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: shearer@ncsu.edu
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.
Grading and Exams:
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:
MAPLE programs:
download from MAC by control-click
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
Academic
Integrity Statement: Students are expected to follow university
policies on academic integrity and the Honor Pledge, which may be
viewed by following the links at: http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.7.php
Further Statements:
Reasonable accommodations will be
made for
students with verifiable disabilities. In order to take advantage of
available accommodations, students must register with Disability
Services for Students at 1900 Student Health Center, Campus Box 7509,
515-7653. For more information on NC State's policy on working with
students with disabilities, please see the
Academic
Accommodations for Students with Disabilities Regulation (REG02.20.1)
There are
no pass through
charges
for this course, such as field trip
costs.
Statement on laboratory safety or risk assumption in courses requiring
physical
activity or field trips: None