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: 872-3659, FAX: 871-2320
Office Hours: 9AM-10AM (MTu_ThF), 1PM-2PM (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 mid-semester test (Friday, March 19, 1999) and a final exam (Tuesday, May 11, 1999, 2:45PM-4:45PM).

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.

90-100	A
80-89	B
70-79	C
60-69	D
0-59	F

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 Euler-Fourier 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 steady-state 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
• Sturm-Liouville Theory
  • General two-point boundary value problem
  • Eigenvalues and eigenfunctions
  • Lagrange's identity and consequences
  • Normalization of eigenfunctions and general eigenfunction expansions
  • Nonhomogeneous boundary value problems