Technical Calculus / Edition 4

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Overview

This book provides readers with necessary mathematics skills, including practical calculus. Mathematics provides the essential framework for and is the basic language of all the technologies. Mathematical, problem-solving, and critical thinking skills are crucial to understanding the changing face of technology. It presents the following major areas: fundamental concepts and measurement; fundamental algebraic concepts; exponential and logarithmic functions; right-triangle trigonometry; the trigonometric functions with formulas and identities; complex numbers; matrices; polynomial and rational functions; basic statistics; analytic geometry; differential and integral calculus with applications; partial derivatives and double integrals; series; and differential equations. An excellent learning aid and resource tool for engineers, especially computer software, hardware, and peripheral manufacturers. Its comprehensive appendices make this an excellent desktop reference.

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Editorial Reviews

Booknews
A textbook for students enrolled in a two-year, four-year, or continuing education engineering technology program that requires developing practical calculus. Assumes a background in algebra and trigonometry. Presents the major areas of analytical geometry, differential calculus, integral calculus, partial derivatives, double integrals, series, and differential equations. Updated from the 1986 edition; first published in 1977. No bibliography. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780130930040
  • Publisher: Prentice Hall
  • Publication date: 7/28/2001
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 636
  • Product dimensions: 7.01 (w) x 9.25 (h) x 0.49 (d)

Read an Excerpt

Technical Calculus, Fourth Edition, provides the calculus skills for students in an engineering technology program that requires a development of practical calculus. This edition has been carefully reviewed, and special efforts have been taken to emphasize clarity and accuracy of presentation.

The text presents the following major areas: analytic geometry, differential calculus, integral calculus, partial derivatives, double integrals, series, and differential equations.

Key Features

  • Numerous detailed, illustrated examples.
  • Chapter review summaries.
  • Chapter review exercises.
  • Important formulas and principles are highlighted.
  • Abundant two-color illustrations.
  • Two-color format that effectively highlights and illustrates important principles.
  • Instruction using a basic graphing calculator (Appendix C) and an advanced graphing calculator (Appendix D) is developed in the appendices with calculator examples integrated throughout the text. A graphing calculator may be used as a faculty option.
  • Chapter introduction and chapter objectives.
  • More than 3400 exercises.
  • An Instructor's Manual with solutions for odd-numbered exercises, answers to even-numbered exercises, and answers to chapter tests.

Illustration of Some Key Features

Examples. Since many students learn by example, a large number of detailed and well-illustrated examples are used throughout the text. Page 261 illustrates this feature.

Page 342 illustrates the use of an advanced graphing calculator to evaluate a definite integral as an alternative to using atrigonometric substitution to integrate. Page 477 illustrates the use of an advanced graphing calculator to solve a nonhomogeneous differential equation. Each graphing calculator feature can easily be omitted without loss of continuity.

Illustrations and Boxes. Page 293 is an example of the abundant and effective use of illustrations and boxes to highlight important principles.

Chapter End Matter. A chapter summary and a chapter review are provided at the end of each chapter to review concept understanding and to help students review for quizzes and examinations.

To the Faculty

The topics have been arranged with the assistance of faculty who teach in a variety of technical programs. However, we have also allowed for many other compatible arrangements. The topics are presented in an intuitive manner with technical applications integrated throughout whenever possible. The large number of detailed examples and exercises are features that students and faculty alike find essential.

Mathematics for Technical Education, serves as a smooth transition to this book, although other equivalent texts are also feasible.

Chapter 1 provides the basic analytic geometry needed for a study of a practical calculus. Chapters 2 through 4 present intuitive discussions about the limit and develop basic techniques and applications of differentiation. Chapters 5 through 7 develop basic integration concepts, some appropriate applications, and more complicated methods of integration. Chapter 8 presents partial derivatives and double integrals. Chapters 9 and 10 provide a basic understanding of progressions and series. Chapters 11 and 12 provide an introduction to differential equations with technical applications.

To the Student

Mathematics provides the essential framework for and is the basic language of all the technologies. With this basic understanding of mathematics, you will be able to quickly understand your chosen field of study and then be able to independently pursue your own life-long education. Without this basic understanding, you will likely struggle and often feel frustrated not only in your mathematics and support sciences courses but also in your technical courses.

Technology and the world of work will continue to change rapidly. Your own working career will likely change several times during your working lifetime. Mathematical, problem-solving, and critical-thinking skills will be crucial as opportunities develop in your own career path in a rapidly changing world.

Acknowledgments

The authors especially thank the many faculty and students who have used the previous editions and those who have offered suggestions. If anyone wishes to correspond with us regarding suggestions, criticisms, questions, or errors, please contact Dale Ewen directly through Prentice Hall or e-mail the authors at MathComments@aol.com.

We extend our sincere and special thanks to our reviewers: Joe Jordan, John Tyler Community College (VA); Maureen Kelly, North Essex Community College (MA); Carol A. McVey, Florence-Darlington Technical College (SC); John D. Meese, DeVry Institute of Technology (OH); Kenneth G. Merkel, Ph.D., PE, University of Nebraska-Lincoln; Susan L. Miertschin, University of Houston; and Pat Velicky, Florence-Darlington Technical College (SC). We would also like to extend thanks to our Prentice Hall editor—Stephen Helba, to our media development editor—Michelle Churma, to our production editor—Louise Sette, Wendy Druck at TECHBOOKS, and to Joyce Ewen for her superb proofing assistance.

