math-ua.0260 / V63.0262:Ordinary Differential Equations
| Term: | Fall 2011 |
| Meeting times: | TR 11:00 A.M.-12:15 P.M. Location TBD |
| Instructor: | Prof. Leslie Greengard |
| Office: | TBA |
| Office hours: | TBA |
| Phone: | 212-998-3306 |
| Email: | greengard@cims.nyu.edu |
Textbook
- E. A. Coddington, "An Introduction to Ordinary Differential Equations", Dover 1989.
- S. H. Strogatz, "Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering", Westview Press, 2001.
Topics
Introduction to QDE'sBasic models, classification, direction fields
First Order ODE'sLinear equations, integrating factors
Separable equations
Modeling with 1st order equations
Exact equations and integrating factors
The existence and uniqueness theorem for linear/nonlinear equations
Autonomous equations and population dynamics
First order difference equations
Separable equations
Modeling with 1st order equations
Exact equations and integrating factors
The existence and uniqueness theorem for linear/nonlinear equations
Autonomous equations and population dynamics
First order difference equations
Second Order Linear ODE's
Homogenous equations with constant coefficients
Fundamental solutions
Linear independence and Wronskian
Complex roots, repeated roots
Nonhomogenous equations
Variation of parameters
Mechanical and electrical vibrations
Forced vibrations
Fundamental solutions
Linear independence and Wronskian
Complex roots, repeated roots
Nonhomogenous equations
Variation of parameters
Mechanical and electrical vibrations
Forced vibrations
Series Solutions of ODE's
Review of power series
General method
General method
Numerical Methods
Euler's method
Improvements on Euler's method, Runge-Kutta method
Error analysis
Improvements on Euler's method, Runge-Kutta method
Error analysis
Nonlinear Differential Equations and Stability
Autonomous systems and stability
Phase plane
Linearization of nonlinear systems
Competing species and predator-prey equations
Liapunov's functions
Phase plane
Linearization of nonlinear systems
Competing species and predator-prey equations
Liapunov's functions
Laplace Transform
Definition solution of initial value problems
Calculation of basic Laplace transforms
Calculation of basic Laplace transforms