Mathematics with Applications

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**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 (R) 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 Castaneda 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**

**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.

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