Dr. Neil Balmforth
Midterm date, after much agonization: 27th February
This course provides an introduction to practical analytical solution
methods for PDEs.
The final exam will take place on April 23rd. It is an (open-book) take-home
affair. The exam will be posted on this page, and must be submitted electronically
via CANVAS (email is acceptable if there are uploading issues).
It will be posted shortly before 12:45pm, due at 3pm.
I will be checking my email if there are any queries about the exam
For those who have accommodations at the Centre for Accessiblity, you
will be granted extra time; your exams will be due at 4.08pm.
I have received email expressing concerns over the possibility that students will
coordinate efforts in completing this examination. Please note that the exam
is intended to be an individual effort; any such collaboration is unfair on
the students that do not indulge in such clandestine activity.
13th April: some typos have been corrected in the solutions to Ass 5 and in the
lecture notes on characteristics
In view of the measures taken given the virus, lectures are now
Lecture notes for the week of March 16-20
Lecture notes for the remainder of the course
Tuesday (March 17) afternoon, I will be preparing video lectures
and will post these on YouTube for your enjoyment. The links will appear here
soon. In the meantime, please look over the lecture notes above.
Videos for the week of March 16-20:
Laplace transforms I
BONUS: spot the deliberate error in the first half of
this lecture ! (Introduced to enhance your
Answer at the bottom of the webpage.
Laplace transforms II
Videos for the week of March 23-27:
Method of characteristics I
Method of characteristics II
Videos for the week of March 30 - April 3:
Method of characteristics III
Method of characteristics IV
Method of characteristics V
(Am afraid I ran out of steam a little in this one...)
I. PDEs and canonical examples
II. Separation of variables and Fourier series
III. Eigenfunction expansions
IV. Transform methods
V. Characteristics methods
Assessment will involve coursework (homework problems) and examination.
Office hours: Tuesday 11am, Thursday at noon.
R. Haberman, ``Applied PDEs''
The TA: Wesley Ridgway (wridgway-at-math)
More summary notes
Ass 1 with solution,
Ass 2 with solution,
Ass 3 with solution,
Ass 4, due March 26,
Ass 5, not to be graded,
Midterm from a previous year (with solution)
Last year's midterm (with solution)
The midterm (with solution)
Additional problems on traffic flow and more sample
final exam problems
Additional relevant problems from Haberman (4th edition):
* Separation of variables and Fourier series -
2.5.3, 2.5.9, 3.4.12, 4.4.3(b)
* Halfway house (requiring Sturm-Louiville theory, but trig functions)
- Worked example of section 5.7 upto eq (5.7.11),
Physical examples of section 5.8
* Separation of variables and Bessel functions - 7.7.1 (assume r is less than
7.7.3 (the frequencies of vibration are the possible values of w
in the cos(wt) and sin(wt) functions of the separation-of-variables
general solution), 7.8.2(d), 7.9.1(b), 9.7.4(a)
Separation of variables and Legendre functions - final example in section 7.10,
More relevant problems from Haberman (4th edition):
* Fourier Transforms - example in Sec 10.4.1;
problems 10.4.3, 10.4.6;
example at the end of Sec 10.6.3;
problems 10.6.1(a), 10.6.18
* Laplace transforms - problems 13.4.3, 13.4.4, 13.5.3
* Characteristics - example starting with eq (12.2.13);
problems 12.2.5(b) and (d);
Sec 12.6.5; problems 12.6.3, 12.6.8, 12.6.9
Answer: The Laplace transform of f(t)=t exp(-t) is