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# Calculus for Business, Economics, Life Sciences and Social Sciences

**by**Barnett, Raymond A.; Ziegler, Michael R.; Byleen, Karl E.

### 9780321613998

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## Summary

## Author Biography

**Raymond A. Barnett,** a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern University; Charles Burke, City College of San Francisco; John Fuji, Merritt College; and Karl Byleen, Marquette University.

**Michael R. Ziegler** (late) received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.

**Karl E. Byleen** received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.

## Table of Contents

**Part One: A Library of Elementary Functions**

**Chapter 1: Linear Equations and Graphs**

1-1 Linear Equations and Inequalities

1-2 Graphs and Lines

1-3 Linear Regression

Chapter 1 Review

Review Exercise

**Chapter 2: Functions and Graphs**

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Polynomial and Rational Functions

2-5 Exponential Functions

2-6 Logarithmic Functions

Chapter 2 Review

Review Exercise

**Part Two: Calculus**

**Chapter 3: Limits and the Derivative**

3-1 Introduction to Limits

3-2 Infinite Limits and Limits at Infinity

3-3 Continuity

3-4 The Derivative

3-5 Basic Differentiation Properties

3-6 Differentials

3-7 Marginal Analysis in Business and Economics

Chapter 3 Review

Review Exercise

**Chapter 4: Additional Derivative Topics**

4-1 The Constant e and Continuous Compound Interest

4-2 Derivatives of Exponential and Logarithmic Functions

4-3 Derivatives of Products and Quotients

4-4 The Chain Rule

4-5 Implicit Differentiation

4-6 Related Rates

4-7 Elasticity of Demand

Chapter 4 Review

Review Exercise

**Chapter 5: Graphing and Optimization**

5-1 First Derivative and Graphs

5-2 Second Derivative and Graphs

5-3 L'Hopital's Rule

5-4 Curve Sketching Techniques

5-5 Absolute Maxima and Minima

5-6 Optimization

Chapter 5 Review

Review Exercise

**Chapter 6: Integration**

6-1 Antiderivatives and Indefinite Integrals

6-2 Integration by Substitution

6-3 Differential Equations; Growth and Decay

6-4 The Definite Integral

6-5 The Fundamental Theorem of Calculus

Chapter 6 Review

Review Exercise

**Chapter 7: Additional Integration Topics**

7-1 Area Between Curves

7-2 Applications in Business and Economics

7-3 Integration by Parts

7-4 Integration Using Tables

Chapter 7 Review

Review Exercise

**Chapter 8: Multivariable Calculus**

8-1 Functions of Several Variables

8-2 Partial Derivatives

8-3 Maxima and Minima

8-4 Maxima and Minima Using Lagrange Multipliers

8-5 Method of Least Squares

8-6 Double Integrals Over Rectangular Regions

8-7 Double Integrals Over More General Regions

Chapter 8 Review

Review Exercise

**Chapter 9: Trigonometric Functions**

9-1 Trigonometric Functions Review

9-2 Derivatives of Trigonometric Functions

9-3 Integration of Trigonometric Functions

Chapter 9 Review

Review Exercise

**Appendixes**

** **

**Appendix A: Basic Algebra Review **

Self-Test on Basic Algebra

A-1 Algebra and Real Numbers

A-2 Operations on Polynomials

A-3 Factoring Polynomials

A-4 Operations on Rational Expressions

A-5 Integer Exponents and Scientific Notation

A-6 Rational Exponents and Radicals

A-7 Quadratic Equations

**Appendix B: Special Topics**

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 Binomial Theorem

** **

**Appendix C: Tables**

Table I Basic Geometric Formulas

Table II Integration Formulas

**Answers**

**Index**

**Applications Index**

**A Library of Elementary Functions**