APMAE4200 - PDEs
Fall 2021
Instructor: Dr. James Scott (he/him)
Affiliation: Applied Physics and Applied Mathematics, SEAS
Email: See "Home" on this website
Office Hours: R 2:00-4:00pm, or by appt
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)
Lecture Notes
September 13 (Introduction & heat equation)
September 15 (Properties of heat equation)
September 20 (Solving the heat equation)
September 22 (Solving the heat equation, ctd. Laplace equation)
September 27 (Solving Laplace's equation on a rectangle and on a disk). Recording Link
September 29 (Qualitative Properties of Laplace's Equation)
October 4 (Fourier Series)
October 6 (Test 1, no class)
October 11 Part 1, Part 2 (Fourier Series ctd., Wave Equation)
October 13 (Sturm-Liouville Theory)
October 18 (Sturm-Liouville theory continued)
October 20 (Sturm-Liouville theory - Rayleigh quotient)
October 25 (Separation of Variables in Multi-d) (Eigenproblem for Laplacian)
October 27 (Eigenproblem for Laplacian) (Inhomogeneous Problems)
November 3 (Test 2 Review) (Green's Functions and the Dirac Delta Measure)
November 8 (Green's Functions and the Dirac Delta Measure)
November 10 (Test 2, no class)
November 15 (Green's Functions in Multi-d and Fredholm Alternative)
November 17 (Green's Functions in Multi-d and Fredholm Alternative)
November 22 (Green's Functions (see above notes), Fourier Transform)
November 29 (Fourier Transform continued, see above notes)
December 1 (Test 3 Review) (Fourier Transform continued, see above notes) (Method of Characteristics) Recording Link
December 6 (Method of Characteristics)
December 8 (Test 3, no class)
December 13 (Method of Characteristics, Other Directions)