Mathematics with Applications

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.  

Chapter 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

Chapter 1 Summary

Chapter 1 Review Exercises

Case Study 1: Consumers Often Defy Common Sense

 

Chapter 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

Chapter 2 Summary

Chapter 2 Review Exercises

Case Study 2: Using Extrapolation to Predict Life Expectancy

 

Chapter 3: Functions and Graphs

3.1 Functions

3.2 Graphs of Functions

3.3 Applications of Linear Functions

3.4 Quadratic Functions

3.5 Applications of Quadratic Functions

3.6 Polynomial Functions

3.7 Rational Functions

Chapter 3 Summary

Chapter 3 Review Exercises

Case Study 3: Architectural Arches

 

Chapter 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

Chapter 4 Summary

Chapter 4 Review Exercises

Case Study 4: Characteristics of the Monkeyface Prickleback

 

Chapter 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

Chapter 5 Summary

Chapter 5 Review Exercises

Case Study 5: Continuous Compounding

 

Chapter 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

Chapter 6 Summary

Chapter 6 Review Exercises

Case Study 6: Matrix Operations and Airline Route Maps

 

Chapter 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

Chapter 7 Summary

Chapter 7 Review Exercises

Case Study 7: Cooking with Linear Programming

 

Chapter 8: Sets and Probability

8.1 Sets

8.2 Applications of Venn Diagrams

8.3 Introduction to Probability

8.4 Basic Concepts of Probability

8.5 Conditional Probability and Independent Events

8.6 Bayes’ Formula

Chapter 8 Summary

Chapter 8 Review Exercises

Case Study 8: Medical Diagnosis

 

Chapter 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

Chapter 9 Summary

Chapter 9 Review Exercises

Case Study 9: QuickDraw® from the New York State Lottery

 

Chapter 10: Introduction to Statistics

10.1 Frequency Distributions

10.2 Measures of Central Tendency

10.3 Measures of Variation

10.4 Normal Distributions

10.5 Normal Approximation to the Binomial Distribution

Chapter 10 Summary

Chapter 10 Review Exercises

Case Study 10: Statistics in the Law–The Castañeda Decision

 

Chapter 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

Chapter 11 Summary

Chapter 11 Review Exercises

Case Study 11: Price Elasticity of Demand

 

Chapter 12: Applications of the Derivative

12.1 Derivatives and Graphs

12.2 The Second Derivative

12.3 Optimization Applications

12.4 Curve Sketching

Chapter 12 Summary

Chapter 12 Review Exercises

Case Study 12: A Total Cost Model for a Training Program

 

Chapter 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

13.7 Differential Equations

Chapter 13 Summary

Chapter 13 Review Exercises

Case Study 13: Bounded Population Growth

 

Chapter 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

Chapter 14 Summary

Chapter 14 Review Exercises

Case Study 14: Global Warming and the Method of Least Squares

 

Appendixes

Appendix A: Graphing Calculators

Appendix B: Tables

    Table 1: Formulas from Geometry

    Table 2: Areas under the Normal Curve

    Table 3: Integrals

 

Answers to Selected Exercises

Index of Applications

Index