** Instructor: ** Dennis DeTurck

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- Welcome to Math 425!
- Here are my solutions to the take-home portion of the final exam and the in-class portion of the final exam (as of 4pm on Sunday, a few typos I encountered while grading have been corrected)
- The answers to the the Fourier transform homework, and the solution of the Black-Scholes equation for call options are posted below. The final exam prep page has been updated to include a Black Scholes option (so to speak).
- Here are some notes on the Heisenberg uncertainty principle (all the details are right, at last!).
- Preparation for the final exam.
- Notes on the Black-Scholes equation.
- Here are notes on the Fourier transform. You will need them to do this week's homework.
- Here are my solutions to the midterm.
- Here is a copy of the midterm
- It is permissible to work on the homework in small (2-3 person) groups and hand in one joint copy of the assignment. Do this sensibly, though!
- There is a TA/grader for this class: her name is Zhen Zeng and her office is DRL 4C13. She will have regular office hours on Fridays from 1-2pm.

- Class meetings are TTh from 10:30 - noon in DRL A4
- The textbook is
*Partial Differential Equations, an introduction*(second edition) by Walter Strauss (pub. Wiley). It is possible to buy this at the bookstore for an exorbitant price. But if you look around on the web you can acquire it for significantly less. - Since I am the Dean of the College of Arts and Sciences, I have two offices. I spend
most of my time in my "Dean's office", 120 Logan Hall (tel. 8-7867).
I also have a Math Department office, DRL
3E5D, tel. 3-9036, but I will
*never*be there because the office is being used this semester by a visitor to the department. I'm also faculty director of Riepe College House in the Quad, where I reside in Magee 209. My email address is deturck@sas.upenn.edu.I will (usually) have "regular" office hours on Mondays from 6-7:30 pm, at my place in the Quad, since that's a pretty central location. "Regular" means that during those times, I'm there for my Math 425 students, and I'm not allowed to tell you I'm busy (unless it's with another student). You are welcome to stop by at other times, but at those times I reserve the right to ask you to come back later if I'm involved with other stuff. There will be other times that I will announce either in class or by email (and they'll always be posted on this website). Occasionally I will have dean stuff on Monday evenings, and I'll let you know about changes to that schedule as well.

- There is a TA/grader for this class: her name is Zhen Zeng and her office is DRL 4C13. She will have regular office hours on Fridays so you can get a jump on the homework. This week (Jan 22) her office hour will be from 4-5. After this week, it will be from 1-2 (on Fridays).

Homework will be assigned at almost every class session (well, at least
weekly).
You will sometimes need to use a computer to do some
of your homework. The hardest thing about the study of PDE is that by its
nature, it deals with functions of several variables, which are
often difficult
to visualize. So I want you to work a little bit all the time (rather than
in a panic the night before some big assignment is due) so that what goes
on in class makes more sense to you. The homework will often contain
instructions for **reading**. Make sure you do the
reading *before * the class for which it is assigned. I will assume you
have done so.

- First midterm: Thursday February 25, 2016.
- Here is a copy of the first midterm
- And here are my solutions
- Here is my first midterm from spring 2010. And here's an older one. And here are some practice problems from 2010.
- Here are my solutions to the spring 2010 exam . Here are the solutions to the older one. And here are the solutions to the practice problems from 2010.

- Second midterm: Thursday March 31, 2016.
- Here is a copy of the second midterm
- Here are my solutions to the secondmidterm.
- Here are some practice problems for exam 2 and the answers.

- Final exam: Wednesday May 4, 2016, from noon - 2 pm in Cohen 402

- January 14
- Notes from week 1 (ODEs).
- Notes on first-order PDEs.
- January 19
- trig.alt?
- January 26 (Now due Thursday, February 4)
- Notes on d'Alembert's solution of the wave equation
- February 4
- Symmetry and the heat equation (slides)
- Initial values for the heat equation (notes)
- February 16
- March 1
- March 17
- April 5
- April 12: Here are notes on the wave equation on the disk. The homework for Tuesday April 19 is to do all the problems at the end of the notes
- Here are note on the Fourier transform.
- April 19.
- Notes on the Black-Scholes equation.
- Here are some notes on the Heisenberg uncertainty principle
- Here are a few hints for the Fourier transform homework. Problem 4(d) is particularly tricky.
- Here is the solution to the Black-Scholes equation for call options.

- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5 (now including Chapter 4 problems)
- Homework 6
- Homework 7
- Homework 8
- Homework 9
- Homework 10