Mathematics with Applications In the Management, Natural, and Social Sciences

About our authors The late Marge Lial  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 found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led 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.  The late Thomas W. Hungerford received his Bachelor's degree from Holy Cross and his PhD from the University of Chicago. He taught for many years at the University of Washington (Seattle) before moving to Cleveland State University in 1980 and then to St. Louis University to in 2003. He wrote 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 Pearson. He passionately promoted the effective use of technology in mathematics instruction. Dr. Hungerford was also a referee and reviewer for various mathematical journals and 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 PhD 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 PhD from the University of Iowa. She is currently professor of mathematics at Birmingham-Southern College (BSC) 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 4 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.

Prerequisite Skills Test
Calculus Readiness Test
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. Energy Efficiency and Long-Term Cost Savings

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. Maximizing Profit

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. Investing in Stocks and Using the Rule of 72

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. 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 and Boxplots
10.4 Normal Distributions
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 of Demand

12. Applications of the Derivative

12.1 Local Extrema
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 Integration by Parts
13.4 Area and the Definite Integral
13.5 The Fundamental Theorem of Calculus
13.6 Applications of Integrals
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

A. Areas under the Normal Curve
B. Solutions to Prerequisite Skills Test and Calculus Readiness Test
C. Table of Integrals

Answers to Selected Exercises Index of Companies, Products, and Agencies Index of Applications Subject Index Photo Credits Reference Endpapers:

Algebra Review
Geometric Formulas
Finite Math Review
Calculus Review