# College Mathematics for Business, Economics, Life Sciences and Social Sciences

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

### 9780321614001

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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: Finite Mathematics**

**Chapter 3: Mathematics of Finance**

3-1 Simple Interest

3-2 Compound and Continuous Compound Interest

3-3 Future Value of an Annuity; Sinking Funds

3-4 Present Value of an Annuity; Amortization

Chapter 3 Review

Review Exercise

**Chapter 4: Systems of Linear Equations; Matrices**

4-1 Review: Systems of Linear Equations in Two Variables

4-2 Systems of Linear Equations and Augmented Matrices

4-3 Gauss-Jordan Elimination

4-4 Matrices: Basic Operations

4-5 Inverse of a Square Matrix

4-6 Matrix Equations and Systems of Linear Equations

4-7 Leontief Input-Output Analysis

Chapter 4 Review

Review Exercise

**Chapter 5: Linear Inequalities and Linear Programming**

5-1 Inequalities in Two Variables

5-2 Systems of Linear Inequalities in Two Variables

5-3 Linear Programming in Two Dimensions: A Geometric Approach

Chapter 5 Review

Review Exercise

**Chapter 6: Linear Programming: Simplex Method**

6-1 A Geometric Introduction to the Simplex Method

6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≥

6-3 The Dual; Minimization with Problem Constraints of the form ≥

6-4 Maximization and Minimization with Mixed Problem Constraints

Chapter 6 Review

Review Exercise

** **

**Chapter 7: Logic, Sets, and Counting**

7-1 Logic

7-2 Sets

7-3 Basic Counting Principles

7-4 Permutations and Combinations

Chapter 7 Review

Review Exercise

**Chapter 8: Probability**

8-1 Sample Spaces, Events, and Probability

8-2 Union, Intersection, and Complement of Events; Odds

8-3 Conditional Probability, Intersection, and Independence

8-4 Bayes' Formula

8-5 Random Variables, Probability Distribution, and Expected Value

Chapter 8 Review

Review Exercise

**Chapter 9: Markov Chains**

9-1 Properties of Markov Chains

9-2 Regular Markov Chains

9-3 Absorbing Markov Chains

Chapter 9 Review

Review Exercise

**Part Three: Calculus**

**Chapter 10: Limits and the Derivative**

10-1 Introduction to Limits

10-2 Infinite Limits and Limits at Infinity

10-3 Continuity

10-4 The Derivative

10-5 Basic Differentiation Properties

10-6 Differentials

10-7 Marginal Analysis in Business and Economics

Chapter 10 Review

Review Exercise

**Chapter 11: Additional Derivative Topics**

11-1 The Constant e and Continuous Compound Interest

11-2 Derivatives of Logarithmic and Exponential Functions

11-3 Derivatives of Products and Quotients

11-4 The Chain Rule

11-4 Implicit Differentiation

11-5 Related Rates

11-7 Elasticity of Demand

Chapter 11 Review

Review Exercise

**Chapter 12: Graphing and Optimization**

12-1 First Derivative and Graphs

12-2 Second Derivative and Graphs

12-3 L'Hopitals's Rule

12-4 Curve Sketching Techniques

12-5 Absolute Maxima and Minima

12-6 Optimization

Chapter 12 Review

Review Exercise

**Chapter 13: Integration**

13-1 Antiderivatives and Indefinite Integrals

13-2 Integration by Substitution

13-3 Differential Equations; Growth and Decay

13-4 The Definite Integral

13-5 The Fundamental Theorem of Calculus

Chapter 13 Review

Review Exercise

**Chapter 14: Additional Integration Topics**

14-1 Area Between Curves

14-2 Applications in Business and Economics

14-3 Integration by Parts

14-4 Integration Using Tables

Chapter 14 Review

Review Exercise

**Chapter 15: Multivariable Calculus**

15-1 Functions of Several Variables

15-2 Partial Derivatives

15-3 Maxima and Minima

15-4 Maxima and Minima Using Lagrange Multipliers

15-5 Method of Least Squares

15-6 Double Integrals Over Rectangular Regions

15-7 Double Integrals Over More General Regions

Chapter 15 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 Area Under the Standard Normal Curve

Table II Basic Geometric Formulas

**Answers**

**Index**

**Applications Index**

**A Library of Elementary Functions**