|
Master
Course Outline
MATH 238
Differential Equations
|
| Credits: 5 |
Clock Hours per Quarter: 50
AA Discipline: [Quantitative] [Natural Sciences]
Lecture Hours:50
|
Description
First-order and higher-order differential equations, systems of linear differential equations, LaPlace transforms, numerical methods, and qualitative analysis of ODE's will be discussed. Prerequisite: Grade C- or higher in MATH& 153 or permission of the Mathematics Department. |
Intended Learning Outcomes
Analyze solutions to separable and linear first-order ODE's. Analytic solutions to ODE's using substitution techniques and integrating factors. Applications of separable and linear first-order ODE's.
Alayze solutions to ODE's using direction fields generated by appropriate technology.
Develop the notions of numeric solutions to ODE's using Euler's method, Runge-Kutta, and other effective algorithms. Utilize a computer algebra system to determine numeric solutions.
Analytic solutions to higher-order constant coefficient ODE's. Utilize numeric techinques to alanyze solutions to these ODE's in addition to analytic solutions. Applications of second-order constant coefficient ODE's.
Develop the notions of a system of first-order ODE's. Utilize eigenvalues to solve analytically such systems. Develop qualitative understanding of the connection between eigenvalues and solutions to the system. Utilize CAS to plot trajectories and a phase plane portrait. Applications of these systems.
Develop Laplace Transforms and use to solve ODE's. Solve ODE's arising from applications that benefit from using Laplace Tranforms.
Develope basic analytical skills useful for investigating solutions to nonlinear ODE's. Utilize appropriate technology to work with these types of ODE's.
Develop competence in utilizing a CAS in solving ODE's; both analytically solutions as weill as numeric solutions.
Optional: Discrete dynamical systems.
|
|
|
Syllabi
Listing
See ALL Quarters
| Course |
Year
Quarter
|
Item
|
Instructor |
|
| MATH 238 |
Spring 2008 |
1491 |
Julianne Sachs |
|
| MATH 238 |
Spring 2007 |
1491 |
HEATHER VAN DYKE |
|
| MATH 238 |
Spring 2004 |
1491 |
Steve Schwartz |
|
|
Two Year Projected Schedule
| Year
One* |
Year
Two** |
Fall |
Winter |
Spring |
Summer |
Mini |
Fall |
Winter |
Spring |
Summer |
Mini |
|
|
X
|
|
|
|
|
X
|
|
|
|
*If fall quarter starts on an odd year (2003, 2005, etc.), it's Year One.
**If fall quarter starts on an even year (2002, 2004, etc.), it's Year Two.
printable version
|
|
