MAT 285 Differential Equations

Lecture: 2 Lab: 2 Clinic: 0 Credits: 3

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear higher-order differential equations, systems of differential equations, numerical methods, series solutions, eigenvalues and eigenvectors, and LaPlace transforms. Upon completion, students should be able to demonstrate understanding of the theoretical concepts and select and use appropriate models and techniques for finding solutions to differential equations-related problems with and without technology.

This course has been approved for transfer under the CAA as a premajor and/or elective course requirement.

Pre-requisite(s): C or better in MAT 272.
Course is typically offered in Fall and Spring.
Course has transfer restrictions - 20 years

Student Learning Outcomes (SLOs)
At the completion of the course, the students should be able to do the following:

Find general solutions to first-order, second-order, and higher-order homogeneous and non-homogeneous differential equations by manual and technology-based methods.
Identify and apply initial and boundary values to find particular solutions to first-order, second-order, and higher order homogeneous and non-homogeneous differential equations by manual and technology-based methods, and analyze and interpret the results.
Select and apply appropriate methods to solve differential equations; these methods will include, but are not limited to, undetermined coefficients, variation of parameters, eigenvalues and eigenvectors, LaPlace and inverse LaPlace transforms.
Select and apply series techniques to solve differential equations; these techniques will include but are not limited to Taylor series.
Select and apply numerical analysis techniques to solve differential equations; these techniques will include but are not limited to Euler, Improved Euler, and Runge-Kutta.
Demonstrate proficiency in using CAS technology to analyze, solve and interpret the various applications.