Fall 2013 Course Syllabus - Mathematics 8141.001

Course: Mathematics 8141.001.
Course Title: Partial Differential Equations I.
Time: Tuesdays and Thursdays 2-3:20PM.
Place: Wachman Hall 527.
Instructor: Gutierrez, Cristian E.
Instructor Office: Wachman Hall 432.
Instructor Email: cristian.gutierrez@temple.edu
Instructor Phone: 1-7284.
Course Web Page: https://math.temple.edu/~gutierre/math8141/8141syllabus.html
Office Hours: by appointment.
Prerequisites: Solid knowledge of advanced calculus.
Textbook: Partial Differential Equations, by L. C. Evans, Graduate Texts in Mathematics vol. 19, American Mathematical Society, 1998, ISBN: 0-8218-0772-2. Elliptic Partial Differential Equations of Second Order, by D. Gilbarg and N. S. Trudinger, Springer, ISBN: 9783540411604. On most topics, class notes will be provided by the instructor.
Course Goals: To cover core material of partial differential equations and applications. The course will be useful for students in analysis and applied mathematics, and it will prepare them to take the pde section of the comprehensive exams.
Topics Covered: A partial differential equation (PDE) is an equation involving functions and their partial derivatives, and since many natural laws can be expressed in terms of rates of changes,PDEs appear and have applications in an enormous number of questions. For example,PDEs describe the propagation of sound or heat, the motion of fluids, the description of electric and magnetic fields, and the behavior of financial markets. In the first semester the course will focus in the study of the three basic equations that contain the ideas and the germ of generality to study more general PDEs: the Laplace equation, the heat equation,and the wave equation. The solutions of these equations have different qualitative and quantitative properties and their study is essential to understand elliptic, parabolic and hyperbolic equations. The emphasis will be on ideas and techniques presented in a modern way and that can be use later to deal with more difficult situations such us nonlinear equations.
Course Grading: based on regular homework, one midterm, and a final exam.
Exam Dates: TBA.
Attendance Policy: Attendance required.

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• The first day of classes is Monday, August 26.
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• Thanksgiving is Thursday, November 28.
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• The last day of classes is Wednesday, December 4.

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