Calculus and Its Applications

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  • Edition: 9th
  • Format: Hardcover
  • Copyright: 2/15/2007
  • Publisher: Pearson
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Calculus and Its Applicationshas, 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.

Author Biography

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

Functions, Graphs, and Models
Graphs and Equations
Functions and Models
Finding Domain and Range
Slope and Linear Functions
Nonlinear Functions and Models
Mathematical Modeling and Curve Fitting
Extended Technology Application: Payrolls of Professional Basketball Teams
Limits: A Numerical and Graphical Approach
Algebraic Limits and Continuity
Average Rates of Change
Differentiation Using Limits of Difference Quotients
Differentiation Techniques: The Power and Sum-Difference Rules
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
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 Economics Applications
Marginals and Differentials
Implicit Differentiation and Related Rates
Extended Technology Application: Maximum Sustainable Harvest
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
The Area Under a Graph
Area, Antiderivatives, and Integrals
Area and Definite Integrals
Properties of Definite Integrals
Integration Techniques: Substitution
Integration Techniques: Integration by Parts
Integration Techniques: Tables
Extended Technology Application: Financial Predictions for Starbucks, Lowes, The Gap, and Intel
Applications of Integration
An Economics Application: Consumer Surplus and Producer Surplus
Applications of the Models
Improper Integrals
Probability: Expected Value The Normal Distribution
Differential Equations
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda
Functions of Several Variables
Functions of Several Variables
Partial Derivatives
Maximum-Minimum Problems
An Application: The Least-Squares Technique
Constrained Maximum and Minimum Values: Lagrange Multipliers
Double Integrals
Extended Technology Application: Minimizing Employees' Travel Time in a Building
Cumulative Review
Review of Basic Algebra
Integration Formulas
Areas for a Standard Normal Distribution
Table of Contents provided by Publisher. All Rights Reserved.

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