Higher Education

Technical Calculus with Analytic Geometry, 5th Edition

  • Peter Kuhfittig Milwaukee School of Engineering
  • ISBN-10: 1133945198  |  ISBN-13: 9781133945192
  • 544 Pages
  • Previous Editions: 2006, 1994, 1988
  • © 2013 | Published
  • College Bookstore Wholesale Price = $209.00
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About

Overview

This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus are introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs.

Features and Benefits

  • Exercises sets have been carefully revised, with more applied problems added throughout.
  • Additional details have been added to many of the examples, making them more understandable for students.
  • There is a greater emphasis on using CAS to amplify and clarify certain concepts, such as tangent and normal lines, graphing parametric and polar curves, and graphing solutions of differential equations. The use of a computer algebra system (CAS) is suggested from time to time in the exercises. However, their use in the course remains completely optional.
  • The author uses notations frequently encountered in technology, to help prepare students for further courses in their careers.
  • Margin notes are used throughout to identify additional concepts and to explain the steps in the solutions to example problems.
  • The emphasis on applications helps students learn calculus skills that are particular to technology. The applications are complemented with a solid base of drill exercises to ensure that students get practice in basic operations.
  • Important concepts are boxed and labeled for easy reference and review.
  • Each chapter ends with a carefully selected set of review exercises that cover all the topics in the chapter. Answers to all of the review questions are included in the back of the book.

Table of Contents

1. INTRODUCTION TO ANALYTIC GEOMETRY.
The Cartesian Coordinate System. The Slope. The Straight Line. Curve Sketching. Discussion of Curves with Graphing Utilities. The Conics. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes; Standard Equations of the Conics. Review Exercises.
2. INTRODUCTION TO CALCULUS: THE DERIVATIVE.
Functions and Intervals. Limits. The Derivative. The Derivative by the Four-Step Process. Derivatives of Polynomials. Instantaneous Rates of Change. Differentiation Formulas. Implicit Differentiation. Higher Derivatives. Review Exercises.
3. APPLICATIONS OF THE DERIVATIVE.
The First-Derivative Test. The Second-Derivative Test. Exploring with Graphing Utilities. Applications of Minima and Maxima. Related rates. Differentials. Review Exercises.
4. THE INTEGRAL.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition. Basic Integration Formulas. Area Between Curves. Improper Integrals. The Constant of Integration. Numerical Integration. Review Exercises.
5. APPLICATION OF THE INTEGRAL.
Means of Root Mean Squares. Volumes of Revolution: Disk and Washer Methods. Volumes of Revolution: Shell Method. Centroids. Moments of Inertia. Work and Fluid Pressure. Review Exercises.
6. DERIVATIVES OF TRANSCENDENTAL FUNCTIONS.
Review of Trigonometry. Derivatives of Sine and Cosine Functions. Other Trigonometric Functions. Inverse Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Derivative of the Logarithmic Function. Derivative of the Exponential Function. L'Hospital's rule. Applications. Newton's Method. Review Exercises.
7. INTEGRATION TECHNIQUES.
The Power Formula Again. The Logarithmic and Exponentials Forms. Trigonometric Forms. Further Trigonometric Forms. Inverse Trigonometric Forms. Integration by Trigonometric Substitution. Integration by Parts. Integration of Rational Functions. Integration by Use of Tables. Additional Remarks. Review Exercises.
8. PARAMETIC EQUATIONS, VECTORS, AND POLAR COORDINATES.
Vectors and Parametric Equations. Arc Length. Polar Coordinates. Curves in Polar Coordinates. Areas in Polar Coordinates. Review Exercises.
9. THREE-DIMENSIONAL SPACE; PARTIAL DERIVATIVES; MULTIPLE INTEGRALS.
Surfaces in Three Dimensions. Partial Derivatives. Applications of Partial Derivatives. Curve Fitting. Integrated Integrals. Volumes by Double Integration. Mass, Centroids, and Moments of Inertia. Volumes in Cylindrical Coordinates. Review Exercises.
10. INFINITE SERIES.
Introduction to Infinite Series. Tests for Convergence. Maclaurin Series. Operations with Series. Computations with Series; Applications. Fourier Series. Review Exercises.
11. FIRST-ORDER DIFFERETIAL EQUATIONS.
What is Differential Equation? Separation of Variables. First-Order Linear Differential Equations. Applications of First-Order Differential Equations. Numerical Solutions. Review Exercises.
12. HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS.
Higher-Order Homogeneous Differential Equations. Auxiliary Equations with Repeating or Complex Roots. Nonhomogeneous Equations. Applications of Second-Order Equations. Review Exercises.
13. THE LAPLACE TRANSFORM.
Introduction and Basic Properties. Inverse Laplace Transforms. Partial Fractions. Solutions of Linear Equations by Laplace Transforms. Review Exercises.
Appendix A: Tables.
Common Units of Measure. A Short Table of Integrals.
Appendix B: Answers to Selected Exercises.
Index.

What's New

  • Approximately 25% new exercises, as well as reordered exercises to yield a more logical sequence for mastering the topics.
  • Expanded use of CAS, particularly in Chapters 7, 12, and 13 to check answers and to aid with performing calculations too cumbersome to do by hand. The use of CAS is not intended to replace traditional techniques. The use of graphing utilities has also been expanded in both examples and exercises.
  • Based on input from reviewers and users of the book, Sections 4.5, 4.7, 7.1, 7.6, and 7.7 were essentially rewritten. In Sections 2.6 and 3.4 new applications to economics have been introduced.

Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Complete Solutions Manual  (ISBN-10: 1285053427 | ISBN-13: 9781285053424)

The Instructor's Solutions Manual contains worked-out solutions to all problems in the text.

Solutions Builder  (ISBN-10: 1285053400 | ISBN-13: 9781285053400)

This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. www.cengage.com/solutionbuilder.

Student Solutions Builder Manual  (ISBN-10: 1285052579 | ISBN-13: 9781285052571)

This manual contains detailed solutions to every odd-numbered problem in the text.

List Price = $97.95  | CengageBrain Price = $97.95  | College Bookstore Wholesale Price = $73.50

Student Supplements

Student Solutions Builder Manual  (ISBN-10: 1285052579 | ISBN-13: 9781285052571)

This manual contains detailed solutions to every odd-numbered problem in the text.

List Price = $97.95  | CengageBrain Price = $97.95  | College Bookstore Wholesale Price = $73.50

Meet the Author

Author Bio

Peter Kuhfittig

Peter Kuhfittig has taught mathematics at the Milwaukee School of Engineering for over thirty years and has served as head of the department for over half of this period. His enthusiasm for teaching has resulted in an award for excellence in teaching, as well as an interest in textbook writing. He has been involved in applications of mathematics through occasional consulting work. More recently, Dr. Kuhfittig has turned to research in wormhole physics.