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Overview

Features of this text include:

  • Clear explanations supported by detailed and well-illustrated examples
  • Calculator examples that are integrated throughout the text, including calculator screen images to illustrate the step-by-step calculator operations
  • More than 8400 exercisesDetailed descriptions of real-world applications of the mathematical concepts presented in the text
  • Two appendices of instructions for using graphing calculators—one for a basic graphing calculator and another for an advanced graphing calculator

This text is supported by the following multimedia:

  • Companion website—includes numerous review questions for each topic covered in the text and provides immediate feedback for each section quiz
  • Study Wizard—includes multiple-choice questions, a timed test option, and a glossary of important mathematical terms
Read More Show Less

Product Details

  • ISBN-13: 9780130255273
  • Publisher: Pearson
  • Publication date: 7/12/2000
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 1200
  • Product dimensions: 7.99 (w) x 10.00 (h) x 0.79 (d)

Read an Excerpt

PREFACE:

Preface

Technical Mathematics with Calculus provides the necessary comprehensive mathematics skills for students in an engineering technology program that requires a development of practical calculus.

The text presents the following major areas: fundamental concepts and measurement; fundamental algebraic concepts; exponential and logarithmic functions; right-triangle trigonometry, the trigonometric functions, and trigonometric formulas and identities; complex numbers; matrices; polynomial and rational functions; statistics for process control; analytic geometry; differential and integral calculus with applications; partial derivatives and 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
  • Comprehensive development and consistent use of measurement and significant digits throughout the text
  • Instruction using a basic graphing calculator (Appendix C) and an advanced graphing calculator (Appendix D) is developed in the appendices. Calculator examples are integrated throughout the text; graphing calculator may be used as a faculty option.
  • Chapter introductions and chapter objectives
  • More than 8400 exercises
  • Essential geometry is reviewed in Appendix A
  • The metric system is developed in Appendix B
  • StudyWizard CD-ROM that contains additionalexercises keyed to each section
  • Companion Website that contains different additional exercises keyed to each section
  • Instructor's Manual with solutions for selected odd-numbered exercises, answers for even-numbered exercises, and sample chapter tests and answers

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.

Exercises: To reinforce key concepts for students, we have provided a large variety of well-illustrated exercises.

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.

Calculator Story Boards: Calculator story boards, including screens, are used to show students the sequence of the step-by-step operations.

Illustrations and Boxes are abundantly and effectively used to highlight important principles.

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 is a feature that students and faculty alike find essential.

The text is written at a language level and a mathematics level that are cognizant of and beneficial to most students in technical programs. The students are assumed to have a mathematics background that includes one year of high school algebra or its equivalent and some geometry. The introductory chapters are written so that students who are deficient in some topics may also be successful. The material in this book should be completed in three or four semesters or equivalent and serves as a foundation for more advanced work in mathematics. This text is intended for use in Associate Degree programs as well as ABET (Accrediting Board for Engineering Technology) programs and BIT (Bachelor of Industrial Technology) programs.

Chapters 1 and 2 provide the basic skills that are needed early in almost any technical program. Chapters 3 through 8 complete the basic algebraic foundation, and Chapters 9 through 13 include the trigonometry necessary for the technologies. Chapters 14 through 17 include some advanced topics needed for some programs. Chapter 18 addresses the basics of statistics for process control. Chapter 19 (analytic geometry) completes a comprehensive mathematics background needed in many programs; some programs include this chapter at the end of the first year while other programs include this chapter at the beginning of the introductory calculus. Chapters 20 through 22 present intuitive discussions about the limit and develop basic techniques and applications of differentiation. Chapters 23 through 25 develop basic integration concepts, some appropriate applications, and more complicated methods of integration. Chapter 26 presents partial derivatives and double integrals. Chapters 27 through 29 provide an introduction to series and differential equations with technical applications.

We have included Appendix C on the basic graphing calculator and Appendix D on the advanced calculator so that faculty have the option of which, if any, graphing calculator is used in their course. Some graphing calculator uses are integrated into some of the examples in the text.

A companion Instructor's Manual with solutions for selected odd-numbered exercises, answers for even-numbered exercises, and sample chapter tests and answers is available.

