2025 Fall Partial Differential Equations Syllabus - Mathematics 8141.001

Partial Differential Equations

3

In person

Tu/Th 11:00am-12:20pm

Wachman 617

Katrina Morgan

morgank@temple.edu

Wachman 614

n/a

Tu 2:00-3:30pm; Th 9:30-11:00am; or by appointment

Primary Text: Partial Differential Equations, 2nd Edition by Lawrence C. Evans
Other Useful Texts:
- Partial Differential Equations I, 2nd Edition, by Michael E. Taylor
- Introduction to Partial Differential Equations, 2nd Edition, by Gerald B. Folland
- A Guide to Distribution Theory and Fourier Transforms, 2nd Edition, by Robert S Strichartz

Course grades will be determined according to the following scheme:

• 40% Homework
• 20% In-class Presentation
• 30% Final Video Presentation
• 10% Course Study Guide

Knowledge of Advanced Calculus is assumed

This course will introduce fundamental results, tools, and techniques in the field of partial differential equations. 

• Introduction to PDEs and basic techniques (examples of PDEs, Green’s theorem, multivariable IBP and polar coordinates, convolutions, etc.)
• Laplace’s/Poisson’s Equation (radial solutions, solutions to inhomogeneous problem, mean-value formulas and related properties, boundary value problem on half-space and half-line, fundamental solutions and Green’s function, energy methods)
• Heat Equation (fundamental solution, mean-value formula, maximum principle, infinite speed of propagation, regularity, energy methods)
• Wave Equation (solutions by spherical means, reflection method, method of descent; finite speed of propagation, Huygens’ principle; energy methods)
• Nonlinear Equations and Method of Characteristics
• Further topics will be discussed as time allows. This may include a brief intro to pseudodifferential operators, including Sobolev spaces, distributions, and Fourier transforms

There will be no exams in this course.

Mandatory

This course has a Canvas page where all assignments and course information will be distributed. An iPad is useful but not required for the final video presentation. Access to a computer with microphone is required for the video presentation. If you have questions or concerns about meeting this technology need, please talk to the instructor.

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