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Applied Calculus 7th Edition

Geoffrey C. Berresford | Andrew M. Rockett

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Overview

Ideal for one- or two-semester applied or business calculus course, the popular APPLIED CALCULUS, 7TH EDITION uses real-world applications to engage students and highlight the practical side of calculus. Contemporary applications draw from finance and business, and interesting topics, such as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance sports cars travel, lives saved by seat belts, and the cost of a congressional victory. Content addresses technology, such as graphing calculators and spreadsheets. Summaries and annotated examples reinforce learning, while exercises offer hands-on practice, diagnostic testing and important algebra review. MindTap® is available.

Geoffrey C. Berresford, Long Island University

Dr. Berresford received his Ph.D. from the Courant Institute of Mathematical Sciences at New York University and taught at the State University of New York at Purchase before joining the faculty at the C.W. Post campus of Long Island University. Besides co-authoring four textbooks with Dr. Rockett, he has published papers in differential equations, linear programming, logic, and probability, and has received several teaching awards and the Distinguished Service Award from The Metropolitan New York Section of the Mathematical Association of America.

Andrew M. Rockett, Long Island University

After completing his Ph.D. at Stony Brook University, Dr. Rockett joined the mathematics faculty at C.W. Post and began his collaborations with Dr. Berresford. His book with Peter Szusz on CONTINUED FRACTIONS (1992) was hailed by Ivan Niven as "an outstanding addition to the literature of mathematics," and he served the Kappa Mu Epsilon mathematics honor society as editor of the mathematics journal The Pentagon from 1989 to 1995. Dr. Rockett serves as a reviewer for several journals, including Mathematical Reviews for the American Mathematical Society.

WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

  • Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. Enhanced WebAssign now includes QuickPrep content to review key precalculus content, available as a CoursePack of prebuilt assignments to assign at the beginning of the course or where needed most.
  • Many of the book's contemporary and interesting applications use real, sourced data from a wide range of fields including athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. A globe icon identifies real-world examples.
  • Sourced exercises establish factual basis and enable further research.
  • Regression (modeling) exercises in Chapter 1 ask students to use calculators to fit equations to actual data, and illustrate the methods used to develop the models in applied exercises throughout the book. Students can also benefit from optional examples on linear regression, power regression, quadratic regression, and exponential regression.
  • The book presents substantial treatment of limits involving infinity, graphing rational functions, and elasticity of demand. In addition to these expanded applications, more challenging exercises are included as well as a complete proof of the Chain Rule based on Carathédory's definition of the derivative.
  • Brief Examples, located immediately to the right of the boxes that summarize results, illustrate and provide immediate reinforcement of the concepts.
  • Optional Graphing Calculator Explorations and exercises explore new topics, allow students to easily carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed, and an icon identifies exercises that require a graphing calculator.
  • Spreadsheet Explorations are included for select chapters of the text for those who prefer Microsoft® Excel or other spreadsheet technology.
  • Chapter Summaries, organized by section, review key concepts and reference specific review exercises that allow students to check their understanding. Chapter-ending Hints and Suggestions offer special reminders of essential facts or "tricks" that students might otherwise overlook.

Applied Calculus

TABLE OF CONTENTS

Preface.
Integrating Excel.
Diagnostic Test.
1. FUNCTIONS.
Real Numbers, Inequalities, and Lines. Exponents. Functions: Linear and Quadratic. Functions: Polynomial, Rational, and Exponential. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
2. DERIVATIVES AND THEIR USES.
Limits and Continuity. Rates of Change, Slopes, and Derivatives. Some Differentiation Formulas. The Product and Quotient Rules. Higher-Order Derivatives. The Chain Rule and the Generalized Power Rule. Nondifferentiable Functions. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
3. FURTHER APPLICATIONS OF DERIVATIVES.
Graphing Using the First Derivative. Graphing Using the First and Second Derivatives. Optimization. Further Applications of Optimization. Optimizing Lot Size and Harvest Size. Implicit Differentiation and Related Rates. Differentials, Approximations, and Marginal Analysis. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Cumulative Review for Chapters 1–3.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions. Differentiation of Logarithmic and Exponential Functions. Two Applications to Economics: Relative Rates and Elasticity of Demand. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
5. INTEGRATION AND ITS APPLICATIONS.
Antiderivatives and Indefinite Integrals. Integration Using Logarithmic and Exponential Functions. Definite Integrals and Areas. Further Applications of Definite Integrals: Average Value and Area Between Curves. Two Applications to Economics: Consumers'' Surplus and Income Distribution. Integration by Substitution. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
6. INTEGRATION TECHNIQUES.
Integration by Parts. Integration Using Tables. Improper Integrals. Numerical Integration. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
7. CALCULUS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Optimizing Functions of Several Variables. Least Squares. Lagrange Multipliers and Constrained Optimization. Total Differentials, Approximate Changes, and Marginal Analysis. Multiple Integrals. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Cumulative Review for Chapters 1–7.
8. TRIGONOMETRIC FUNCTIONS.
Triangles, Angles, and Radian Measure. Sine and Cosine Functions. Derivatives of Sine and Cosine Functions. Integrals of Sine and Cosine Functions. Other Trigonometric Functions. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
9. DIFFERENTIAL EQUATIONS.
Separation of Variables. Further Applications of Differential Equations: Three Models of Growth. First-Order Linear Differential Equations. Approximate Solutions of Differential Equations: Euler''s Method. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
10. SEQUENCES AND SERIES.
Geometric Series. Taylor Polynomials. Taylor Series. Newton''s Method. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test.
10. PROBABILITY.
Discrete Probability. Continuous Probability. Uniform and Exponential Random Variables. Normal Random Variables. Chapter Summary with Hints and Suggestions. Review Exercises and Chapter Test. Cumulative Review for Chapters 1–11.
APPENDICES.
A. Graphing Calculator Basics.
B. Algebra Review.
C. Normal Probabilities from Tables.
Answers to Selected Exercises.

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

FOR INSTRUCTORS

Complete Solutions Manual with Instructor's Web Site

ISBN: 9781305112278
This manual contains solutions to all exercises from the text, including Chapter Review Exercises and Cumulative Reviews. This manual can be found on the Instructors Companion Site.

Cengage Learning Testing, powered by Cognero Instant Access

ISBN: 9781305112292
Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to author, edit, and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom or wherever you want. This is available online at login.cengage.com.

Student Solutions Manual

ISBN: 9781305107953
This manual contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.

FOR STUDENTS

Student Solutions Manual

ISBN: 9781305107953
This manual contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.