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 lifelong 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

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 express thanks to our Prentice Hall editor, Stephen Helba; to our Prentice Hall associate editor, Michelle Churma; to our production editor, Louise Sette; to Kirsten Kauffman (York Production Services); and to Joyce Ewen for her superb proofing assistance.

If anyone wishes to correspond with us regarding suggestions, criticisms, questions, or errors, please contact Dale Ewen directly at Parkland Community College, 2400 W. Bradley, Champaign, IL 61821, or through Prentice Hall.

Dale Ewen
Joan S. Gary
James E. Trefzger

Read More Show Less

Table of Contents

(NOTE: All chapters end with a Summary and Review section)
1. Fundamental Concepts.

The Real Number System. Zero and Order of Operations. Scientific Notation and Powers of 10. Measurement. Operations with Measurements. Algebraic Expressions. Exponents and Radicals. Multiplication of Algebraic Expressions. Division of Algebraic Expressions. Linear Equations. Formulas. Substitution of Data into Formulas. Applications Involving Linear Equations. Ratio and Proportion. Variation.

2. Right-Triangle Trigonometry.
The Trigonometric Ratios. Values of the Trigonometric Ratios. Solving Right Triangles. Applications of the Right Triangle.

Application: The Global Positioning System. 3. Equations and Their Graphs.

Functions. Graphing Equations. The Straight Line. Parallel and Perpendicular Lines. The Distance and Midpoint Formulas.

4. Factoring and Algebraic Fractions.
Special Products. Factoring Algebraic Expressions. Other Forms of Factoring. Equivalent Fractions. Multiplication and Division of Algebraic Functions. Addition and Subtraction of Algebraic Fractions. Complex Fractions. Equations with Fractions.

5. Systems of Linear Equations.
Solving a System of Two Linear Equations. Other Systems of Equations. Solving a System of Three-Linear Equations. Determinants. Properties of Determinants. Solving a System of Linear Equations Using Determinants. Partial Fractions.

Application: Solar Cell Technology. 6. Quadratic Equations.

Solving a Quadratic Equation by Factoring. Solving Quadratic Equations by Completing the Square. The Quadratic Formula. Applications.

7. Exponents and Radicals.
Integral Exponents. Fractional Exponents. Simplest Radical Form. Addition and Subtraction of Radicals. Multiplication and Division of Radicals. Equations with Radicals. Equations in Quadratic Form.

8. Exponentials and Logarithms.
The Exponential Function. The Logarithm. Properties of Logarithms. Common Logarithms. Natural Logarithms. Solving Exponential Equations. Solving Logarithmic Equations. Applications: Solving Exponential and Logarithmic Equations. Data Along a Straight Line.

Application: Airbags. 9. Trigonometric Functions.

The Trigonometric Functions. Trigonometric Functions of Any Angle. Radian Measure. Use of Radian Measure.

10. Oblique Triangles and Vectors.
Law of Sines. The Ambiguous Case. Law of Cosines. Applications of Oblique Triangles. Addition of Vectors: Graphical Methods. Addition of Vectors: Trigonometric Methods. Vector Components. Vector Applications.

11. Graphing the Trigonometric Functions.
Graphing the Sine and Cosine Functions. Phase Shift. Graphing the Other Trigonometric Functions. Graphing Composite Curves. Simple Harmonic Motion.

Application: Improving Color Television. 12. Trigonometric Formulas and Identities.

Basic Trigonometric Identities. Formulas for the Sum and the Difference of Two Angles. Double- and Half-Angle Formulas. Trigonometric Equations. Inverse Trigonometric Relations. Inverse Trigonometric Functions.

13. Complex Numbers.
Complex Numbers in Rectangular Form. Trigonometric and Exponential Forms of Complex Numbers. Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms. Powers and Roots.

14. Matrices.
Basic Operations. Multiplication of Matrices. Finding the Inverse of a Matrix. Solving a System of Equations by a Matrix Method.

15. Polynomials of Higher Degree.
Polynomial Functions. Real Solutions of Polynomial Equations. Complex Solutions of Polynomial Equations.

