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A textbook for students enrolled in a twoyear, fouryear, 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.Product Details
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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
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. 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.
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 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
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 email 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, 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 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
Table of Contents
1. Analytic Geometry.
Functions. Graphing Equations. The Straight Line. Parallel and Perpendicular Lines. The Distance and Midpoint Formulas. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes. The General SecondDegree Equation. Systems of Quadratic Equations. Polar Coordinates. Graphs in Polar Coordinates.
2. 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.
3. Applications of the Derivative.
Curve Sketching. Using Derivatives in Curve Sketching. More on Curve Sketching. Newton's Method for Improving Estimated Solutions. Maximum and Minimum Problems. Related Rates. Differentials and Linear Approximations.
4. Derivatives of Transcendental Functions.
The Trigonometric 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. L'Hospital's Rule. Applications.
5. The Integral.
The Indefinite Integral. The Constant of Integration. Area Under a Curve. The Definite Integral.
6. Applications of Integrations.
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.
7. 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 Using Tables. Integration by Trigonometric Substitution. Integration Using Tables. Numerical Methods of Integration. Areas in Polar Coordinates. Improper Integrals.
8. ThreeSpace: Partial Derivatives and Double Integrals.
Functions in ThreeSpace. Partial Derivatives. Applications in Partial Derivatives. Double Integrals.
9. Progressions and the Binomial Theorem.
Arithmetic Progressions. Geometric Progressions. The Binomial Theorem.
10. 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.
11. FirstOrder Differential Equations.
Solving Differential Equations. Separation of Variables. Use of Exact Differentials. Linear Equations of First Order. Applications of FirstOrder Differential Equations.
12. SecondOrder Differential Equations.
HigherOrder Homogenous Differential Equations. Repeated Roots and Complex Roots. Nonhomogenous Equations. Applications of SecondOrder Differential Equations. The Laplace Transform. Solutions by Method of Laplace Transforms.
Appendix A: U.S. Weights and Measures.
English Weights and Measures. Conversion Tables.
Appendix B: Table of Integrals.
Appendix C: Using a Graphic Calculator.
Introduction to the Keyboard of the TI83 PLUS. 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 TI89 Keyboard. Variables and Editing. The Home Screens 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.
Answers to OddNumbered Exercises and Chapter Reviews.
Index.
Preface
The text presents the following major areas: analytic geometry, differential calculus, integral calculus, partial derivatives, 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. 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.
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 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
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 email 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, 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 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