Differential Equations

I. Course Description

An introduction to ordinary differential equations and their applications. Topics
include first- order equations , second- and higher- order linear equations,
vibrational motion, electrical circuits, power series solutions, Laplace transforms,
systems of equations , numerical methods, and matrix methods for systems of
equations.

II. Prerequisites

Math 173-174 (Calculus with Analytic Geometry I-II) or equivalent.

III. Introduction

This course is an introduction to ordinary differential equations and their
applications. In this course, it is expected that the student will not only become
proficient in solving many classes of differential equations by hand calculations, but
will become familiar with how to solve differential equations using symbolic
manipulation software available for computers today. Additionally , the student
should acquire an ability to model real world situations in terms of differential
equations.

IV. Instructional Materials

Textbook: A First Course in Differential Equations with Modeling Applications
(7th edition) by Dennis G. Zill;
Brooks/Cole (ITP) Publishing Company, 2001.

Optional: Student’s Solutions Manual by Warren S. Wright.

Required: Scientific calculator or graphing calculator (preferred).

V. Disability Services Policy:

Reasonable accommodations will be made for students with disabilities provided
those students have registered with the Office of Disability Services. Present your
teacher with the documentation.

TIDEWATER COMMUNITY COLLEGE
CLASSROOM AND LABORATORY
EMERGENCY PROCEDURES FOR FACULTY

In the event of a bomb threat, tornado, or fire, students and staff may be asked to
evacuate the building or move to a secure location within the building. Evacuation
routes for movement to an external location or to a shelter within the building are
posted at the front of the room. Students should review the maps and make sure
that the exit route and assembly location for the building are clearly understood. If
you have a disability that may require assistance during an evacuation, please let
your faculty know at the end of the first class.

VI. COURSE CONTENT

Chapter One: Introduction to Differential Equations

1.1 Definitions and Terminology
1.2 Initial- Value Problems
1.3 Differential Equations as Mathematical Models

Chapter Two : First-Order Differential Equations

2.2 Separable Variables
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitution

Chapter Three: Modeling with First-Order Differential Equations

3.1 Linear Equations

Chapter Four: Differential Equations of Higher Order

4.1 Preliminary Theory: Linear Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients-Superposition Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equation
4.8 Systems of Linear Equations by Elimination
4.9 Nonlinear Equations

Chapter Six: Series Solutions of Linear Equations

6.1 Solutions about Ordinary Points: Review of Power Series; Power
Series Solutions
6.2 Solutions About Singular Points

Chapter Seven: Laplace Transforms

7.1 Definition of the Laplace Transform
7.2 Inverse Transforms and Transforms of Derivatives
7.3 Translation Theorems

Chapter Eight: Systems of Linear First Order Differential Equations

8.1 Preliminary Theory
8.2 Homogeneous Linear Systems with Constant Coefficients
8.3 Variation of Parameters

Assignments and Test Schedule for
A First Course in Differential Equations by Zill (7^th edition)