Lecture: Mon, 10:30–12:15 in HG00.086 (1st quarter) / HG00.310 (2nd quarter)
Tutorial: Thu, 13:30–15:15 in HG03.054 (1st quarter) / HG00.114 (2nd quarter)
Exam: Thu, January 17, 2019, 16:30–19:30, HG00.071
Lecturer: Dr. Annegret Burtscher, HG03.744
Teaching assistant: Evert-Jan Hekkelman
Office hours: Tue, 13:00–14:00, and by appointment
Course description: Partial differential equations describe a wide range of phenomena (heat, sound, fluid dynamics etc.) and thus play an important role in many applications. In this course we will introduce and study the basic types of partial differential equations. Solution methods, representation formulas for solutions and properties of solutions for classical linear equations of second order (Laplace, heat and wave equation) will be discussed. We are mainly concerned with existence, uniqueness and regularity of solutions. This involves the use of fundamental solutions, the maximum principle for elliptic equations etc. Furthermore, nonlinear partial differential equations of first order will be considered via the method of characteristics.
The idea is to give a first overview of the vast field of partial differential equations. This is based on a more hands-on approach and does not (yet) require much background in functional analysis.
Lecture notes and textbooks: Some lecture notes will be provided, but you are advised to also take notes during lectures. The following textbooks contain similar material and can be used for additional reading (in this order):
– Lawrence C. Evans, Partial differential equations, 2nd edition, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. ISBN: 978-0-8218-4974-3
– Walter A. Strauss, Partial differential equations. An introduction, 2nd edition, John Wiley Sons, Ltd., Chichester, 2008. ISBN: 978-0-470-05456-7
– Fritz John, Partial differential equations, Reprint of the 4th edition, Applied Mathematical Sciences, 1. Springer-Verlag, New York, 1991. ISBN: 0-387-90609-6
Prerequisites: A solid understanding of linear algebra, calculus, analysis and to some extent ordinary differential equations is required.
Assignments and tutorial: New problems will be assigned each week. You will try these problems at home yourself first, and then get the opportunity to discuss them with fellow students and the teaching assistant during the tutorial. [More information will be provided later.]
Academic Integrity: You will work cooperatively on the problems and are also encouraged to discuss the assignments with your fellow students and the teaching assistant. The solutions, however, have to be written up independently by each student and must be expressed in her/his own words. Citations must be provided for external input such as books, web pages etc.
Grading: The final grade will be based on a weighted average of the homework and the final exam as follows:
- Homework ….. 20%
- Final exam ….. 80%
Please contact me if you have any questions.