V63.0262:Ordinary Differential Equations
| Term: | Spring 2011 |
| Meeting times: | Tues & Thurs, 9:30-10:45am |
| Instructor: | Oliver Bühler |
| Office: | 913 WWH |
| Office hours: | Thurs, 3-5pm, room 913 WWH |
| Phone: | 212-998-3265 |
| Email: | obuhler@cims.nyu.edu |
Prerequisites
Students who wish to enroll in V63.0262 must meet the following prerequisites:
- V63.0122 Calculus II, V63.0123 Calculus III and V63.0140 Linear Algebra with a grade of C or better or the equivalent.
Goals and Topics
First and second order equations. Series solutions. Laplace transforms. Introduction to partial differential equations and Fourier series.
Course Details
Textbook and Materials
Boyce & DiPrima, “Elementary Differential Equations and
Boundary Value Problems”,
9th Edition
.
Homework
weeklyExams
Midterms dates to be
determined
Final The final exam
is scheduled for 5/17 8:00 am to 9:50 am
Grading policy: mid-term, final exam, homework.
Calendar
| Week | Topic |
|---|---|
| 1 | Introduction: basic models and examples, direction fields, classification |
| 2,3 | First-order equations: separable equations, linear and
nonlinear examples, existence and uniqueness theorems. |
| 4, 5 |
Second-order linear equations: general solution of equations
with constant coefficients, variation of parameters, vibrations. |
| 6, 7 |
Series solutions: power series method, singular points |
| 8, 9 |
Systems of linear equations: matrix method, eigenvalues and
eigenvectors, complex and repeated eigenvalues. |
| 10,11 |
Numerical methods: explicit Euler method, stability, implicit
Euler method |
| 12 |
Nonlinear dynamics: phase plane, stability, predator—prey
models |
| 13,14 |
Boundary-value problems: Sturm-Liouville problems,
eigenfunctions, and Green’s functions. |