Dr. Neil Balmforth COURSES Applied PDEs This course provides an introduction to practical analytical solution methods for PDEs. Anouncements: 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: Wed at 2pm, Fri at 1pm Recommended text: R. Haberman, ``Applied PDEs'' The TA: Merlin Pelz (merlinpelz at math) Hours in MLC: Mon 2:30-3:30, 6:00-7:00 (online), Thurs 2:00-3:00, 5:00-6:00 (online) Lecture notes: I, II, III, IV, V, VI, VII (Beware! These are a work in progress and may contain typos - please let me know if you spot any) Synopses from a previous year: 1, 2, 3, 4, 5, 6a, 6b, 7a, 7b, 8, 9, 10a, 10b, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, More lecture notes: Laplace transforms, Method of characteristics Laplace transform question From Michael Ward: Worked problems Notes Assignments: Assi 1 (due Sep 29). By popular demand, and because I am a complete push-over, now due October 2nd. figure (pd23a.png), MATLAB code (pd23a) Assi 2 (due ??; preliminary version). figure (pd23b.png), MATLAB code (pd23b) Midterm: Provisional date - Oct 20 Sample 80min exams: 1, 2, 3 Older 50min midterm Previous finals: 2018, 2019 Additional problems on traffic flow and more sample final exam problems Video lectures for the final few weeks of the course, should I become mysteriously waylaid: Laplace transforms I (beware of a slip in this lecture - the Laplace transform of f(t)=t exp(-t) is 1/(s+1)^2) Laplace transforms II Method of characteristics I Method of characteristics II Method of characteristics III Method of characteristics IV Method of characteristics V 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), 7.9.4(a) * Separation of variables and Legendre functions - final example in section 7.10, problem 7.10.2 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