Differential Equations of Mathematical Physics


Recent news

I have finished the lecture notes, you can download them below. In case you find any more typos or mistakes, please send me an e-mail with these corrections. I have also added a first list of topics regarding the final exam.


Max Lein
Earth Sciences Centre
22 Russell Street
Office no. 3141

Office hours: Tuesday, 10:30-12:00, Thursday, 11:30-12:30

Teaching assistant

Daniel Fusca

Location in space-time

Tuesdays     9–10    SS 1074
Thursdays    9–11    SS 1074

Lecture notes

Download here (last update: 2014.09.19)

The lecture notes are complete now. However, I still appreciate any feedback and questions, in particular when it comes to typos.

All necessary course material will be contained in the lecture notes and the homework assignments, unless explicitly stated otherwise. Each chapter also contains references to supplementary material which may be of interest.

Homework assignments

Students will have one week to complete homework assignments.

Sheet 01        (due 2013.09.19)        problems        solutions
Sheet 02        (due 2013.09.26)        problems        solutions
Sheet 03        (due 2013.10.03)        problems        solutions
Sheet 04        (due 2013.10.10)        problems        solutions
Sheet 05        (due 2013.10.17)        problems        solutions
Sheet 06        (due 2013.10.24)        problems        solutions
Sheet 07        (due 2013.10.31)        problems        solutions
Sheet 08        (due 2013.11.14)        problems        solutions
Sheet 09        (due 2013.11.21)        problems        solutions
Sheet 10        (due 2013.11.28)        problems        solutions
Sheet 11        (due 2014.01.16)        problems        solutions
Sheet 12        (due 2014.01.16)        problems        solutions
Sheet 13        review
Sheet 14        (due 2014.02.06)        problems        solutions
Sheet 15        (due 2014.02.13)        problems        solutions
Sheet 16        (due 2014.02.27)        problems        solutions
Sheet 17        (due 2014.03.06)        problems        solutions
Sheet 18        (due 2014.03.13)        problems        solutions
Sheet 19        review
Sheet 20        (due 2014.03.27)        problems        solutions
Sheet 21        (due 2014.04.03)        problems        solutions
Sheet 22        review


20 % weekly homework (two will be dropped)
40 % 3 term tests
40 % final exam


The exact dates have not yet been fixed, but expect the tests to be scheduled in the following time periods:

term test 1: 5 November 2013, Galbraith Building, Room GB 119, 17-19
term test 2: 30 January 2014, Sidney Smith Hall, Room SS 1074, 9-11
term test 3: 20 March 2014, Sidney Smith Hall, Room SS 1074, 9-11
final exam: 29 April 2014, Central Exams Facility, Room EX 310, 14-17

Please make sure to arrive on time and bring a photo and a student id with you. The use of cell phones and any other electronic equipment is not permitted.

Please let me know of any collisions with other exams by mail. Note that due to (under)staffing issues, it may take some time until the exact dates will be announced.

Test 1

Test 1 covers all material up to and including Chapter 5.2 as well as all homework problems up to and including sheet 07.

Test 01        test        solutions

Test 2

Test 2 covers all material from Chapter 5.3 up to and including Chapter 7 as well as all homework problems from sheets 8-12. I have compiled a list of topics and exercises on sheet 13.

Test 02        test        solutions

Test 3

Test 3 covers all material from Chapter 8 up to and including Chapter 9 as well as all homework problems from sheets 14-18. I have compiled a list of topics and exercises on sheet 19.

Test 03        test        solutions

Final exam

The final exam covers the material from the whole course, i. e. the lecture notes front to back as well as all homework assignments. It will take place on 29 April 2014, 14:00-17:00, EX 310. This room is located in the Central Exams Facility, 255 McCaul St. just south of College St. I have uploaded a review sheet which covers the material not found on the review sheets for Tests 2 and 3.

The final exam covers everything from Chapter 1 to Chapter 10, and its style will be very similar to Tests 1–3. I will release a list of topics for the things which are not covered by Tests 2 and 3 shortly. Here are a few suggestions on how to prepare:

  • Work smart. Perhaps you are taking another class where the same material is covered (e. g. classical mechanics).
  • Being surefooted in computations helps. For instance, I expect that you know standard integration techniques (e. g. integration by parts or simple substitutions) and multivariable calculus (e. g. partial derivatives).
  • Rewrite Tests 1–3 after studying. If you want to impose an extra challenge on yourself, reduce the time by 15 minutes. Reducing time also provokes avoidable mistakes (e. g. sign mistakes in computations), and exposes your weaknesses more clearly.

Feel free to stop by my office for questions or send me a mail.