# 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)

SECTION | PAGE | ASSIGNMENT |

1.1 | 10 | 1-11 odd, 15,17,19,21,23,27 |

1.2 | 19 | 1,3,7,13-25 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 | 1-23 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 | 11,15,19-37 odd |

7.2 | 322 | 1-37 odd |

7.3 | 333 | 1-25 odd,29 |

8.1 | 373 | 1,3,7-23 odd |

8.2 | 389 | 1,5,7,19,25,33 |

8.3 | 397 | 1,5 |

TEST 3 |

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