Application: Matrices Used to Encode Information. 16. Inequalities and Absolute Value.

Inequalities. Equations and Inequalities Involving Absolute Value. Other Types of Inequalities. Inequalities in Two Variables.

17. Progressions and the Binomial Theorem.
Arithmetic Progressions. Geometric Progressions. The Binomial Theorem.

Application: Statistics in the Manufacturing Process. 18. Statistics for Process Control.

Graphic Presentation of Data. Measures of Central Tendency. Measures of Dispersion. The Normal Distribution. Fitting Curves to Data Sets. Statistical Process Control.

19. Analytic Geometry.
The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes. The General Second-Degree Equation. Systems of Quadratic Equations. Polar Coordinates. Graphs in Polar Coordinates.

20. The Derivative.
Motion. The Limit. The Slope of a Tangent Line to a Curve. The Derivative. Differentiation of Polynomials. Derivatives of Products and Quotients. The Derivative of a Power. Implicit Differentiation. Proofs of Derivative Formulas. Higher Derivatives.

21. Applications of the Derivative.
Curve Sketching. Using Derivatives in Curve Sketching. More on Curve Sketching. Maximum and Minimum Problems. Related Rates. Differentials.

22. Derivatives of the Transcendental Functions.
Derivatives of Sine and Cosine Functions. Derivatives of Other Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Applications.

23. The Integral.
The Indefinite Integral. The Constant of Integration. Area under a Curve. The Definite Integral.

24. Applications of Integration.
Area Between Curves. Volumes of Revolution: Disk Method. Volumes of Revolution: Shell Method. Center of Mass of a System of Particles. Center of Mass of Continuous Mass Distributions. Moments of Inertia. Work, Fluid Pressure, and Average Value.

25. Methods of Integration.
The General Power Formula. Logarithmic and Exponential Forms. Basic Trigonometric Forms. Other Trigonometric Forms. Inverse Trigonometric Forms. Integration Using Partial Fractions. Integration by Parts. Integration by Trigonometric Substitution. Integration Using Tables. Numerical Methods of Integration. Areas in Polar Coordinates.

26. Three-Space: Partial Derivatives and Double Integrals.
Functions in Three-Space. Partial Derivatives. Applications of Partial Derivatives. Double Integrals.

27. Series.
Series and Convergence. Ratio and Integral Tests. Alternating Series and Conditional Convergence. Power Series. Maclaurin Series. Operations with Series. Taylor Series. Computational Approximations. Fourier Series.

28. First-Order Differential Equations.
Solving Differential Equations. Separation of Variables. Use of Integrating Factors. Linear Equations of First Order. Applications of First-Order Differential Equations.

Application: Differential Equations and the Gateway Arch. 29. Second-Order Differential Equations.

Higher-Order Homogeneous Differential Equations. Repeated Roots and Complex Roots. Nonhomogeneous Equations. Applications of Second-Order Differential Equations. The Laplace Transform. Solutions by the Method of Laplace Transforms.

Appendix A: Review of Geometry.
Angles and Lines. Triangles. Quadrilaterals. Circles. Areas and Volumes of Solids.

Appendix B: The Metric System.
Introduction. Length. Mass. Volume and Area. Temperature, Time, Current, and Power. Other Conversions. Appendix B Review.

Appendix C: Using a Graphing Calculator.
Introduction to the TI-83 Keyboard. Computational Examples. Graphing Features. Examples of Graphing. Trigonometric Functions and Polar Coordinates. Equation-Solving and TABLE Features. The Numeric SOLVER. Matrix Features. LIST Features and Descriptive Statistics. The Line of Best Fit (Linear Regression). Calculus Features. Sequences and Series.

Appendix D: Using an Advanced Graphing Calculator.
Introduction to the TI-89 Keyboard. Variables and Editing. The Home Screen Menus. The Keyboard Menus. Graphing Functions. Examples of Graphing. Trig Functions and Polar Coordinates. Numerical GRAPH and TABLE Features. Sequences and Series. The Numeric Solver. Matrix Features. The Data Editor and Descriptive Statistics. The Line of Best Fit (Linear Regression). Symbolic Algebra Features. Basic Calculus Features. Graphing in 3D. Advanced Calculus Features.

