# 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