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# Calculus and Its Applications

**by**Bittinger, Marvin L.; Ellenbogen, David J.; Surgent, Scott J.

### 9780321694331

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## Summary

## Author Biography

**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.

## Table of Contents

Preface

Diagnostic Test

**R. Functions, Graphs, and Models**

R.1 Graphs and Equations

R.2 Functions and Models

R.3 Finding Domain and Range

R.4 Slope and Linear Functions

R.5 Nonlinear Funtions and Models

R.6 Mathematical Modeling and Curve Fitting

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Average Price of a Movie Ticket

**1. Differentiation**

1.1 Limits: A Numerical and Graphical Approach

1.2 Algebraic Limits and Continuity

1.3 Average Rates of Change

1.4 Differentiation Using Limits of Difference Quotients

1.5 Differentiation Techniques: The Power and Sum-Difference Rules

1.6 Differentiation Techniques: The Product and Quotient Rules

1.7 The Chain Rule

1.8 Higher-Order Derivatives

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Path of a Baseball: The Tale of the Tape

**2. Applications of Differentiation**

2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs

2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs

2.3 Graph Sketching: Asymptotes and Rational Functions

2.4 Using Derivatives to Find Absolute Maximum and Minimum Values

2.5 Maximum-Minimum Problems; Business and Economics Applications

2.6 Marginals and Differentials

2.7 Implicit Differentiation and Related Rates

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Maximum Sustainable Harvest

**3. Exponential and Logarithmic Functions**

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Applications: Uninhibited and Limited Growth Models

3.4 Applications: Decay

3.5 The Derivatives of a^{x} and log_{a} ^{x}

3.6 An Economics Application: Elasticity of Demand

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Business: Motion Picture and DVD Revenue

**4. Integration**

4.1 Antidifferentiation

4.2 Antiderivatives

4.3 Area and Definite Integrals

4.4 Properties of Definite Integrals

4.5 Integration Techniques: Substitution

4.6 Integration Techniques: Integration by Parts

4.7 Integration Techniques: Tables

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Business: Distribution of Wealth

**5. Applications of Integration**

5.1 An Economics Application: Consumer Surplus and Producer Surplus

5.2 Applications of the Integration of Growth and Decay Models

5.3 Improper Integrals

5.4 Probability

5.5 Probability: Expected Value; The Normal Distribution

5.6 Volume

5.7 Differential Equations

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda

**6. Functions of Several Variables**

6.1 Functions of Several Variables

6.2 Partial Derivatives

6.3 Maximum-Minimum Problems

6.4 An Application: The Least-Squares Technique

6.5 Constrained Optimization

6.6 Double Integrals

Chapter Summary

Chapter Review Exercises

Chapter Test

Extended Technology Application: Minimizing Employees' Travel Time in a Building

Cumulative Review

Appendix A: Review of Basic Algebra

Appendix B: Regression and Microsoft Excel

Appendix C: The TI MathPrint Operating System

Tables

Answers

Index of Applications

Index