APMAE4200 - PDEs
Spring 2024
Spring 2024
Time: TR 1:10pm-2:25pm
Place: 633 Mudd Building
Zoom Room: https://columbiauniversity.zoom.us/j/698568318918
Instructor: Dr. James Scott (he/him)
Affiliation: Applied Physics and Applied Mathematics, SEAS
Email: See "Home" on this website
Office Hours: M 10:00am-11:00am, T 2:30-3:30pm, 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:
Introduction to Partial Differential Equations. Peter J. Olver. 2014 Springer, ISBN: 9783319020983
Optional textbooks:
Applied Partial Differential Equations with Fourier Series and Boundary Value Problems. Richard Haberman. 2012 Addison-Wesley, ISBN: 9780321797063
Partial Differential Equations: An Introduction. Walter Strauss. 2008 Wiley, ISBN: 9780470054567
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 Tuesday. 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)
Desmos online graphing calculator
Class Session Notes
January 16 (Introduction)
January 16 (Linear and nonlinear waves - transport equations)
January 18 (Linear and nonlinear waves - nonlinear transport equations)
January 23 (Linear and nonlinear waves - wave equation)
January 25 (Introduction to Fourier series - introduction via the heat equation)
January 30 (Fourier series - convergence)
February 1 (Fourier series - calculus. The heat equation - derivation)
February 6 (The heat equation - separation of variables)
February 8 (Test 1)
February 13 (The wave equation - separation of variables)
February 15 (The Laplace/Poisson equation - separation of variables)
February 20 (Green's functions)
February 27 (Multi-d Green's functions)
February 29 (Fourier Transform)
March 5 (Fourier Transform)
March 7 (Fourier Transform, Test 2 Review)
March 12 - March 14 (spring break, no class) (link to practice problems)
March 19 (Test 2)
March 21 (General Framework for linear PDEs)
March 28 (Heat/wave equations in 2 dimensions)
April 2 (General Poisson problems)
April 4 (Inhomogeneous IBVPs)
April 9 (no class)
April 11 (Inhomogeneous IBVPs)
April 16 (Fundamental solutions in 3D)
April 18 (Separation of variables in 3D)
April 23 (Review/Overlook)
April 25 (Test 3)
Tests
Test 1 (Feb 8)
Information
Solutions
Test 2 (Mar 19)
Information
Solutions
Test 3 (Apr 25)
Information
Solutions