Calculus and Its Applications

by Bittinger, Marvin L.; Ellenbogen, David J.

• ISBN13: 9780321395344
• ISBN10: 0321395344
• Edition: 9th
• Format: Hardcover
• Copyright: 2007-02-15
• Publisher: Pearson

Summary

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

Differentiation

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

Integration

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

Probability: Expected Value The Normal Distribution

Volume

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

Tables

Integration Formulas

Areas for a Standard Normal Distribution

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