Ordinary Differential Equations, Fall 2012

Instructor

Aleksandar Donev, 1016 Warren Weaver Hall
E-mail: donev@courant.nyu.edu ; Phone: (212) 992-7315
Office hours: 3-5 pm Tuesdays, or by appointment

Recitation

Fri 3.30 PM - 4.45 PM at CIWW room 101, starting Sept. 14th
Travis Askham, askham@cims.nyu.edu
Office hours (starting Friday Sept 7th):
Wednesdays 10-11am, Fridays 4:45-5:45pm, 508 Warren Weaver Hall

Course description

If you want to print this information download the Syllabus.

Introduction (classification, direction fields, applications in the sciences). First and second order equations (integrating factors, separable equations, existence and uniqueness). Series solutions (power series, singular points). Systems of linear equations (matrix-based methods). Numerical methods (including hands-on computing using Maple or MATLAB). Dynamical systems (phase space, stability, Liapunov functions). Laplace and Fourier transforms.

Textbooks

Required textbooks are:

E. A. Coddington, "An Introduction to Ordinary Differential Equations", Dover 1989
R. K. K. Miller and A. N. Michel, "Ordinary Differential Equations", Dover 2007

An optional but also cheap and very nice textbook is:

Fred Brauer and John A. Nohel, "The Qualitative Theory of ODEs: An Introduction", Dover 1989.

Prerequisites

Students who wish to enroll must meet the following prerequisites with a grade of C or better or the equivalent:

Calculus II
Calculus III
Linear Algebra

Assignments and grading

There will be regular (approximately weekly) assignments due the second class of each week, a midterm and a final. No late assignments will be accepted. The grade will be 40% based on assignments, 20% on midterm (Thursday Oct. 11th), and 40% on the final (December 18th, 10 - 11:50).

The grade scale will be based on the percentiles:

>92.5 = A
87.5-92.5 = A-
80.0-87.5 = B+
72.5-80.0 = B
65.0-72.5 = B-
57.5-65.0 = C+
50.0-57.5 = C
42.5-50.0 = C-
<42.5 = D or F

Academic integrity policies will be strictly enforced for homework assignments. Copying homework problems from someone else is a serious violation that can lead to expulsion from your program.

Computing

In the second half of the course we will learn how to use computers to solve ODEs. The Courant Institute has computer labs with Linux workstations that have Matlab (matlab), Maple (xmaple), Mathematica (mathematica), and other useful software installed.

Communication

There is a message and discussion board on the course Blackboard page that will be used for messages related to the assignments and any scheduling changes. If you register for the class, you automatically have access to the message board. All course materials including lecture notes and assignments will be posted on this site as they become available.

You should feel free to email the instructor with any questions, concerns, or special requests such as meeting outside of office hours, etc.

MATH-UA.0262-1

Ordinary Differential Equations