Calculus and Its Applications

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife, Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.  David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and the University of Vermont. Professor Ellenbogen has been active in the Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from the University of Massachusetts at Amherst. A cofounder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack.  Scott Surgent received his B.S. and M.S. degrees in mathematics from the University of California—Riverside, and has taught mathematics at Arizona State University in Tempe, Arizona, since 1994. He is an avid sports fan and has authored books on hockey, baseball, and hiking. Scott enjoys hiking and climbing the mountains of the western United States. He was active in search and rescue, including six years as an Emergency Medical Technician with the Central Arizona Mountain Rescue Association (Maricopa County Sheriff’s Office) from 1998 until 2004. Scott and his wife, Beth, live in Scottsdale, Arizona.

• R. Functions, Graphs, and ModelsR.1 Graphs and EquationsR.2 Functions and ModelsR.3 Finding Domain and RangeR.4 Slope and Linear FunctionsR.5 Nonlinear Functions and ModelsR.6 Mathematical Modeling and Curve FittingChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application Average Price of a Movie Ticket  1. Differentiation1.1 Limits: A Numerical and Graphical Approach1.2 Algebraic Limits and Continuity1.3 Average Rates of Change 1.4 Differentiation Using Limits of Difference Quotients1.5 The Power and Sum—Difference Rules1.6 The Product and Quotient Rules1.7 The Chain Rule1.8 Higher-Order DerivativesChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–Path of a Baseball: The Tale of the Tape  2. Applications of Differentiation2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs2.3 Graph Sketching: Asymptotes and Rational Functions2.4 Using Derivatives to Find Absolute Maximum and Minimum Values2.5 Maximum—Minimum Problems; Business, Economics, and General Applications2.6 Marginals and Differentials2.7 Elasticity of Demand2.8 Implicit Differentiation and Related RatesChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–Maximum Sustainable Harvest  3. Exponential and Logarithmic Functions3.1 Exponential Functions3.2 Logarithmic Functions3.3 Applications: Uninhibited and Limited Growth Models3.4 Applications: Decay3.5 The Derivatives of ax and loga x3.6 A Business Application: AmortizationChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–The Business of Motion Picture Revenue and DVD Release  4. Integration4.1 Antidifferentiation4.2 Antiderivatives as Areas4.3 Area and Definite Integrals4.4 Properties of Definite Integrals4.5 Integration Techniques: Substitution4.6 Integration Techniques: Integration by Parts4.7 Integration Techniques: TablesChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–Business: Distribution of Wealth  5. Applications of Integration5.1 Consumer Surplus and Producer Surplus5.2 Integrating Growth and Decay Models5.3 Improper Integrals5.4 Probability5.5 Probability: Expected Value; The Normal Distribution5.6 Volume5.7 Differential EquationsChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–Curve Fitting and Volumes of Containers  6. Functions of Several Variables6.1 Functions of Several Variables6.2 Partial Derivatives6.3 Maximum—Minimum Problems6.4 An Application: The Least-Squares Technique6.5 Constrained Optimization6.6 Double IntegralsChapter SummaryChapter Review ExercisesChapter TestExtended Technology Application–Minimizing Employees’ Travel Time in a Building  Cumulative Review  Appendix A: Review of Basic AlgebraAppendix B: Regression and Microsoft ExcelTable A: Areas for a Standard Normal Distribution  AnswersIndex of ApplicationsIndexAdditional Instructor’s Answers  Calculus and Its Applications: Expanded Version (ISBN: 978-0-321-83820-9) contains these additional chapters:7. Trigonometric Functions8. Differential Equations9. Sequences and Series10. Probability Distributions