MAT352: Intro to Differential Equations
Required
Catalog Description
This course covers the development of ordinary differential equations from special applications
and concentrates on the derivation of methods. First order equations, linear equations and
systems of equations and Laplace Transforms are discussed as well as further applications.
Prerequisites
MAT 222 or MAT 221 and instructor's consent
Textbook
Elementary Differential Equations, 10th Edition, Boyce & DiPrima
Course Learning Outcomes
The student will demonstrate an understanding of qualitative, analytic and numerical approaches
for solving various kinds of differential equations.
Topics Covered
First-Order Equations:
 Classification of differential equations
 Initial value problems
 Separation of variables
 Linear differential equations
 Exact equations
 Integrating factors
 Euler's method for single variable problems
Higher-Order Equations:
 Homogeneous Equations with Constant Coefficients
 Nonhomogeneous Equations using Undetermined Coefficients
 Nonhomogeneous Equations using Variation of Parameters
 The method of undetermined coefficients
 Resonance and phasors
 Qualitative analysis for harmonic oscillators
LaPlace Transforms:
 Definition and creation of formulas
 Solving second-order equations
 Impulse and Delta forcing functions
First-Order Systems:
 Predator-Prey model
 Analytic methods for finding solutions to systems
 Analyzing direction fields and the phase plane for systems
 Euler's method for autonomous systems
Linear Systems:
 Special properties
 Straight-line solutions
 Interpreting the Phase plane
 Eigenvalues and their meaning
Course Schedule
3 hours lecture per week
Contribution to ABET Criterion 5
This course contributes to the engineering topics component of Criterion 5
Relationship to Program Outcomes
(a) the ability to apply knowledge of mathematics, science, and engineering
Description Prepared by
Daniel Watson
9/28/15