Calculus for Business, Economics, Life Sciences and Social Sciences

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 received his B.S. from Shippensburg StateCollege 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 currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science.  Dr. Ziegler has published over a dozen research articles in complex analysis and has co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.  Karl E. Byleen received the 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.  Why We wrote This Book: This text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible.  We emphasize computational skills, ideas, and problem solving rather than mathematical theory.  Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept.  General concepts and results are usually presented only after particular cases have been discussed.  Graphing calculators and computers are playing an increasing role in mathematics education and in real-world applications of mathematics.  This books deals with the mathematics that is required to use modern technology effectively as an OPTIONAL feature.  In appropriate places in the text, there are clearly identified examples and exercises related to graphing calculators and computers, illustrations of applications of spreadsheets, and sample computer output. All of these may be omitted without loss of continuity.

PART 1 A LIBRARY OF ELEMENTARY FUNCTIONS

 

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

 

2 Functions and Graphs

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Exponential Functions

2-5 Logarithmic Functions

Chapter 2 Review

Review Exercise

 

PART 2 CALCULUS

 

3 Limits and the Derivative

3-1 Introduction to Limits

3-2 Continuity

3-3 Infinite Limits and Limits at Infinity

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

 

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

 

5 Graphing and Optimization

5-1 First Derivative and Graphs

5-2 Second Derivative and Graphs

5-3 L’Hôpital’s Rule

5-4 Curve-Sketching Techniques

5-5 Absolute Maxima and Minima

5-6 Optimization

Chapter 5 Review

Review Exercise

 

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

 

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

 

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

 

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

 

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

 

B Special Topics

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 Binomial Theorem

 

C Tables

Table I Basic Geometric Formulas

Table II Integration Formulas

 

Answers

Index

Applications Index

A Library of Elementary Functions