
- Nov 1: Non-Homogeneous equations. Energy Method.
- Nov 3: 2D wave
equation. Sturm Liouville Theory (1)
- Week 8:
- Nov 8: Midterm
- Nov 10: Sturm-Liouville Theory (2).
- Week 9:
- Nov 15: Sturm-Liouville Theory (3). Fourier Transform method.
- Nov 17: Greens functions; Elliptic equations
- Week 10:
- Nov 22: Greens functions; Elliptic equations
- Thanksgiving.
- Week 11: (December)
- Nov 29: Greens
functions; Elliptic equations
- Dec 1: Review