Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition with MathZone

Laurence D. Hoffmann November 2011 I consider myself to be a writer and expositor as well as a mathematician, and these traits led to the original version of this text published in 1975. Before assuming my current position as a Senior Investment Management Consultant with Morgan Stanley Smith Barney, I was a tenured professor of mathematics at Claremont McKenna College, where, on three occasions, I was honored to be the recipient of the Huntoon Award for Excellence in Teaching, a best-teacher award determined by a vote of the students. In addition to my current profession and my ongoing involvement with this text, I serve on the Strategic Planning committee of the Claremont Community foundation and on the Investment Committee of the Rancho Santa Ana Botanic Gardens in Claremont. My wife, Janice, and I love to travel, enjoy music and the arts, have two grown sons, three grandchildren and two Maltese dogs. I am an avid (but average) tennis player, am addicted to the Sunday Puzzle on NPR, and have been trying for several years to become fluent in Italian. Long ago, I received by BA in mathematics from Brown University and my Ph.D. in mathematics from the University of Wisconsin. After receiving my undergraduate degree at Harvey Mudd College and my PhD from Caltech, I joined the Mathematics Department at Claremont McKenna College, where I have continued to teach, specializing in calculus, linear algebra, and differential equations. I love to write, and in addition to this text have written published texts on engineering calculus and linear algebra. My wife, Jaqui, and I are active supporters of recording textbooks for the blind and dyslexic. We also travel whenever we get a chance and especially enjoy cruising. Our favorite destinations have been Crete, Barcelona, and Singapore. Im a lifelong Boston Red Sox, Los Angeles Lakers, and USC Trojan football fan, and write science fiction novels in my spare time. We have two sons, a newborn grandson, and seven cats, although its not clear whether we have the cats or they have us. We also raise foster kittens for a local shelter until they are ready to be adopted, and yes, three of our cats are fosters that we could not resist adopting ourselves.

Preface1 Functions, Graphs, and Limits1.1 Functions1.2 The Graph of a Function1.3 Linear Functions1.4 Functional Models1.5 Limits1.6 One-Sided Limits and ContinuityChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 1Review ProblemsExplore! UpdateThink About It2 Differentiation: Basic Concepts2.1 The Derivative2.2 Techniques of Differentiation2.3 Product and Quotient Rules; Higher Order Derivatives2.4 The Chain Rule2.5 Marginal Analysis and Approximations Using Increments2.6 Implicit Differentiation and Related RatesChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 2Review ProblemsExplore! UpdateThink About It3 Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization3.5 Additional Applied OptimizationChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 3Review ProblemsExplore! UpdateThink About It4 Exponential and Logarithmic Functions4.1 Exponential Functions4.2 Logarithmic Functions4.3 Differentiation of Logarithmic and Exponential Functions4.4 Additional Exponential ModelsChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 4Review ProblemsExplore! UpdateThink About It5 Integration5.1 Antidifferentiation: The Indefinite Integral5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Area Between Curves and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 5Review ProblemsExplore! UpdateThink About It6 Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Improper Integrals6.3 Numerical IntegrationChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 6Review ProblemsExplore! UpdateThink About It7 Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 7Review ProblemsExplore! UpdateThink About It8 Differential Equations8.1 Introduction to Differential Equations8.2 First-Order Linear Differential Equations8.3 Additional Applications of Differential Equations8.4 Approximate Solutions of Differential Equations8.5 Difference EquationsChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 8Review ProblemsExplore! UpdateThink About It9 Infinite Series and Taylor Series Approximations9.1 Infinite Series9.2 Tests for Convergence9.3 Functions as Power Series; Taylor SeriesChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 9Review ProblemsExplore! UpdateThink About It10 Probability and Calculus10.1 Discrete Random Variables10.2 Continuous Random Variables10.3 Expected Value and Variance of Continuous Random Variables10.4 Normal and Poisson Probability DistributionsChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 10Review ProblemsExplore! UpdateThink About It11 Trigonometric Functions11.1 The Trigonometric Functions11.2 Differentiation and Integration of Trigonometric Functions11.3 Additional Applications Involving Trigonometric FunctionsChapter SummaryImportant Terms, Symbols, and FormulasCheckup for Chapter 11Review ProblemsExplore! UpdateThink About ItAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L'Hôpital's RuleAppendix SummaryImportant Terms, Symbols, and FormulasReview ProblemsThink About ItTablesI Powers of eII The Natural Logarithm (Base e)III Trigonometric FunctionsText SolutionsAnswers to Odd-Numbered Problems, Chapter Checkup Problems, and Chapter Review ProblemsIndex