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- Spring 2019
- Dates: MWF 9-10 am
- Place: Etcheverry 3106
- Prerequisites: Math 53, Math 54. Math 104 is useful, but not necessary.
- Material: A description of covered topics, homework assignments, and all announcements will be posted weekly on the course webpage.
- GSI Office Hours (Evans 745): Mo 1-2:30pm, Th 11am-12:30pm
- My Office Hours: M 10-11am, W 10am-noon

**About the Course**

This is a first course in partial differential equations (PDE), a field which might be described as “a mathematical attempt to understand the world around us”. PDE arise as the most basic laws of nature which makes them ubiquitous in physics and other sciences; also in engineering and finance, PDE play a crucial role. During the first part of the class, we will mostly focus on three fundamental equations: Laplace's equation, the diffusion (or heat) equation, and the wave equation. We will introduce Fourier series and the Fourier transform, Green's functions, distributions, and numerical methods for solving PDE. Finally, we will discuss some nonlinear PDE and the calculus of variations.

Basic linear algebra (Math 53) and a strong command of multivariable calculus (Math 54) are necessary to follow the class. Prior knowledge in real and complex analysis or ordinary differential equations can be helpful but is not necessary.

MWF 9-10 am in Etcheverry 3106

Our GSI Albert Ai will provide regular office hours in 745 Evans Hall at the following times:

Mo 1-2:30pm, Tu 11am-12:30pm

You can find me in 895 Evans Hall by appointment or during my regular office hours:

Mo 10-11am, We 10am-noon

I have reserved a print version of the primary textbook of the course:

Walter A. Strauss: *Partial Differential Equations: An Introduction* (2nd Ed.), John Wiley & Sons, Ltd. (2007). ISBN: 978-0470-05456-7

You can rent it for 2 hours at the Mathematics/Statistics Library in Evans Hall. If you want to buy the book, you may want to try to find a used version of the book at a more favorable price. However, the first edition is not recommended.

The following two books might be useful:

L. Craig Evans: *Partial Differential Equations*, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, 1998.

Michael Shearer and Rachel Levy: *Partial Differential Equations: An Introduction to Theory and Applications*, Princeton University Press, 2015.

There are many versions of Craig Evans' book available at the library. I have reserved the book of Shearer and Levy for 2-hour loans in the Mathematics/Statistics library for you.

Homework | 20% | |

Midterm | 30% | |

Final Exam | 50% |

When computing your final score, the lowest score of your homework assignments will be dropped. If your score in the final exam is better than your midterm grade, the latter will be replaced by the former: \[ \text{Final Grade} = \frac{2H+3\max\{M,F\}+5F}{10}, \] where \(H\) is your total homework score, \(M\) your midterm grade, and \(F\) your final exam grade.

There will be weekly homework assignments posted on the course webpage at least one week prior to the due date. You can hand in your solutions at the beginning of class, or in my office by 9:00 am the same day, either in person or by sliding them under my door. Late homework will not be accepted under any circumstance; but the lowest score will be dropped when computing your final grade.

Group work is highly encouraged, but each student has to write the final solution in their own words. Please acknowledge who you collaborated with by writing their names on the top of your homework. Copying homework from other students or from other sources will be considered cheating. A good rule of thumb for you is: Discussing the problem and explaining ideas is acceptable, but reading another student's solution (or having it read to you) is not.

The midterm exam will take place in the classroom at the usual time of class (i.e. Berkeley Time). The final exam will start on time, not at Berkeley Time. Please arrive some minutes earlier for the exams to not interrupt your fellow students.

Midterm: | Friday, March 15, 9-10am |

Final exam: | Monday, May 13, 7-10pm |

There will be no make-up exams but the final exam score can replace your midterm score.

If you have a documented disability and require special accommodations of any kind, please e-mail me as soon as possible, and no later than Friday, February 8.

If you are officially representing the university and if there is a conflict with any of the midterms or the final exam, please e-mail me as soon as possible, and no later than Friday, February 8.

Prof. Dr. Tim Laux

Contact:

Prof. Dr. Tim Laux

Faculty of Mathematics

University of Regensburg

tim.laux(at)ur.de

+49 228 / 73-62225