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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; righttriangle 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
Illustration of Some Key Features
Examples: Since many students learn by example, a large number of detailed and wellillustrated examples are used throughout the text.
Exercises: To reinforce key concepts for students, we have provided a large variety of wellillustrated 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 stepbystep 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 oddnumbered exercises, answers for evennumbered 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, problemsolving, and criticalthinking 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, FlorenceDarlington Technical College (SC); John D. Meese, DeVry Institute of Technology (OH); Kenneth G. Merkel, Ph.D., PE, University of NebraskaLincoln; Susan L. Miertschin, University of Houston; and Pat Velicky, FlorenceDarlington 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
Table of Contents
(NOTE: All chapters end with a Summary and Review section)
1. Fundamental Concepts.
2. RightTriangle Trigonometry.
Application: The Global Positioning System. 3. Equations and Their Graphs.
4. Factoring and Algebraic Fractions.
5. Systems of Linear Equations.
Application: Solar Cell Technology. 6. Quadratic Equations.
7. Exponents and Radicals.
8. Exponentials and Logarithms.
Application: Airbags. 9. Trigonometric Functions.
10. Oblique Triangles and Vectors.
11. Graphing the Trigonometric Functions.
Application: Improving Color Television. 12. Trigonometric Formulas and Identities.
13. Complex Numbers.
14. Matrices.
15. Polynomials of Higher Degree.
Application: Matrices Used to Encode Information. 16. Inequalities and Absolute Value.
17. Progressions and the Binomial Theorem.
Application: Statistics in the Manufacturing Process. 18. Statistics for Process Control.
19. Analytic Geometry.
20. The Derivative.
21. Applications of the Derivative.
22. Derivatives of the Transcendental Functions.
23. The Integral.
24. Applications of Integration.
25. Methods of Integration.
26. ThreeSpace: Partial Derivatives and Double Integrals.
27. Series.
28. FirstOrder Differential Equations.
Application: Differential Equations and the Gateway Arch. 29. SecondOrder Differential Equations.
Appendix A: Review of Geometry.
Appendix B: The Metric System.
Appendix C: Using a Graphing Calculator.
Appendix D: Using an Advanced Graphing Calculator.
Appendix E: Tables.
Answers to OddNumbered Exercises and Chapter Reviews.
Index.
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; righttriangle 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
Illustration of Some Key Features
Examples: Since many students learn by example, a large number of detailed and wellillustrated examples are used throughout the text.
Exercises: To reinforce key concepts for students, we have provided a large variety of wellillustrated 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 stepbystep 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 oddnumbered exercises, answers for evennumbered 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, problemsolving, and criticalthinking 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, FlorenceDarlington Technical College (SC); John D. Meese, DeVry Institute of Technology (OH); Kenneth G. Merkel, Ph.D., PE, University of NebraskaLincoln; Susan L. Miertschin, University of Houston; and Pat Velicky, FlorenceDarlington 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