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Differential Equations
I. Course Description
An introduction to ordinary differential equations and their applications.
Topics
include firstorder 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 173174 (Calculus with Analytic Geometry III) 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: FirstOrder Differential Equations
2.2 Separable Variables
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitution
Chapter Three: Modeling with FirstOrder 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 CoefficientsSuperposition Approach
4.6 Variation of Parameters
4.7 CauchyEuler 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)
SECTION  PAGE  ASSIGNMENT 
1.1  10  111 odd, 15,17,19,21,23,27 
1.2  19  1,3,7,1325 odd 
1.3  31  1,9.11,13,15,17,23 
2.2  57  1,3,7,9,11,17,19,21,22,23,25,27 
2.3  69  1,3,7,11,17,19,23,25,30 
2.4  78  123 odd, 31 
2.5  84  1,7,9,11,13,15,17,21 
3.1  103  1,3,5,7,13,17 
TEST 1  
4.1  151  1,3,5,9,13,15,17,21,23,25,31 
4.2  157  1,3,7,11,13 
4.3  163  1,5,9,11,17,25,29,31,37 
4.4  176  1,5,11,13,19,23,29,33 
4.6  192  1,7,11,17,19 
4.7  199  1,3,5,7,11,13,15,23,25 
4.8  205  1,3,9,13 
4.9  211  3,5,7 
TEST 2  
6.1  278  1,3,5,9,11,15,19,25,27 
6.2  289  1,3,5,7,9,11,15,25 
7.1  312  11,15,1937 odd 
7.2  322  137 odd 
7.3  333  125 odd,29 
8.1  373  1,3,723 odd 
8.2  389  1,5,7,19,25,33 
8.3  397  1,5 
TEST 3 
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