Math 401  Applied Differential Equations II     Spring, 2013

TuTh  1:30 - 2:45 pm;   Room: POE 517.

Web page: http://www4.ncsu.edu/eos/users/s/shearer/www/ma401_2013.html

Instructor  Michael Shearer     Office
: SAS 3228     Phone: 515-3298    Email:

Office Hours:   Mondays, 3:00-3:30 p.m., and by appointment.

Book:  Partial Differential Equations with Fourier Series and Boundary Value Problems,
2nd edition.     Author: Nakhle Asmar

Prerequisite: MA301 or MA 341 Differential Equations.

1. Weekly Homework Assignments (10% of final grade)
due Tuesdays.
2. Two in-class exams (25% each).
Tentative Dates:  Tuesday, February 26th;  Thursday, April 17th.
3. Final exam (40%): Tuesday, May 7th, 1-4 p.m.

Basic Grading Scale: 90%-100%: A, 80%-89%: B, etc.   (+ and - will also be used.)

Syllabus:

Introduction
Sturm-Liouville Problems
Fourier Series
Maple code for Fourier series
Convergence of Fourier Series
Introduction to Partial Differential Equations (PDEs)
Separation of Variables
One-dimensional Wave Equation:
MAPLE code for initial boundary value problems
One-dimensional Heat Equation
Higher Dimensional Equations and Laplace’s Equation
MAPLE code for 2-dim wave equation.
MAPLE code for Bessel functions
ODEs: power series solutions
PDEs in Polar Coordinates
PDEs in Spherical Coordinates

Course Objectives: Math 401 is an introduction to series solutions of PDEs. At the end of the course you will be able to solve initial boundary value problems for various PDEs, and will have the techniques for solving a large class of linear PDEs using Fourier series and separation of variables. The mathematics of this approach is largely centered on issues of convergence of the Fourier series; we will also examine properties of the solutions that can be deduced from the series, and the interpretation of solutions in terms of the physical processes modeled by the PDEs.

Class Policies:
1. I encourage you to discuss homework with other students, or with me during office hours. You should be aware that the homework is intended for you to learn from the course; working on homework at least in part on your own will help you master the material, keep up with the course and prepare for tests. Homework will be graded on a scale of 1-10. Points will be awarded for amount of homework attempted; selected problems will be graded in detail.
2. I expect you to read sections of the book around the time of lectures and homework from those sections. The book has additional examples and discussion that you will find helpful. Some test questions may resemble examples from the book.
3. You are expected to attend all classes on time. Classroom discussion and questions in class help clarify issues in this course, so please feel free to participate by asking questions.
4. Arriving late for a class or leaving early is very disruptive of class. If you need to leave early, please let me know at the beginning of class, and sit near the door so you can slip out quietly.
5. If you are unavoidably absent from a test, a score for that test will be assessed at the end of the semester, based on your performance in homework, the other tests, and on the final, with an emphasis on the material of the missed test.  Attendance regulations can be found at http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.3.php