Synopses & Reviews
Calculus and Its Applications has, for years, been a best-selling text for one simple reason: it anticipates, then meets the needs of today's applied calculus student. Knowing that calculus is a course in which students typically struggle--both with algebra skills and visualizing new calculus concepts--Bittinger and Ellenbogen speak to students in a way they understand, taking great pains to provide clear and careful explanations. Since most students taking this course will go on to careers in the business world, large quantities of real data, especially as they apply to business, are included as well.
About the Author
Marvin Bittinger For over thirty-eight years, Professor Marvin L. Bittinger has been teaching math at the university level. 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 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 co-founder 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.
Table of Contents
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Each chapter concludes with a Summary and Review, and a Chapter Test.)
1. Functions, Graphs, and Models.
Graphs and Equations.
Functions and Models.
Finding Domain and Range.
Slope and Linear Functions.
Other Functions and Models.
Mathematical Modeling and Curve Fitting.
Extended Technology Application: The Ecological Effect of Global Warming.
2. Differentiation.
Limits and Continuity: Numerically and Graphically.
Limits: Algebraically.
Average Rates of Change.
Differentiation Using Limits of Difference Quotients.
Differentiation Techniques: The Power and Sum-Difference Rules.
Instantaneous Rates of Change.
Differentiation Techniques: The Product and Quotient Rules.
The Chain Rule.
Higher-Order Derivatives.
Extended Technology Application: Path of a Baseball: The Tale of the Tape.
3. Applications of Differentiation.
Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs.
Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs.
Graph Sketching: Asymptotes and Rational Functions.
Using Derivatives to Find Absolute Maximum and Minimum Values.
Maximum-Minimum Problems: Business and Economic Applications.
Differentials.
Implicit Differentiation and Related Rates.
Extended Technology Application: Maximum Sustainable Harvest.
4. Exponential and Logarithmic Functions.
Exponential Functions.
Logarithmic Functions.
Applications: The Uninhibited Growth Model, dP/dt = kP.
Applications: Decay.
The Derivatives of a x and logax.
An Economics Application: Elasticity of Demand.
Extended Technology Application: The Business of Motion Picture Box-Office Revenue.
5. Integration.
Integration.
Area and Definite Integrals.
Limits of Sums and Accumulations.
Properties of Definite Integrals.
Integration Techniques: Substitution.
Integration Techniques: Integration by Parts.
Integration Techniques: Tables.
Extended Technology Application: Financial Predictions for Sherwin-Williams, Intel, DeBrand, and the Gap.
6. Applications of Integration.
An Economics Application: Consumer's Surplus and Producer's Surplus.
Applications of the Models and .
Improper Integrals.
Probability.
Probability: Expected Value; The Normal Distribution.
Volume.
Differential Equations.
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda.
7. Functions of Several Variables.
Functions of Several Variables.
Partial Derivatives.
Higher-Order Partial Derivatives.
Maximum-Minimum Problems.
An Application: The Least-Squares Technique.
Constrained Maximum and Minimum Values: Lagrange Multipliers.
Multiple Integration.
Extended Technology Application: Minimizing Employees' Travel Time in a Building.
Cumulative Review.
Appendix: Review of Basic Algebra.
Tables.
Integration Formulas.
Areas for a Standard Normal Distribution.
Answers.
Index.