Dale Ewen
Joan S. Gary
James E. Trefzger

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Table of Contents

1 Analytic Geometry 1
2 The Derivative 79
3 Applications of the Derivative 129
4 Derivatives of Transcendental Functions 172
5 The Integral 227
6 Applications of Integration 252
7 Methods of Integration 313
8 Three-Space: Partial Derivatives and Double Integrals 371
9 Progressions and the Binomial Theorem 401
10 Series 414
11 First-Order Differential Equations 453
12 Second-Order Differential Equations 477
App. A Using a Graphing Calculator 513
App. B: Tables 540
Answers to Odd-Numbered Exercises and Chapter Reviews 550
Index 596
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Preface

Technical Calculus, Fourth Edition, provides the calculus skills for students in an engineering technology program that requires a development of practical calculus. This edition has been carefully reviewed, and special efforts have been taken to emphasize clarity and accuracy of presentation.

The text presents the following major areas: analytic geometry, differential calculus, integral calculus, partial derivatives, double integrals, series, and differential equations.

Key Features

  • Numerous detailed, illustrated examples.
  • Chapter review summaries.
  • Chapter review exercises.
  • Important formulas and principles are highlighted.
  • Abundant two-color illustrations.
  • Two-color format that effectively highlights and illustrates important principles.
  • Instruction using a basic graphing calculator (Appendix C) and an advanced graphing calculator (Appendix D) is developed in the appendices with calculator examples integrated throughout the text. A graphing calculator may be used as a faculty option.
  • Chapter introduction and chapter objectives.
  • More than 3400 exercises.
  • An Instructor's Manual with solutions for odd-numbered exercises, answers to even-numbered exercises, and answers to chapter tests.

Illustration of Some Key Features

Examples. Since many students learn by example, a large number of detailed and well-illustrated examples are used throughout the text. Page 261 illustrates this feature.

Page 342 illustrates the use of an advanced graphing calculator to evaluate a definite integral as an alternative to using atrigonometric substitution to integrate. Page 477 illustrates the use of an advanced graphing calculator to solve a nonhomogeneous differential equation. Each graphing calculator feature can easily be omitted without loss of continuity.

Illustrations and Boxes. Page 293 is an example of the abundant and effective use of illustrations and boxes to highlight important principles.

Chapter End Matter. A chapter summary and a chapter review are provided at the end of each chapter to review concept understanding and to help students review for quizzes and examinations.

To the Faculty

The topics have been arranged with the assistance of faculty who teach in a variety of technical programs. However, we have also allowed for many other compatible arrangements. The topics are presented in an intuitive manner with technical applications integrated throughout whenever possible. The large number of detailed examples and exercises are features that students and faculty alike find essential.

Mathematics for Technical Education, serves as a smooth transition to this book, although other equivalent texts are also feasible.

Chapter 1 provides the basic analytic geometry needed for a study of a practical calculus. Chapters 2 through 4 present intuitive discussions about the limit and develop basic techniques and applications of differentiation. Chapters 5 through 7 develop basic integration concepts, some appropriate applications, and more complicated methods of integration. Chapter 8 presents partial derivatives and double integrals. Chapters 9 and 10 provide a basic understanding of progressions and series. Chapters 11 and 12 provide an introduction to differential equations with technical applications.

To the Student

Mathematics provides the essential framework for and is the basic language of all the technologies. With this basic understanding of mathematics, you will be able to quickly understand your chosen field of study and then be able to independently pursue your own life-long education. Without this basic understanding, you will likely struggle and often feel frustrated not only in your mathematics and support sciences courses but also in your technical courses.

Technology and the world of work will continue to change rapidly. Your own working career will likely change several times during your working lifetime. Mathematical, problem-solving, and critical-thinking skills will be crucial as opportunities develop in your own career path in a rapidly changing world.

Acknowledgments

The authors especially thank the many faculty and students who have used the previous editions and those who have offered suggestions. If anyone wishes to correspond with us regarding suggestions, criticisms, questions, or errors, please contact Dale Ewen directly through Prentice Hall or e-mail the authors at MathComments@aol.com.

We extend our sincere and special thanks to our reviewers: Joe Jordan, John Tyler Community College (VA); Maureen Kelly, North Essex Community College (MA); Carol A. McVey, Florence-Darlington Technical College (SC); John D. Meese, DeVry Institute of Technology (OH); Kenneth G. Merkel, Ph.D., PE, University of Nebraska-Lincoln; Susan L. Miertschin, University of Houston; and Pat Velicky, Florence-Darlington Technical College (SC). We would also like to extend thanks to our Prentice Hall editor—Stephen Helba, to our media development editor—Michelle Churma, to our production editor—Louise Sette, Wendy Druck at TECHBOOKS, and to Joyce Ewen for her superb proofing assistance.

Dale Ewen
Joan S. Gary
James E. Trefzger

Read More Show Less

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