Math 404 - Introduction to Partial Differential Equations
Location: Math/Psych 104
Time: TTh 1:00-2:15pm

Course Information

Office: Math/Psych 436
Email: bpeercy@umbc.edu
Phone: 410-455-2436
Office Hours: T/Th after class 2:15-3:00 and by appointment
Prerequisite: MATH 251 and MATH 225 with a C or better.
Course Textbook: The course will be taught from notes created by Dr. Jonathan Bell. These notes are available at http://www.math.umbc.edu/~jbell/pde_notes/. An additional Intro PDE text by John M. Davis Introduction to Partial Differential Equations may be useful for the second part of the course. The textbook by Peter J. Olver, Introduction to Partial Differential Equations may also be a useful support text.

Course Description
In an Introduction to Partial Differential Equations (PDEs) we appreciate the nature of multiple independent variables and how various quantities depend on them and their rates of change. We will define, classify and derive PDEs in various contexts, but focus on the classical transport, heat/diffusion, wave, and Laplace's equations. We will develop an understanding of solutions and the methods to obtain them on an unbounded domain and on bounded domains. We will utilize software to plot solutions.

Focused Objectives:

• Be able to confirm a solution of a PDE
• Be able to characterize a PDE as
1. linear, semi-linear, quasi-linear, or nonlinear
2. homogeneous or nonhomogeneous
3. order
4. parabolic, hyperbolic, or elliptic for 2nd order PDEs
• Understand the derivation of several classic PDEs such as wave, transport, and diffusion equations.
• Be able to solve 1st order, linear or semi-linear PDEs using method of characteristics
• Be able to use the heat kernel to solve PDE on the infinite domain
• Be able to derive the Heat kernel using separation of variables and transforms (Boltzman, Fourier, Laplace)
• Be able to apply Duhamel's principle to change non-homogenous equations.
• Be able to solve the wave equation using d'Alembert's solution.
• Understand the Domain of Dependence.
• Understand Dispersion and Dissipation in the telegrapher's equation.
• Be able to apply Fourier Transforms to reduce PDEs.
• Be able to apply Laplace transform to reduce PDEs.
• Understand interpretation of Neumann, Dirichlet, and Robin boundary conditions.
• Be able to apply separation of variables to PDEs and solve the associated eigenvalue problems.
• Be able to calculate Fourier series solutions and their coefficients.
• Be able to calculate solutions to the Sturm-Liouville eigenvalue problem.
• Understand what a Green's function is and how to calculate it.