
20242025 College Catalog

MAT 262  Differential Equations [SUN# MAT 2262] 3 Credits, 3 Contact Hours 3 lecture periods 0 lab periods Introduction to differential equations. Includes first order differential equations, higher order differential equations, systems of linear differential equations, Laplace transforms, and approximating methods. Also includes applications.
Prerequisite(s): MAT 231 GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Solve first order and higher order differential equations.
 Solve linear systems of first order differential equations using matrices and eigenvalues.
 Calculate the Laplace transform of a function, find the inverse transform, and use both to solve linear differential equations with constant coefficients.
Performance Objectives:
 Solve first order differential equations including separable, linear, and those solved by substitution techniques.
 Solve higher order linear differential equations with constant and variable coefficients; find a particular solution using undetermined coefficients and variation of parameters; find power series solutions.
 Solve linear systems of first order differential equations using matrices and eigenvalues.
 Define and compute the Laplace transform of a function; find the inverse transform; use Laplace transforms to solve linear equations with constant coefficients.
 Use graphical and numerical methods to interpret and approximate solutions to differential equations.
 Use differential equations to model and interpret scientific and mathematical applications.
Outline:
 First Order Differential Equations
 Separable
 Linear
 Exact (optional)
 Solvable by substitution
 Applications
 Higher Order Linear Differential Equations
 Wronskian and linear independence of functions
 Reduction of Order
 Homogeneous equations
 Nonhomogeneous equations
 Undetermined coefficients
 Variation of parameters
 CauchyEuler equations (optional)
 Power series solutions
 Applications
 Systems of Linear First Order Differential Equations
 Method of eigenvalues
 Applications
 Laplace Transforms
 Definitions and existence
 Properties
 Inverse Transform
 Applications to solutions of linear equations with constant coefficients
 Approximating Methods
 Numerical
 Graphical
 Applications
 First order
 Higher order
 Linear systems
 Laplace Transforms
Effective Term: Fall 2015

