
Master
Course Outline
MATH 238
Differential Equations

Credits: 5 
Clock Hours per Quarter: 50
AA Discipline: [Quantitative] [Natural Sciences]
Lecture Hours:50

Description
Firstorder and higherorder 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 firstorder ODE's. Analytic solutions to ODE's using substitution techniques and integrating factors. Applications of separable and linear firstorder 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, RungeKutta, and other effective algorithms. Utilize a computer algebra system to determine numeric solutions.
Analytic solutions to higherorder constant coefficient ODE's. Utilize numeric techinques to alanyze solutions to these ODE's in addition to analytic solutions. Applications of secondorder constant coefficient ODE's.
Develop the notions of a system of firstorder 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 2017 
7193 
Julianne Sachs 

MATH 238 
Spring 2016 
7193 
Julianne Sachs 

MATH 238 
Spring 2015 
0845 
Julianne Sachs 

MATH 238 
Spring 2014 
0845 
Julianne Sachs 

MATH 238 
Spring 2011 
1473 
Julianne Sachs 


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.

