APMAE4200 - PDEs
Fall 2023
Fall 2023
Time: MW 10:10am-11:25am
Place: 633 Mudd Building
Instructor: Dr. James Scott (he/him)
Affiliation: Applied Physics and Applied Mathematics, SEAS
Email: See "Home" on this website
Office Hours: M 11:30am-12:30pm, T 2:00-3:30pm, and Canvas discussions.
Office Location: 287D Engineering Terrace (accessible by going through the APAM offices)
Course Content: Course in partial differential equations. Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered.
Textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems. Richard Haberman. 2012 Addison-Wesley, ISBN: 9780321797063
Grades: Homework (40%), Exam 1 (20%), Exam 2 (20%), Exam 3 (20%).
You are required to complete the homework problems. Weekly homework assignments will be assigned on Mondays and submitted via Gradescope (on Courseworks) by 11:59 pm the next Monday. The lowest homework score will be dropped. As you will only become adept in solving problems through continual practice, this is a key component of the course. If you have questions about the homework problems, please come to office hours or email me. You are welcome to work together on homework. However, each student must turn in their own assignment.
There will be three non-cumulative exams given synchronously (they will begin and end during the class session). The online link for each exam will be available only for the 75-minute class time. The exams will be submitted via Gradescope.
Uploading Files to Gradescope: See this PDF and this video.
Additional Resources
Paul's Online Math Notes
Differential Equations (also some linear algebra)
Homework
Homework 11 (due Dec 18, 11:59 pm)
pdf
Solutions
Class Session Notes
September 6 (Introduction & heat equation)
September 11 (Heat equation, separation of variables)
September 13 (Separation of variables continued)
September 18 (Laplace Equation)
September 20 (Properties of Laplace Equation)
September 25 (Fourier Series)
September 27 (Test 1 Review)
October 2 (Wave Equation)
October 9 (Sturm-Liouville theory, part 1)
October 16 (Sturm-Liouville theory, part 2)
October 18 (Separation of variables in higher dimensions)
October 23 (Eigenproblem for the Laplacian)
October 25 (Inhomogeneous Boundary Conditions)
October 28 (Test 2 Review)
October 30 (Green's functions)
November 13 (Multi-dimensional Green's functions and Fredholm Alternative)
November 27 (Fourier Transform)
December 4 (Fourier Transform for wave equation)
December 4 (Method of characteristics)
Tests
Test 1 (Oct. 4)
Information
Solutions
Test 2 (Nov. 8)
Information
Solutions
Test 3 (Dec. 6)
Information
Solutions