Partial Differential Equations
Spring Semester 1999
MATH 467.01 (3 credits), M W F, 2:00PM2:50PM, Wickersham 109

Textbook:

Elementary Differential Equations and Boundary Value Problems,
6th edition,
William E. Boyce and Richard C. DiPrima,
John Wiley & Sons,
1997.

Prerequisites:

A grade of C or better in
MATH 365 (Ordinary Differential Equations) is a prerequisite for this course.

Instructor:

Dr. Buchanan
Office: Wickersham 113, Phone: 8723659, FAX: 8712320
Office Hours: 9AM10AM (MTu_ThF), 1PM2PM (W),
or by appointment
Email:
Robert.Buchanan@millersville.edu

Attendance:

Students are expected to attend all class meetings.
Much of the material presented in class supplements the textbook,
therefore it is very important for students to be in class every day.
If you must be absent from class you are expected to complete class
requirements (tests and/or homework assignments) prior to the absence.
Students who miss a test should provide a valid excuse, otherwise you
will not be allowed to make up the test.
Tests should be made up within one week of their scheduled date.
No final exam exemptions.

Homework:

Students are expected to do their homework and participate in class.
Homework problems will be collected frequently and graded.
Included in the category of homework will be a course project on a
topic from PDEs.
The project will have a written component (a paper) which you will
hand in to me.
There will also be a public presentation to other interested students
during Math Awareness Week (during April 1999).

Tests:

A midsemester test (Friday, March 19, 1999)
and a final exam (Tuesday,
May 11, 1999, 2:45PM4:45PM).
If you feel that an error was made in the grading of a test or
homework assignment, you
should explain the error on a separate sheet of paper and return both
it and the test to me within three class periods after the test or
homework is
returned to you.

Grades:

Course grade will be calculated as follows.
Midterm  1/3 
Exam  1/3 
Homework  1/3 
The course letter grades will be calculated as follows.
90100  A 
8089  B 
7079  C 
6069  D 
059  F 
Course Contents
Topics covered in this course will include the following.
The material will be presented in a logical order, though not
necessarily in the order shown below.
Other topics will be added as time and interests allow.
 Introduction

Extremely
brief review of topics from ordinary differential equations

Heat equation as model of heat conduction in a rod

Separation of variables

Fundamental solutions and superposition of solutions
 Fourier series

Orthogonality and EulerFourier formulas

Periodicity

The Fourier Convergence Theorem

Even and odd functions; sine and cosine series

Extensions of functions to even and odd functions
 The Heat Equation

Solution of initial/boundary value problems

Homogeneous Dirichlet boundary conditions

Nonhomogeneous boundary conditions and steadystate solutions

Other boundary conditions

A Maximum Principle and uniqueness of solution for the heat equation
 The Wave Equation

Solution of initial/boundary value problems

Characteristic coordinates and a general solution

D'Alembert's solution of the initial value problem

Energy integrals and uniqueness of solution for the wave equation
 Laplace's Equation

Boundary value problems in rectangular coordinates

Boundary value problems in polar coordinates

Periodic boundary conditions

Neumann problems and mixed boundary conditions

Lack of uniqueness of solution

Necessary conditions for the existence of a solution

Uniqueness of solution

Mean Value Property

Weak form of the Maximum Principle

Uniqueness of solutions of the Dirichlet problem
 SturmLiouville Theory

General twopoint boundary value problem

Eigenvalues and eigenfunctions

Lagrange's identity and consequences

Normalization of eigenfunctions and general eigenfunction expansions

Nonhomogeneous boundary value problems
Page maintained by: Robert.Buchanan
Robert.Buchanan@millersville.edu
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