2018 Spring Course Syllabus - Mathematics 4041.001
Course: Mathematics 4041.001.
Course Title: Partial Differential Equations.
Time: MWF 13:00-13:50.
Place: Wachman 407.
Instructor: Gerardo A. Mendoza.
Instructor Office: Wachman 618.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Course Web Page: http://math.temple.edu/~gmendoza
Office Hours: By appointment, but you can come any time, if I am in and I can see you, I will.
Prerequisites: Linear algebra and ordinary differential equations. Some of this material will be reviewed as needed.
Textbook: J. David Logan, Applied Partial Differential Equations, 3rd Edition. Undergraduate Texts in Mathematics, Springer (ISBN 978-3-319-30769-5).
Course Goals: By the end of the course, you should be able to derive the classical partial differential equations in mathematical physics, understand the various possible initial and boundary value problems you can pose for these equations, and be able to solve them in special cases. You should also have a basic understanding of Hilbert spaces, orthonormal bases, and Fourier series. Finally, you should also have a working knowledge of the Fourier transform and its usefulness in solving partial differential equations.
Topics Covered: The aim of the course is to develop a practical understanding of basic aspects of Partial Differential Equations through studying the four basic linear equations of mathematical physics, the heat equation, Laplace's equation, the wave equation and Schroedinger's equation. These equations will be solved in specific situations using separation of variables and the companion method of Fourier transform. This will require us to study Fourier series (either as actual trigonometric series or more general series) in particular. All this will be developed as needed. Time permitting, we will undertake to study the so called WKB method (which produces approximate solutions). We will always keep present the physical meaning and applications of the equations, and, time permitting, we'll make a serious attempt at understanding the simplest model of the hydrogen atom. More formally, the course will cover: 1. First order partial differential equations, linear and non linear. An introduction to ordinary differential equations. 2. The fundamental models of the four classical differential equations of mathematical physics. Problems associated with them: initial and/or boundary value problems. 3. The method of separation of variables. Sturm-Liouville problems, spaces of functions, including an introduction to Hilbert spaces, Fourier series and Fourier transforms. 4. Solution of selected problems for the four classical PDE's. 5. Time permitting, a model for the hydrogen atom.
Course Grading: Evaluation: assigned homework and two take-home exams (50% + 25% + 25%). No final exam. For assigned homework, you are allowed to work in groups. But the paper you submit with your answers must be written alone, after all discussions with classmates (or others) are over. You must work alone on the take-home exams, but are allowed to consult any book, and with me (only). For both homework and exams I will require a clean and clear presentation of your work. Lack of a clean, clear exposition of your solution to a problem will result in 0 points for that problem.
Exam Dates: Due dates for take-home partial exams: February 21, April 25.
Attendance Policy: Attendance is required.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
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The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here. (Opens in new tab/window)