Technical mathematics with calculus Includes indexes

1152 Pages·2011·22.495 MB·English

by  Calter, Paul A;Calter, Michael A

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accessible, affordable,
active learning
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SIXTH
EDITION
TECHNICAL MATHEMATICS
WITH CALCULUS
PAUL A. CALTER, MSME, MFA
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Professor Emeritus
Vermont Technical College
MICHAEL A. CALTER, PH.D.
◆◆◆ ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆
Associate Professor
Wesleyan University
JOHN WILEY & SONS, INC.
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Preface
This textbook has been in continuous classroom use since 1980, and it was again
time to polish and refine the material and fill in where needed. It was also an op-
portunity to carry out suggestions for improvements made by many reviewers and
colleagues, as well as those that occurred to the authors while using the preceding
edition. Much has been rewritten to be cleaner and clearer, and new features have
been introduced. To reduce size and weight, some peripheral topics have been
moved to the Web. One chapter previously moved to the Web, Introduction to Statis-
tics and Probability, has been returned to the text at the request of reviewers. Also,
Analytic Geometry, formerly in the calculus version only, is now in both versions.
Features of the Book
Each chapter begins with a listing of Chapter Objectives that state specifically
what the student should be able to do upon completion of the chapter. Following
that, we have tried to present the material as clearly as possible, preferring an intu-
itive approach rather than an overrigorous one. Realizing that a mathematics book
is not easy reading, we have given information in small segments, included many il-
lustrations, and have designed each page with care.
The numerous Examples form the backbone of the textbook, and we have
added to their number. In many we have added intermediate steps to make them
easier to follow. They are fully worked out and are chosen to help the student do the
exercises. Examples have markers above and below to separate them clearly from
the text discussion.
To give students the essential practice they need to learn mathematics, we in-
clude thousands of Exercises. Exercises given after each section are graded by
difficulty and grouped by type, to allow practice on a particular area. These are
indicated by title, as well as by number. The Chapter Review Problemsare scram-
bled as to type and difficulty. Answers to all odd-numbered problems are given in
the Answer Key in the Appendix, every answer is included in the Annotated In-
structor’s Edition, and complete solutions to every problem are contained in the
Instructor’s Solutions Manual. Complete solutions to every other odd problem
are given in the Student’s Solutions Manual.
The book contains hundreds of high-quality, clear illustrations, each care-
fully selected for its inclusion. When the same figure is used twice but in differ-
ent locations, it is now included in both locations so that students do not have to
search for it.
The examples, the text, and the exercises include many Technical Applica-
tions. We have added applications, especially for the building trades, machine shop,
and woodworking shop. Many chapters have a large block of applications, and
some of these have been moved forward into the preceding text to provide motiva-
tion for the student.
Students are encouraged to try some applications outside their chosen field,
and everything they need to work these problems is given right here in this text.
However, space does not permit the full discussion of all the background material
for each technical field.
v
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vi Preface
We have tried to avoid contrived “school” problems with neat solutions and in-
clude many Problems with Approximate Solutions. These include expressions
and equations with approximate constants, but those that do not yield to many of
the exact methods we teach, and must be tackled with an approximate method.
The Index to Applicationsshould help in finding specific applications.
We have all seen wild answers on homework and exams, such as “the cost of
each pencil is $300.” To try to avoid that, we have added Estimationsteps to many
examples, where we have tried to show students how to estimate an answer in order
to check their work. We give suggestions for estimation in the chapter on word
problems. Thereafter, many applications examples begin with an estimation step or
end with a check, either by graphing, by computer, by calculator, by an alternate
solution, by making a physical model, or simply to Examine the Answer for
Reasonableness.
Formulasused in the text are boxed and numbered and listed in the Appendix
as the Summary of Facts and Formulas. This listing can function as a “hand-
book” for a mathematics course and for other courses as well and provides a
common thread between chapters. We hope it will also help a student see intercon-
nections that might otherwise be overlooked. The formulas are grouped logically in
the Summary of Facts and Formulas and are numbered sequentially there. Therefore,
the formulas do not necessarily appear in numerical order in the text.
When a listed formula is needed, it is now given right in the text so students do
not have to flip through the formula summary to find it.
In addition to mathematical formulas, we include some from technology, mo-
tion, electric circuits, and so on. These are grouped together at the end of the For-
mula Summary and have formula numbers starting with 1000.
We continue the popular feature of Common Error Boxesto emphasize some
of the pitfalls and traps that “get” students year after year.
The Graphics Calculator has been fully integrated throughout. Calculator in-
struction and examples are given in the text, where appropriate, and calculator
problems are given in the exercises. To avoid being too vague and general, we
specifically give keystrokes for the Texas Instruments TI-83, TI-84, and TI-89. Our
hope is that other calculators are similar enough for these instructions to be useful.
Many problems are given that can be solved practically onlyby a graphics calcu-
lator, and the graphics calculator is sometimes used to verify a solution found by an-
other method. However, we have still retained most of the noncalculator methods,
such as manual graphing by plotting of point pairs, for those who want to present
these methods. Graphical and calculator methodsare emphasized much more than
