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INSTRUCTOR’S RESOURCE GUIDE
EDWARD B. SAFF
Vanderbilt University

A. DAVID SNIDER
University of South Florida

FUNDAMENTALS
OF DIFFERENTIAL EQUATIONS
SIXTH EDITION

FUNDAMENTALS OF
DIFFERENTIAL EQUATIONS
AND BOUNDARY VALUE PROBLEMS
FOURTH EDITION
R. Kent Nagle
Edward B. Saff
A. David Snider

Reproduced by Pearson Addison-Wesley from electronic files supplied by the authors.Copyright © 2004 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston MA 02116
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior
written permission of the publisher. Printed in theUnited States of America.
ISBN

0-321-17318-X

1 2 3 4 5 6 QEP 06 05 04 03

Contents
Notes to Instructor
Software Supplements

1
1

Instructional Utility Software

1

Interactive Differential Equations CD-ROM

2

Instructor’s Maple/Matlab/Mathematica Manual

2

Computer Labs

2

Group Projects

2

Technical Writing Exercises

3

Student Presentations

3Homework Assignments

3

Syllabus Suggestions

3

Numerical, Graphical, and Qualitative

4

Engineering/Physics Applications

5

Biology/Ecology Applications

6

Supplemental Group Projects
Answers to Even-Numbered Problems

8
15

Chapter 1

15

Chapter 2

21

Chapter 3

25

Chapter 4

31

Chapter 5

43

Chapter 6

57

Chapter 7

61

Chapter 8

71Chapter 9

81

Chapter 10

91

Chapter 11

97

Chapter 12

103

Chapter 13

117

Notes to the Instructor
One goal in our writing has been to create flexible texts that afford the instructor a variety of topics and make
available to the student an abundance of practice problems and projects. We recommend that the instructor read
the discussion given in the preface inorder to gain an overview of the prerequisites, topics of emphasis, and
general philosophy of the texts.
An additional resource to accompany the texts is the on-line tool, MyMathLab. MyMathLab is ideal for lecturebased, lab-based, and on-line courses and provides students and instructors with a centralized point of access to
the multimedia resources available with the texts. The pages of theactual text are loaded into MyMathLab and
extensive course-management capabilities, including a host of communication tools for course participants, are
provided to create a user-friendly and interactive on-line learning environment. Instructors can also remove,
hide, or annotate Addison-Wesley preloaded content, add their own course documents, or change the order in
which material is presented. Alink to the Instructional Utility Software package is also included. For more
information visit our Web site at www.mymathlab.com or contact your Addison-Wesley sales representative for
a live demonstration.
INSTRUCTIONAL UTILITY SOFTWARE
Written specifically for the texts and available via MyMathLab, this utility has the following items:
GRAPHICAL METHODS
Graph, tabulate or evaluatefunctions
Direction field
Phase plane diagram
MATRIX OPERATIONS
Solve a system of linear equations
Determinant and inverse of a matrix
Matrix multiplication
Eigenvalues and eigenvectors
NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS
Euler’s method subroutine
Euler’s method with tolerance
Improved Euler’s method subroutine
Improved Euler’s method with tolerance
Fourth order Runge-Kutta methodsubroutine
Fourth order Runge-Kutta method with tolerance
FOURTH ORDER RUNGE-KUTTA METHOD FOR SYSTEMS
System with 2 equations
System with 3 equations
System with 4 equations
OTHER COMPUTATIONAL METHODS
Roots of a polynomial equation
Newton’s method
Simpson’s Rule for definite integrals
Simpson’s Rule for linear differential equations

2

NOTES TO THE INSTRUCTOR

INTERACTIVE...
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