Math 4545 - Fourier Series and PDEs

This is a first course in partial differential equations, introducing a number of fundamental tools and solving techniques. Topics may include: Fourier series and Sturm-Liouville problems; the heat, wave, and Laplace equations; separation of variables techniques; eigenfunction expansions; Fourier and Laplace transforms; Green's functions.

Instructor: Alina Marian, a.marian@neu.edu, office in 557 Lake Hall.

Lectures: Mon & Thurs 11:45-1:25 pm, YMCA 110.

Office hours: Mon & Wed 5-6 pm.

Textbook: Solution Techniques for Elementary Partial Differential Equations, by Christian Costanda.

Exams: There will be one midterm exam, one final exam, and occasional quizzes.

Prerequisites: Familiarity with multivariable calculus, linear algebra, and ordinary differential equations.

Homework: There will be weekly problem sets, due Thursday in class.

• Homework 1 (due September 11): Chapter 1 - 3, 6, 10, 12, 14, 18.
• Homework 2 (due September 18): Chapter 2 - 4, 6, 8, 15, 18, 22.
• Homework 3 (due September 25): Chapter 3 - 8, 10, 13, 14, 16.
• Homework 4 (due October 2): Chapter 3 - 2, 4, 17, 19, 26, 28, 32.
• Homework 5 (due October 9): Chapter 3 - 60, 62; Chapter 5 - 30, 34, 36, 42, 46.
• Homework 6 (due October 16): Chapter 7 - 22, 23, 26, 28, 32.
• Homework 7 (sample midterm problems, due October 23): Chapter 2 - 14, 16, 21; Chapter 3 - 15, 27, 61; Chapter 5 - 16, 23; Chapter 7 - 13, 16, 20, 31.
• No homework due October 30.
• Homework 8 (due November 6): Chapter 5 - 53, 55; Chapter 7 - 40, 44, 52, 54.
• Homework 9 (due November 13): Chapter 7 - 49, 51, also 52, 54 moved over from Homework 8.
• Homework 10 (due November 20): Chapter 9 - 1, 2, 4, 12, 14, 15, 18.
• Homework 11 (due December 1): Chapter 9 - 22, 24, 30, 35.