Math 404  Introduction to Partial Differential Equations
Location: Math/Psych 104
Time: TTh 1:002:15pm
Course Information
Instructor: Dr. Bradford E. Peercy
Office: Math/Psych 436
Email: bpeercy@umbc.edu
Phone: 4104552436
Office Hours: T/Th after class 2:153:00 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
 linear, semilinear, quasilinear, or nonlinear
 homogeneous or nonhomogeneous
 order
 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 semilinear 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 nonhomogenous 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 SturmLiouville eigenvalue problem.
 Understand what a Green's function is and how to calculate it.
Grading Policy
There will be several components to your grade.
 Weekly homework (40%).
 Three Exams (36%)
 Final exam (24%)
You will be allowed to drop two homework scores. No late homework will be accepted. I expect your homework to be legible and wellorganized.
Blackboard will be used to post grades (Login to https://my.UMBC.edu).
Academic Integrity Statement
By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage www.umbc.edu/integrity, or the Graduate School website www.umbc.edu/gradschool.
Tentative Course Schedule
Thurs Aug 27  Introduction: What is a PDE? 
Tues Sept 1  Useful background from ODE, Lin Alg, and Multivariable Calculus 
Thurs Sept 3  Classification/Derivations of Some Classical PDEs.  Due HW1: 
Tues Sept 8  First Order PDEs 
Thurs Sept 10  First Order PDEs continued  Due HW2: 
Tues Sept 15  Wave equation Derivation 
Thurs Sept 17  D'Alembert's Solution  Due HW3: 
Tues Sept 22  Domain of Dependence/Influence, Well Posedness, Nonhomogeneous Wave Equation 
Thurs Sept 24  Diffusion/Heat Equation  Due HW4: 
Tues Sept 29  Exam #1 
Thurs Oct 1  Nonhomogeneous Diffusion Equation 
Tues Oct 6  Telegraph equation/Dispersion Relation  Due HW5: 
Thurs Oct 8  Integral Transforms: Fourier 
Tues Oct 13  Integral Transforms: Laplace  Due HW6: 
Thurs Oct 15  Boundary Value Problems (BVPs) 
Tues Oct 20  Separation of variables/Eigenvalue problems  Due HW7: 
Thurs Oct 22  More Problems on the Finite Domain 
Tues Oct 27  
Thurs Oct 29  Convergence results, Gibb's Phenomena  Due HW8: 
Tues Nov 3  Exam #2 
Thurs Nov 5  Source problems for BVPs  Due HW9: 
Tues Nov 10  SturmLiouville Theory 
Thurs Nov 12  Eigenfunction Theory  Due HW10: 
Tues Nov 17  Laplace equation/Poisson's Formula 
Thurs Nov 19  Laplace Equation Properties  Due HW11: 
Tues Nov 24  
Thurs Nov 26  Thanksgiving Break 
Tues Dec 1  SelfAdjoint Form, Green's Functions for ODEs 
Thurs Dec 3  Green's Functions for PDEs  Due HW12: 
Tues Dec 8  Exam #3  Last day of classes 
Thurs Dec 10  Reading Day 
Tues Dec 15  FINAL EXAM 1:003:00 MP 104 
