Ordinary Differential Equations
Revised: February 2015
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
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
- 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.
C.H. Edwards and D.E. Penney,
Differential Equations: Computing and Modeling, 4th ed., Pearson/Prentice Hall.
Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to
general university policy.
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
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
Chapter 4: Systems of Differential Equations. (4 class days)
First-Order Systems and Applications, Method of Elimination, Numerical Methods
Chapter 5: Linear Systems of Differential Equations. (6 class days)
Matrices and Linear Systems, Eigenvalue Method for Homogeneous Systems, Multiple
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