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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.

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.

Christopher Stocker received his B.S. in mathematics and computer science from St. John’s University in Minnesota and his M.A. and Ph.D. degrees in mathematics from the University of Illinois in Urbana-Champaign.  He is currently an Adjunct Assistant Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University.  He has published eight research articles in the areas of graph theory and combinatorics.

I. 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 Summary and Review

Review Exercises

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 Summary and Review 

Review Exercises 

II. FINITE MATHEMATICS

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 Summary and Review 

Review Exercises

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 Summary and Review 

Review Exercises 

5. Linear Inequalities and Linear Programming 

5.1 Linear 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 Summary and Review 

Review Exercises

6. Linear Programming: The Simplex Method

6.1 The Table Method: An Introduction to the Simplex Method

6.2 The Simplex Method: Maximization with Problem Constraints of the Form ≤ 

6.3 The Dual Problem: Minimization with Problem Constraints of the Form ≥ 

6.4 Maximization and Minimization with Mixed Problem Constraints 

Chapter 6 Summary and Review 

Review Exercises 

7. Logic, Sets, and Counting 

7.1 Logic

7.2 Sets 

7.3 Basic Counting Principles 

7.4 Permutations and Combinations 

Chapter 7 Summary and Review 

Review Exercises

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 Variable, Probability Distribution, and Expected Value 

Chapter 8 Summary and Review 

Review Exercises 

III. CALCULUS

9. Limits and the Derivative

9.1 Introduction to Limits 

9.2 Infinite Limits and Limits at Infinity 

9.3 Continuity 

9.4 The Derivative 

9.5 Basic Differentiation Properties 

9.6 Differentials 

9.7 Marginal Analysis in Business and Economics 

Chapter 9 Summary and Review

Review Exercises 

10. Additional Derivative Topics 

10.1 The Constant e and Continuous Compound Interest 

10.2 Derivatives of Exponential and Logarithmic Functions 

10.3 Derivatives of Products and Quotients 

10.4 The Chain Rule 

10.5 Implicit Differentiation 

10.6 Related Rates

10.7 Elasticity of Demand 

Chapter 10 Summary and Review 

Review Exercises 

11. Graphing and Optimization

11.1 First Derivative and Graphs

11.2 Second Derivative and Graphs

11.3 L’Hôpital’s Rule 

11.4 Curve-Sketching Techniques 

11.5 Absolute Maxima and Minima 

11.6 Optimization 

Chapter 11 Summary and Review 

Review Exercises 

12. Integration 

12.1 Antiderivatives and Indefinite Integrals 

12.2 Integration by Substitution

12.3 Differential Equations; Growth and Decay

12.4 The Definite Integral 

12.5 The Fundamental Theorem of Calculus 

Chapter 12 Summary and Review

Review Exercises 

13. Additional Integration Topics

13.1 Area Between Curves

13.2 Applications in Business and Economics 

13.3 Integration by Parts 

13.4 Other Integration Methods 

Chapter 13 Summary and Review 

Review Exercises 

14. Multivariable Calculus

14.1 Functions of Several Variables 

14.2 Partial Derivatives 

14.3 Maxima and Minima 

14.4 Maxima and Minima Using Lagrange Multipliers

14.5 Method of Least Squares 

14.6 Double Integrals over Rectangular Regions 

14.7 Double Integrals over More General Regions 

Chapter 14 Summary and Review 

Review Exercises  

15. Markov Chains (online at goo.gl/8SZkyn ) 

15.1 Properties of Markov Chains 

15.2 Regular Markov Chains 

15.3 Absorbing Markov Chains 

Chapter 15 Summary and Review

Review Exercises 

Appendix A: Basic Algebra Review 

A.1 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 (online at goo.gl/mjbXrG)  

B.1 Sequences, Series, and Summation Notation 

B.2 Arithmetic and Geometric Sequences

B.3 Binomial Theorem 

B.4 Interpolating Polynomials and Divided Differences

Appendix C: Tables 

Table I Integration Formulas

Table II Area under the Standard Normal Curve 

Answers

Index

Index of Applications 

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