This book presents the content and applications in an accessible manner while maintaining an appropriate level of rigor. The authors proceed from familiar material to new, and from concrete examples to general rules and formulas. This edition retains its focus on real-world problem solving, but has been refreshed with a wealth of new data in the examples and exercises–39% of the 623 examples are new or revised, and 28% of the 5,288 exercises are new or revised.
Marge Lial has always been 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, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced 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 taught for five years at Youngstown State University prior to arriving at Cleveland State University in Fall 2000. He is an associate professor and frequently collaborates 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.
Index of Applications.
To the Student.
1. Fundamentals of Algebra.
The Real Numbers/
Exponents and Radicals.
Case 1: Consumers Often Defy Common Sense.
2. Graphs, Equations, and Inequalities.
Slope and the Equations of a Line.
Applications of Linear Equations.
Polynomial and Rational Inequalities.
Case 2: Depreciation.
3. Functions and Graphs.
Graphs of Functions.
Applications of Linear Functions.
Case 3: Marginal Cost--Booz, Allen and Hamilton.
4. Polynomial And Rational Functions.
Applications of Quadratic Functions.
Case 4: Error-Correcting Codes.
5. Exponential and Logarithmic Functions.
Applications of Exponential Functions.
Applications of Logarithmic Functions.
Case 5: Characteristics of the Monkeyface Prickleback.
6. Mathematics of Finance.
Simple Interest and Discount.
Present Value of an Annuity: Amortization.
Applying Financial Formulas.
Case 6: Time, Money, and Polynomials.
7. Systems of Linear Equations and Matrices.
Systems of Linear Equations.
The Gauss-Jordan Method.
Basic Matrix Operations.
Matrix Products and Inverses.
Case 7: Leontief's Model of the American Economy.
8. Linear Programming.
Graphing Linear Inequalities in Two Variables.
Linear Programming: The Graphical Method.
Applications of Linear Programming.
The Simplex Method: Maximization.
The Simplex Method: Duality and Minimization.
The Simplex Method: Nonstandard Problems.
Case 8: A Minimum Cost Balanced Organic Fertilizer Mix.
9. Sets and Probability.
Applications of Venn Diagrams.
Basic Concepts of Probability.
Conditional Probability; Independent Events.
Case 9: Medical Diagnosis.
10. Further Topics in Probability.
Permutations and Combinations.
Applications of Counting.
Probability Distributions; Expected Value.
Case 10: Optimal Inventory for a Service Truck.
11. Introduction to Statistics.
Frequency Distributions; Measures of Central Tendency.
Measures of Variation.
Case 11: Statistical Process Control.
12. Differential Calculus.
Rates of Change.
Tangent Lines and Derivatives.
Techniques for Finding Derivatives.
Derivatives of Products and Quotients.
The Chain Rule.
Derivatives of Exponential and Logarithmic Functions.
Continuity and Differentiability.
Case 12: Price Elasticity of Demand.
13. Applications of the Derivative.
Derivatives and Graphs.
The Second Derivative.
Curve Sketching (Optional).
Case 13: A Total Cost Model for a Training Program.
14. Integral Calculus.
Integration by Substitution.
Area and the Definite Integral.
The Fundamental Theorem of Calculus.
Applications of Integrals.
Tables of Integrals (Optional).
Case 14: Estimating Depletion Dates for Minerals.
15. Multivariate Calculus.
Functions of Several Variables.
Extrema of Functions of Several Variables.
A: Graphing Calculators.
Part 1: Introduction.
Part 2: Program Appendix.
Answers to Selected Exercises.
Index of Applications.