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.
Midterm: Thursday before reading week
Office hours: Monday, Tuesday and Thursday at 11am

Ass 1 (with solutions)
Ass 2 (with solutions)
Ass 3 (with solutions)
Ass 4 (with solutions)
Ass 5 (due March 28; typo in L{delta(x-vt)} = v^(-1) exp(-sx/v) corrected)
Bonus problem

Sample midterm
Actual midterm plus solution
Some additional problems from Haberman (4th edition):
Separation of variables (7.8.2(d), 7.9.1(b), 7.9.4(a)
Sec 7.10 final example, 7.10.2). Transforms (example in Sec 10.4.1, 10.4.3, 10.4.6, 10.6.18)
Characteristics (example starting with eq (12.2.13); 12.2.5(b) and (d); Sec 12.6.5; 12.6.3, 12.6.8, 12.6.9)
Recommended text:
R. Haberman, ``Applied PDEs''

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