com This page intentionally left blank calte_TMC_fm_i-xvi-hr.qxd 10-02-2011 13:39 Page i www.com accessible, affordable, active learning :LOH\3/86LVDQLQQRYDWLYHUHVHDUFKEDVHGRQOLQHHQYLURQPHQWIRU HIIHFWLYHWHDFKLQJDQGOHDUQLQJ :LOH\3/86 «PRWLYDWHVVWXGHQWVZLWK «VXSSRUWVLQVWUXFWRUVZLWK FRQÀGHQFHERRVWLQJ UHOLDEOHUHVRXUFHVWKDW IHHGEDFNDQGSURRIRI UHLQIRUFHFRXUVHJRDOV SURJUHVV LQVLGHDQGRXWVLGHRI WKHFODVVURRP ,QFOXGHV ,QWHUDFWLYH 7H[WERRN 5HVRXUFHV :LOH\3/86 /HDUQ 0RUH ZZZZLOH\SOXVFRP calte_TMC_fm_i-xvi-hr.qxd 10-02-2011 13:39 Page ii www.com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calte_TMC_fm_i-xvi-hr2.qxd 21-02-2011 15:12 Page iii www.com SIXTH EDITION TECHNICAL MATHEMATICS WITH CALCULUS ◆◆◆ PAUL A. CALTER, MSME, MFA ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ Professor Emeritus Vermont Technical College ◆◆◆ MICHAEL A. ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ Associate Professor Wesleyan University JOHN WILEY & SONS, INC. calte_TMC_fm_i-xvi-hr.qxd 10-02-2011 13:39 Page iv www.com ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ To Rachel, Christopher, and Kaitlin VP & PUBLISHER Laurie Rosatone EDITOR Jennifer Brady MARKETING MANAGER Debi Doyle MEDIA EDITOR Melissa Edwards PRODUCTION MANAGER Dorothy Sinclair PRODUCTION EDITOR Sandra Dumas DESIGNER Wendy Lai PHOTO DEPARTMENT MANAGER Hilary Newman PRODUCTION MANAGEMENT SERVICES Preparé, Inc.
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Outside of the United States, please contact your local representative. ISBN 13 978-0470-46472-4 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 calte_TMC_fm_i-xvi-hr.qxd 10-02-2011 13:39 Page v www.com 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 Problems are 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 calte_TMC_fm_i-xvi-hr.qxd 10-02-2011 13:39 Page vi www.com 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 Applications should 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 Estimation steps 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. Formulas used 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 Boxes to 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 only by 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 methods are 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 Calculator and 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 Projects to foster “collaborative learning,” and Internet ac- 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. calte_TMC_fm_i-xvi-hr1.qxd 16-02-2011 16:17 Page vii www.com 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 Manual contains 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 Manual gives 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.