Appendix E: Tables.
English Weights and Measures. Metric System Prefixes. Conversion Tables. Physical Quantities and Their Units. Table of Integrals.

Answers to Odd-Numbered Exercises and Chapter Reviews.
Index.
Read More Show Less

Preface

PREFACE:

Preface

Technical Mathematics with Calculus provides the necessary comprehensive mathematics skills for students in an engineering technology program that requires a development of practical calculus.

The text presents the following major areas: fundamental concepts and measurement; fundamental algebraic concepts; exponential and logarithmic functions; right-triangle trigonometry, the trigonometric functions, and trigonometric formulas and identities; complex numbers; matrices; polynomial and rational functions; statistics for process control; analytic geometry; differential and integral calculus with applications; partial derivatives and 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
  • Comprehensive development and consistent use of measurement and significant digits throughout the text
  • Instruction using a basic graphing calculator (Appendix C) and an advanced graphing calculator (Appendix D) is developed in the appendices. Calculator examples are integrated throughout the text; graphing calculator may be used as a faculty option.
  • Chapter introductions and chapter objectives
  • More than 8400 exercises
  • Essential geometry is reviewed in Appendix A
  • The metric system is developed in Appendix B
  • StudyWizard CD-ROM that containsadditionalexercises keyed to each section
  • Companion Website that contains different additional exercises keyed to each section
  • Instructor's Manual with solutions for selected odd-numbered exercises, answers for even-numbered exercises, and sample chapter tests and answers

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.

Exercises: To reinforce key concepts for students, we have provided a large variety of well-illustrated exercises.

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.

Calculator Story Boards: Calculator story boards, including screens, are used to show students the sequence of the step-by-step operations.

Illustrations and Boxes are abundantly and effectively used to highlight important principles.

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 is a feature that students and faculty alike find essential.

The text is written at a language level and a mathematics level that are cognizant of and beneficial to most students in technical programs. The students are assumed to have a mathematics background that includes one year of high school algebra or its equivalent and some geometry. The introductory chapters are written so that students who are deficient in some topics may also be successful. The material in this book should be completed in three or four semesters or equivalent and serves as a foundation for more advanced work in mathematics. This text is intended for use in Associate Degree programs as well as ABET (Accrediting Board for Engineering Technology) programs and BIT (Bachelor of Industrial Technology) programs.

Chapters 1 and 2 provide the basic skills that are needed early in almost any technical program. Chapters 3 through 8 complete the basic algebraic foundation, and Chapters 9 through 13 include the trigonometry necessary for the technologies. Chapters 14 through 17 include some advanced topics needed for some programs. Chapter 18 addresses the basics of statistics for process control. Chapter 19 (analytic geometry) completes a comprehensive mathematics background needed in many programs; some programs include this chapter at the end of the first year while other programs include this chapter at the beginning of the introductory calculus. Chapters 20 through 22 present intuitive discussions about the limit and develop basic techniques and applications of differentiation. Chapters 23 through 25 develop basic integration concepts, some appropriate applications, and more complicated methods of integration. Chapter 26 presents partial derivatives and double integrals. Chapters 27 through 29 provide an introduction to series and differential equations with technical applications.

We have included Appendix C on the basic graphing calculator and Appendix D on the advanced calculator so that faculty have the option of which, if any, graphing calculator is used in their course. Some graphing calculator uses are integrated into some of the examples in the text.

A companion Instructor's Manual with solutions for selected odd-numbered exercises, answers for even-numbered exercises, and sample chapter tests and answers is available.

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 lifelong 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

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 express thanks to our Prentice Hall editor, Stephen Helba; to our Prentice Hall associate editor, Michelle Churma; to our production editor, Louise Sette; to Kirsten Kauffman (York Production Services); and to Joyce Ewen for her superb proofing assistance.

If anyone wishes to correspond with us regarding suggestions, criticisms, questions, or errors, please contact Dale Ewen directly at Parkland Community College, 2400 W. Bradley, Champaign, IL 61821, or through Prentice Hall.

Dale Ewen
Joan S. Gary
James E. Trefzger

Read More Show Less

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