Dr. Neil Balmforth COURSES 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, with solution Ass 4, with solutions Ass 5, with solutions Sample problems on traffic flow and for the final (with some typos fixed) 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