Revised 8/2018

MTH 267 - Differential Equations (3 CR.)

Course Description

Introduces ordinary differential equations. Includes first order differential equations, second and higher order ordinary differential equations with applications and numerical methods. Lecture 3 hours. Total 3 hours per week. Total 3 hours per week.

General Course Purpose

The general purpose is to give the student a solid grasp of the methods solving and applying differential equations and to prepare the student for further coursework in mathematics, engineering, computer science and the sciences.

Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264 or equivalent with a grade of C or better.

Course Objectives

  • First Order Differential Equations
    • Classify a differential equation as linear or nonlinear.
    • Understand and create a directional field for an arbitrary first-order differential equation.
    • Determine the order, linearity or nonlinearity, of a differential equation.
    • Solve first order linear differential equations.
    • Solve Separable differential equations.
    • Solve initial value problems.
  • Numerical Approximations
    • Use the Euler or tangent line method to find an approximate solution to a linear differential equation.
  • Higher Order Differential Equations
    • Solve second order homogenous linear differential equations with constant coefficients including those with complex roots and real roots.
    • Determine the Fundamental solution set for a linear homogeneous equation.
    • Calculate the Wronskian.
    • Use the method of Reduction of order.
    • Solve nonhomogeneous differential equations using the method of undetermined coefficients.
    • Solve nonhomogeneous differential equations using the method of variation of parameters.
  • Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
    • Solve applications of differential equations as applied to Newton's Law of cooling, population dynamics, mixing problems, and radioactive decay. (1st order)
    • Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
    • Solve application problems involving external inputs (non-homogenous problems).
  • Laplace Transforms
    • Use the definition of the Laplace transform to find transforms of simple functions
    • Find Laplace transforms of derivatives of functions whose transforms are known
    • Find inverse Laplace transforms of various functions.
    • Use Laplace transforms to solve ODEs.

Major Topics to Be Included

  • First Order Differential Equations
  • Numerical Approximations
  • Higher Order Differential Equations
  • Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
  • Laplace Transforms