2018 Fall Course Syllabus - Mathematics 8141.001
Course: Mathematics 8141.001.
Course Title: Partial Differential Equations I.
Time: T/Th 1:00pm-2:20pm.
Place: Wachman 617.
Instructor: Cristian E. Gutierrez.
Instructor Office: Wachman 1022.
Instructor Email: cristian.gutierrez@temple.edu
Instructor Phone: 215-204-7284.
Office Hours: By appointment.
Prerequisites: Advanced Calculus.
Textbook: Partial Differential Equations by L. C. Evans, ISBN: 978-0-8218-0772-9. Notes and assignments will be posted regularly in Canvas.
Course Goals: Introduce fundamental concepts and results in the theory of elliptic, parabolic and hyperbolic differential equations. Problem solving to prepare students 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 starts with the study of first order pdes. We will next focus on the study of the three basic second order 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 di fficult situations such us nonlinear equations. These extensions will be the subject of the second semester. 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, click here.
Course Grading: It will be based on homework, one midterm, and a final exam.
Exam Dates: TBA.
Attendance Policy: Attendance to the lectures is recommended.
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)