This book uses intriguing real-world applications to engage readers' interest and show them the practical side of calculus. Its many applications are related to finance, business, and such general-interest topics as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance traveled by sports cars, lives saved by seat belts, and the cost of a congressional victory. The Seventh Edition maintains the hallmark features that have made BRIEF APPLIED CALCULUS so popular: contemporary and interesting applications including many that are new or updated); careful and effective use of technology, including graphing calculator and spreadsheet coverage; constant pedagogical reinforcement through section summaries, chapter summaries, annotated examples, and extra practice problems; Just-in-Time algebra review material; and a variety of exercises that allow readers to practice and hone their problem-solving skills.
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. Differential Equations. Further Applications of Differential Equations: Three Models of Growth. 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.
APPENDICES.
A. Graphing Calculator Basics.
B. Algebra Review.
Answers to Selected Exercises.
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Geoffrey C. Berresford
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.
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Andrew M. Rockett
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.
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A Diagnostic Test has been added to help students identify skills that may need review. This test appears before Chapter 1.
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An Algebra Review appears in an appendix, keyed to parts of the text, for additional reference.
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New material on parallel and perpendicular lines has been added to Section 1.1, "Real Numbers, Inequalities, and Lines."
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Section 3.7, "Differentials, Approximations, and Marginal Analysis," is new to the seventh edition. This section is optional and can be omitted without loss of continuity.
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New exercises have been added and over 100 updated (including all of the Wall Street financial exercises) with current real-world data and accompanying sources. New "Explorations and Excursions" exercises give further details or theoretical underpinnings of the topics in the main narrative.
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A Diagnostic Test has been added to help you identify skills that may need review. This test appears before Chapter 1.
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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.
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Sourced exercises establish factual basis and enable further research.
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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.
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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.
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Brief Examples, located immediately to the right of the boxes that summarize results, illustrate and provide immediate reinforcement of the concepts.
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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.
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Spreadsheet Explorations are included for select chapters of the text for those who prefer Microsoft® Excel or other spreadsheet technology.
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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.
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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.