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: Monday, Tuesday and Thursday at 11am
Recommended text:
R. Haberman, ``Applied PDEs''

Midterm: Thursday, Feb 15th.

Ass 1 (with solution)
Ass 2 (with solution)

Sample midterm

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

Actual midterm (with solution)

Ass 3 - due Tuesday, March 6

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