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SOLVING SECOND ORDER NON-HOMOGENEOUS DIFFERENTIAL EQUATIONS
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# Ordinary Differential Equations

## Ronald Farris

Instructor Information

## Instructor

E-mail: Ronald Farris

Ron Farris has been employed at the Applied Physics Laboratory since 1973 and is a member of the Principal Professional Staff. Mr. Farris received his a MS in Physics from the University of Illinois and is also a graduate of the Engineering Programs for Professionals.

443-778-5570 (Work)

Course Information

## Course Description

This course provides an introduction to the theory, solution and application of ordinary differential equations.  Topics discussed in the course include methods of solving first-order differential equations, existence and uniqueness theorems, second-order linear equations, power series solutions, higher-order linear equations, systems of equations, non-linear equations, Sturm-Liouville theory, and applications.  The relationship between differential equations and linear algebra is emphasized in this course.   An introduction to numerical solutions is also provided.  Applications of differential equations in physics, engineering, biology and economics are presented.

## Prerequisites

Two or more terms of calculus are required.  Course in linear algebra would be helpful.

## Course Goal

The goal of this course is to provide the student with an understanding of the solutions and applications of ordinary differential equations. The course serves as an introduction to both nonlinear differential equations and provides a prerequisite for futher study in those areas.

## Course Objectives

• Understand and solve first and second order linear homogeneous and non-homogeneous differential equations.
• Solve second order equations using power series methods.
• Solve separable boundary value problems.
• Understand applications of ODE in physics, biology and economics.

## When This Course is Typically Offered

This course is offered in Spring of each year at the Applied Physics Laboratory.

Syllabus

## Topics Covered

• Solving Linear homogeneous and non-homogeneous First Order ODE
• Methods for solving Nonlinear 1st Order ODE
• Systems of 1st order linear equations
• Qualitative Methods for Nonlinear Differential Equations
• Numerical Methods for solving differential equations
• Solving homogeneous and non-homogeneous 2nd Order Linear ODE
• Series Solution of 2nd order Linear ODE
• Solving Boundary Value Problems of Seperable Partial Differential Equations

## Student Assessment Criteria

 Homework 25% Midterm and Final Exams 75%

## Computer and Technical Requirements

Although not required in the course, the use of Matlab is encouraged for solving linear systems and using numerical methods. WebCT is used to establish to a course website on which assignments, answer sheets, exam and grades are posted.

## Textbooks

Textbook information for this course is available online through the appropriate bookstore website:
• For courses offered at Montgomery Co. & DC, search the ProTech Books website at or call 301-972-4000.
• For courses offered at all other locations and for online courses, search the Barnes & Noble Bookstore website at .

## Course Notes

There are no notes for this course.

( 11-28-2005 at 11:27:36 AM) 