COURSE SYLLABUS

 

Ohio Northern University

College of Arts and Sciences

Department of Mathematics

 

Date:  Winter  2005-06                                                                                                          

 

 

Course  MATH - 275             Name:  Differential Equations

 

Credit hours: 4                      Lecture hours/week: 4          Lab hours/week:  0

 

Instructor:      Staff

 

Usual student level:   Sophomore

 

Course required of students in:       Mathematics, Engineering, and Physics

 

Course frequency per quarter/year:           Winter and Spring

 

Average enrollment per year:          100

 

This course has a prerequisite:        Math 165

 

This course is a prerequisite for:      Math 362, Math 462

 

Catalogue Description:

 

First and second order linear differential equations with applications.  Laplace transforms

 

Prerequisites:  MATH 165

 

Course Objectives:

 

The student will gain facility in categorizing differential equations and in selecting an appropriate strategy for solving them.  Each class of differential equations is associated with a variety of real world phenomena.  These phenomena are addressed by constructing mathematical models and relating the solutions of the resulting differential equations to the behavior of the phenomena.

 

Textbook: Elementary Differential Equations, by C.H. Edwards and D.E. Penney, 5th edition

 

Outline of content follows:

      (see attached)

Course Outline

Math – 275

Differential Equations

 

Chapter  1      First Order Differential Equations

 

1.1       Differential Equations & Math Models

1.2       Integrals as Solutions

1.3       Slope Fields & Solution Curves

1.4       Separable Equations and Applications

1.5       Linear First Order Equations

1.6       Substitution Methods & Exact Eqs

1.7       Population Models

1.8*     Acceleration-Velocity Models

 

Chapter  2      Linear Equations of Higher Order

 

2.1       Introduction: 2nd order linear equations

2.2       General Solutions of Linear Equations

2.3       Homogeneous Eqs with Constant Coefficients

2.4       Mechanical Vibrations

2.5       Nonhomogeneous Equations and Undertermined Coefficients

2.6       Forced Oscillations and Resonance

2.7*     Electrical Circuits

Review

 

Chapter  4      The Laplace Transform

 

4.1       Laplace Transforms and Inverse Transforms

4.2       Transformation of Initial Value Problems

4.3       Translation and Partial Fractions

4.4       Derivatives, Integrals, and Products of Transforms

4.5       Periodic and Piecewise Continuous Input Functions

4.6*  Impulses and Delta Functions

 

Additional Optional Topics:

The starred sections above are optional.  If time permits, these topics could also be added:

·                     Solutions of systems of equations by Laplace Transform

·                     Solutions of systems of equations by elimination method