Mathematics with Applications In the Management, Natural and Social Sciences

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received bachelor's and master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often find their way into her books as applications, exercise sets, and feature sets. Her interest in archeology lead to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.   Thomas W. Hungerford received his bachelor’s degree from Holy Cross and his Ph.D. from the University of Chicago. He taught for many years at the University of Washington (Seattle) before moving to Cleveland State University in 1980. He has been at St. Louis University since 2003. He has written a number of research articles in algebra and several in mathematics education. Dr. Hungerford is the author or coauthor of more than a dozen mathematics textbooks, ranging from high school to graduate level, several of which are published by Addison-Wesley. He is active in promoting the effective use of technology in mathematics instruction. Dr. Hungerford has also been a referee and reviewer for various mathematical journals and has served on National Science Foundation panels for selecting grant recipients.   John P. Holcomb, Jr. received his bachelor's degree from St. Bonaventure University and his Ph.D. from the University at Albany, State University of New York. He is professor and chair and frequently publishes with researchers in a variety of disciplines where he provides statistical analysis. Dr. Holcomb has also authored several papers in statistical education and is very active in the American Statistical Association and the Mathematical Association of America. He was named a Carnegie Scholar in 2000 by the Carnegie Foundation for the Advancement of Teaching and Learning and in 2003 received the Waller Award from the American Statistical Association for outstanding teaching of introductory statistics.    Bernadette Mullins received her bachelor’s degree from Western Illinois University and her Ph.D. from the University of Iowa. She is currently professor of mathematics at Birmingham-Southern College in Birmingham, Alabama, where she arrived in 2000. She has published numerous articles in the fields of commutative ring theory and mathematics education. She has served as co-investigator for several National Science Foundation grants related to improving mathematics education. Dr. Mullins has won four awards for her excellence in teaching, including the Bob Whetstone award at BSC. Throughout her career, she has been active in Project NExT (New Experiences in Teaching) and the Mathematical Association of America, and was elected Alabama State Director of the MAA in 2013.

1. Algebra and Equations

1.1 The Real Numbers

1.2 Polynomials

1.3 Factoring

1.4 Rational Expressions

1.5 Exponents and Radicals

1.6 First-Degree Equations

1.7 Quadratic Equations

            Summary and Review

            Case Study 1 Consumers Often Need to Just Do the Math

 

2. Graphs, Lines, and Inequalities

2.1 Graphs

2.2 Equations of Lines

2.3 Linear Models

2.4 Linear Inequalities

2.5 Polynomial and Rational Inequalities

            Summary and Review

            Case Study 2 Using Extrapolation and Interpolation for Prediction

 

3. Functions and Graphs

3.1 Functions

3.2 Graphs of Functions

3.3 Applications of Linear Functions

3.4 Quadratic Functions and Applications

3.5 Polynomial Functions

3.6 Rational Functions

            Summary and Review

            Case Study 3 Architectural Arches

 

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Applications of Exponential Functions

4.3 Logarithmic Functions

4.4 Logarithmic and Exponential Equations

            Summary and Review

            Case Study 4 Gapminder.org

 

5. Mathematics of Finance

5.1 Simple Interest and Discount

5.2 Compound Interest

5.3 Annuities, Future Value, and Sinking Funds

5.4 Annuities, Present Value, and Amortization

            Summary and Review

            Case Study 5 Continuous Compounding

 

6. Systems of Linear Equations and Matrices

6.1 Systems of Two Linear Equations in Two Variables

6.2 Larger Systems of Linear Equations

6.3 Applications of Systems of Linear Equations

6.4 Basic Matrix Operations

6.5 Matrix Products and Inverses

6.6 Applications of Matrices

            Summary and Review

            Case Study 6 Matrix Operations and Airline Route Maps

 

7. Linear Programming

7.1 Graphing Linear Inequalities in two Variables

7.2 Linear Programming: The Graphical Method

7.3 Applications of Linear Programming

7.4 The Simplex Method: Maximization

7.5 Maximization Applications

7.6 The Simplex Method: Duality and Minimization

7.7 The Simplex Method: Nonstandard Problems

            Summary and Review

            Case Study 7 Cooking with Linear Programming

 

8. Sets and Probability

8.1 Sets

8.2 Applications of Venn Diagrams and Contingency Tables

8.3 Introduction to Probability

8.4 Basic Concepts of Probability

8.5 Conditional Probability and Independent Events

8.6 Bayes' Formula

            Summary and Review

            Case Study 8 Medical Diagnosis

 

9. Counting, Probability Distributions, and Further Topics in Probability

9.1 Probability Distributions and Expected Value

9.2 The Multiplication Principle, Permutations, and Combinations

9.3 Applications of Counting

9.4 Binomial Probability

9.5 Markov Chains

9.6 Decision Making

            Summary and Review

            Case Study 9 Quick Draw®from the New York State Lottery

 

10. Introduction to Statistics

10.1 Frequency Distributions

10.2 Measures of Center

10.3 Measures of Variation

10.4 Normal Distributions and Boxplots

10.5 Normal Approximation to the Binomial Distribution

            Summary and Review

            Case Study 10 Standard Deviation as a Measure of Risk

 

11. Differential Calculus

11.1 Limits

11.2 One-sided Limits and Limits Involving Infinity

11.3 Rates of Change

11.4 Tangent Lines and Derivatives

11.5 Techniques for Finding Derivatives

11.6 Derivatives of Products and Quotients

11.7 The Chain Rule

11.8 Derivatives of Exponential and Logarithmic Functions

11.9 Continuity and Differentiability

            Summary and Review

            Case Study 11 Price Elasticity

 

12. Applications of the Derivative

12.1 Derivatives and Graphs

12.2 The Second Derivative

12.3 Optimization Applications

12.4 Implicit Differentiation

12.5 Related Rates

12.6 Curve Sketching

            Summary and Review

            Case Study 12 A Total Cost Model for a Training Program

 

13. Integral Calculus

13.1 Antiderivatives

13.2 Integration by Substitution

13.3 Area and the Definite Integral

13.4 The Fundamental Theorem of Calculus

13.5 Applications of Integrals

13.6 Tables of Integrals (Optional)

13.7 Differential Equations

            Summary and Review

            Case Study 13 Bounded Population Growth

 

14. Multivariate Calculus

14.1 Functions of Several Variables

14.2 Partial Derivatives

14.3 Extrema of Functions of Several Variables

14.4 Lagrange Multipliers

            Summary and Review

            Case Study 14 Global Warming and the Method of Least Squares

 

Appendices

Appendix A. Graphing Calculators

Appendix B: Tables

            Table 1: Formulas from Geometry

            Table 2: Areas under the Normal Curve

            Table 3: Integrals

Appendix C. Learning Objectives

Appendix D. Solutions to Prerequisite Skills Tests

 

Answers to Selected Exercises

Index of Companies, Products, and Agencies

Index of Applications

Subject Index