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

About our authors 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 4 years. Raymond Barnett has authored or co-authored 18 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. The late Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing postdoctoral 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 11 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 J. 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 8 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