MATH 320 Syllabus

Ordinary Differential Equations

Revised: February 2015

Course Description

Modeling, first order differential equations, existence and uniqueness of solutions, mathematical models and numerical methods, linear equations of higher order, systems of differential equations, and Laplace transforms. Prerequisite: MATH 255. Three semester hours.

Student Learning Objectives

By the end of the course students should be able to

  • formulate differential equations via modeling;
  • use geometric, numeric, and analytic techniques to solve and/or examine differential equations;
  • work with systems of differential equations in terms of matrices and find their solutions using eigenvalues; and
  • interpret the solutions to differential equations.
  • Use mathematical software to solve and/or examine differential equations.

Text

C.H. Edwards and D.E. Penney, Differential Equations: Computing and Modeling, 4th ed., Pearson/Prentice Hall.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

  • Chapter 1: First-Order Differential Equations. (9 class days)
    Modeling, Analytic Techniques, Qualitative Techniques (Slope Fields), Numerical Techniques, Existence and Uniqueness, Linear First-Order Equations, and Integrating Factors.
  • Chapter 2: Mathematical Models and Numerical Method (7 class days)
    Population Models, Critical Points, Equilibrium and Stability, Acceleration-Velocity Models, Euler's Method, and Runge-Kutta Method.
  • Chapter 3: Linear Equations of Higher Order. (9 class days)
    Second-Order Linear Equations, General Solutions of Linear Equations, Homogeneous Equations with Constant Coefficients, Mechanical Vibrations, Method of Undetermined Coefficients.
  • Chapter 4: Systems of Differential Equations. (4 class days)
    First-Order Systems and Applications, Method of Elimination, Numerical Methods for Systems.
  • Chapter 5: Linear Systems of Differential Equations. (6 class days)
    Matrices and Linear Systems, Eigenvalue Method for Homogeneous Systems, Multiple Eigenvalue Solutions.
  • Chapter 7: Laplace Transform Methods. (7 class days)
    Laplace Transforms and Inverse Transforms, Transformation of Initial Value Problems, Translation and Partial Fractions, with Additional Topics as Time Allows
Office of Web Services