Dr. Neil Balmforth

Applied PDEs

This course provides an introduction to practical analytical solution methods for PDEs.

The syllabus:
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.
Recommended text:
R. Haberman, ``Applied PDEs''

The TA: Arun Rajendran (rajendranarun95@gmail), who has generously offered to give additional office hours (Monday, 10:30am, in LSK 300)

Midterm: March 7th

Ass 1, with solutions and more pde400-1.m (plot with dots showing truncated series)

Ass 2, with solution (and with the correct Bessel functions and the right warm-up problem 3) pde400-2.m

Ass 3, with solution (and THE typo fixed)

Sample midterm

Midterm from a previous year (with solution)

The Midterm with solution

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 a), 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, problem 7.10.2

Ass 4, due Tuesday March 26

Ass 5, due Thursday April 4

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

Sample problems on traffic flow and for the final (typo fixed in question 3 of the traffic flow problems)

Last year's final

Department of Mathematics / Fluid Labs / Neil Balmforth / Courses