before. We give calculator screens, when a calculator topic is introduced, and per-
haps for a few more examples. Screens for those operations are then dropped to avoid
cluttering the pages. To our treatment of the arithmetic scientific calculator, we have
added the Symbolic Scientific Calculatorand show screens where appropriate.
We have expanded the use of Guided Explorations. Our hope is that they will
lead the student to make personal discoveries and gain a more personal appreciation
for the concepts.
Every chapter contains optional enrichment activities with the title Writing,
Projects, or Internet. These were formerly at the end of each chapter, but we have
now moved them to the exercise that is most appropriate. Our hope is that a few
students may be attracted to the magic and history of mathematics and welcome a
guided introduction into this world. Here we put Writing Questions to test and
expand a student’s knowledge of the material and perhaps explore areas outside of
those covered, Team Projectsto foster “collaborative learning,” and Internetac-
tivities, including references to our companion Web site.
With the margins of the book becoming crowded with calculator screens, in ad-
dition to illustrations, we have moved many of the Marginal Notes to the text.
They are used mostly for encouragement and historical notes.
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Preface vii
Teaching and Learning Resources
We provide several supplements to aid both the instructor and the student.
An Annotated Instructor’s Edition (AIE) of this text contains answers to
every exercise and problem. The answers are placed in red right in the exercise or
problem. The AIE also has red marginal notes to the instructor, giving teaching tips,
applications, and practice problems. ISBN: 978-0470-53495-3
An Instructor’s Solution Manualcontains worked out solutions to every prob-
lem in the text and a listing of all computer programs. ISBN: 978-1118-06124-4
The Student Solutions Manualgives the solution to every other odd problem.
They are usually worked in more detail than in the Instructor’s Solution Manual.
ISBN: 978-0470-53494-6
WileyPLUS is a powerful online tool that provides instructors with an inte-
grated suite of resources, including an online version of the text, in one easy-to-use
Web site. Organized around the essential activities you perform in class, Wiley-
PLUS allows you to create class presentations, assign homework and quizzes for
automatic grading, and track student progress. Please visit www.wileyplus.com or
contact your local Wiley representative for a demonstration and further details.
A Computerized Test Item File is a bank of test questions with answers.
Questions may be mixed, sorted, changed, or deleted. It consists of a test file disk
and a test generator disk, ready to run. ISBN: 978-0470-53497-7
Our Companion Web Site (www.wiley.com/college/calter) contains all the
less frequently used material moved from the preceding edition, as well as complete
solutions to every problem in the text.
Acknowledgments
We are extremely grateful to reviewers of this edition and the earlier editions of the book, reviewers of the supplements and
the writing questions, and participants in group discussions about the book. They are
A. David Allen, Ricks College Wendell Johnson, Akron, Ohio
Byron Angell, Vermont Technical College Joseph Jordan, John Tyler Community College
David Bashaw, New Hampshire Technical Institute Frank L. Juszli
Jim Beam, Savannah Area Vo-Tech Rob Kimball, Wake Technical Community College
Elizabeth Bliss, Trident Technical College John Knox, Vermont Technical College
Franklin Blou, Essex County College Bruce Koopika, Northeast Wisconsin Technical College
Donna V. Boccio, Queensboro Community College Ellen Kowalczyk, Madison Area Technical College
Jacquelyn Briley, Guilford Technical Community College Fran Leach, Delaware Technical College
Frank Caldwell, York Technical College Jon Luke, Indiana University-Purdue University
James H. Carney, Lorain County Community College Michelle Maclenar, Terra Community College
Cheryl Cleaves, State Technical Institute at Memphis Paul Maini, Suffolk County Community College
Ray Collings, Tri-County Technical College Edgar M. Meyer, St. Cloud State, Minnesota
Miriam Conlon, Vermont Technical College David Nelson, Western Wisconsin Technical College
Robert Connolly, Algonquin College Mary Beth Orange, Erie Community College
Amy Curry, College of Lake County Harold Oxsen, Walnut Creek, California
Kati Dana, Norwich University Ursula Rodin, Nashville State Technical Institute
Linda Davis, Vermont Technical College Jason Rouvel, Western Technical College
Dennis Dura, Cuyahoga Community College Donald Reichman, Mercer County Community College
John Eisley, Mott Community College Bob Rosenfeld, Nassau Community College and University of Vermont
Walt Granter, Vermont Technical College Nancy J. Sattler, Terra Technical College
Crystal Gromer, Vermont Technical College Frank Scalzo, Queensborough Community College
Richard Hanson, Burnsville, Minnesota Ned Schillow, Lehigh Carbondale Community College
Tommy Hinson, Forsythe Community College Blin Scatterday, University of Akron Community and Technical College
Margie Hobbs, State Technical Institute at Memphis Edward W. Seabloom, Lane Community College
Martin Horowitz, Queensborough Community College Robert Seaver, Lorain Community College
Glenn Jacobs, Greenville Technical College Saeed Shaikh, Miami Dade Community College
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viii Preface
Thomas Stark, Cincinnati Technical College Roy A. Wilson, Cerritos College
Fereja Tajir, Illinois Central College Jeffrey Willmann, Maine Maritime Academy
Dale H. Thielker, Ranken Technical College Douglas Wolansky, North Alberta Institute of Technology
William N. Thomas, Jr., Thomas & Associates Group Karl Viehe, University of the District of Columbia
Joel Turner, Blackhawk Technical Institute Henry Zatkis, New Jersey Institute of Technology
Tingxiu Wang, Western Missouri State University
The solutions to all problems were checked by Susan Porter, who also did developmental editing. Accuracy checking and
proofreading were done by John Morin and James Ricci and the copyediting was done by Martha Williams. The authors are
grateful to our Project Editor at John Wiley & Sons, Jennifer Brady, Production Editor Sandra Dumas, and Publisher Laurie
Rosatone, who have helped to bring this book to completion.
Thank you all.
Michael A. Calter Paul A. Calter
Middletown, CT Randolph Center, VT
[email protected] [email protected]
www.wesleyan.edu/chem/faculty/calter/ http://www.sover.net/~pcalter/