Finite Mathematics and Applied Calculus,
8th Edition

0. PRECALCULUS REVIEW.
Real Numbers. Exponents and Radicals. Using Exponent Identities. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane. Logarithms.
1. FUNCTIONS AND APPLICATIONS.
Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression.
2. NONLINEAR FUNCTIONS AND MODELS.
Quadratic Functions and Models. Exponential Functions and Models. The Number e and Exponential Growth and Decay. Logistic and Logarithmic Functions and Models.
3. THE MATHEMATICS OF FINANCE.
Simple Interest. Compound Interest. Annuities, Loans, and Bonds.
4. SYSTEMS OF LINEAR EQUATIONS AND MATRICES.
Systems of Two Linear Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations.
5. MATRIX ALGEBRA AND APPLICATIONS.
Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Game Theory. Input-Output Models.
6. LINEAR PROGRAMMING.
Graphing Linear Inequalities. Solving Linear Programming Problems Graphically. The Simplex Method: Solving Standard Maximization Problems. The Simplex Method: Solving General Linear Programming Problems. The Simplex Method and Duality.
7. SETS AND COUNTING.
Set Operations. Cardinality. Decision Algorithms: The Addition and Multiplication Principles. Permutations and Combinations.
8. PROBABILITY.
Sample Spaces and Events. Relative Frequency. Probability and Probability Models. Probability and Counting Techniques. Conditional Probability and Independence. Bayes' Theorem and Applications. Markov Systems.
9. RANDOM VARIABLES AND STATISTICS.
Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions.
10. INTRODUCTION TO THE DERIVATIVE.
Limits: Numerical and Graphical Viewpoints. Limits: Algebraic Viewpoint. Limits and Continuity. Average Rate of Change. The Derivative: Numerical and Graphical Viewpoints. The Derivative: Algebraic Viewpoint.
11. TECHNIQUES OF DIFFERENTIATION.
Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation.
12. APPLICATIONS OF THE DERIVATIVE.
Maxima and Minima. Applications of Maxima and Minima. Higher Order Derivatives: Acceleration and Concavity. Analyzing Graphs. Related Rates. Elasticity.
13. THE INTEGRAL.
The Indefinite Integral. Substitution. The Definite Integral. The Fundamental Theorem of Calculus.
14. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL.
Integration by Parts. Area Between Two Curves. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications.
15. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications.
16. TRIGONOMETRIC MODELS.
Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications.

• Stefan Waner

  Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching.

• Steven Costenoble

  Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching.

• UPDATED, UNSURPASSED EXAMPLES AND EXERCISES HIGHLIGHT REAL, RELEVANT DATA. Many exercises at all difficulty levels integrate data on relatable topics. Updated applications discuss the rapid rise of cryptocurrencies and the unanticipated global COVID pandemic, while others focus on instantly recognizable corporations or network technology students constantly use. Exercises spotlight notable historic events like the 1990s Dot Com boom, the 2005-2006 real estate bubble and resulting economic crisis, the 2010 stock market "flash crash," and the SARS and Ebola outbreaks of 2003 and 2014.

• NEW INTERACTIVE ONLINE LEARNING RESOURCES IN WEBASSIGN AND THE AUTHOR WEBSITE REINFORCE MASTERY. Randomizable, interactive versions of key examples, interactive graphs and other learning tools are available in WebAssign and on the authors' AppliedMathSite.net. Interactive elements in nonrandom mode engage students in class participation. For students experiencing difficulties, adaptive practice sessions within the interactive examples offer help with prerequisites all the way to basic algebra.

• NEW KEY CONCEPTS AND "PRACTICE THIS SKILL" FEATURES GUIDE STUDENT LEARNING. Each section now opens with a brief margin list of topics and skills discussed in that section. Key Concept boxes throughout each chapter contain Quick Examples that highlight and reinforce key topics and skills. In addition, "Practice This Skill" features in the margins and examples in the text correspond with specific exercises that are based on those examples as well as online "Your Turn" interactive exercises. Many of these exercises ask students to revisit the specific examples on which they are based.

• STREAMLINED INTRODUCTORY CHAPTER ON FUNCTIONS AND APPLICATIONS IS NOW MORE FOCUSED. This chapter is more concise and streamlined while discussion of some topics, like carbon dating, now appears in later chapters, where it's more appropriate. This edition's approach to data sets is less complex and the section on mathematical models is significantly more concise and manageable.

• REVISED CHAPTER ON NONLINEAR FUNCTIONS AND MODELS (CH. 2) OFFERS BETTER FLOW OF INFORMATION. The previous section on exponentials is now split into two shorter, more manageable sections. Previous separate sections on logarithms and logistic functions are now combined into one section, allowing a better comparison of the two types of models for long-term trends. In addition, the authors have moved basic material on logarithms that previously appeared in this chapter to this edition's coverage of algebra review for a more cohesive flow.

• UPDATED CASE STUDIES ADDRESS CURRENT TOPICS TO ENGAGE READERS. One new case featuring nonlinear models discusses recent trends in college enrollment, while another case focused on matrix algebra highlights social network analysis. Yet another new case examines techniques of differentiation, applying logistic functions and their derivatives to obtain a surprisingly accurate model of the first three waves of the COVID-19 pandemic in the U.S.

• UPDATED PRECALCULUS REVIEW OFFERS A REVISED, DEDICATED APPROACH TO ASSIST STUDENTS IN MASTERY. This review now includes more information on exponents and radicals as well as an extended discussion of logarithms.

• WEBASSIGN ONLINE COURSE SOLUTION PROVIDES SUPPORT FOR YOU AND YOUR STUDENTS. Fully integrated with this printed edition of the text, WebAssign offers a powerful online learning platform that engages students in learning math. New end-of-chapter exercises and pre-built assignments, vetted by trusted subject matter experts, work with robust content, questions and online testing to help you foster a deeper understanding of course concepts. Many of the online tools available in the authors' website are also accessible in WebAssign.

• PROVEN AUTHOR WEBSITE OFFERS POWERFUL INSTRUCTOR RESOURCES. The authors' website, AppliedMathSite.net -- almost three decades strong -- provides powerful online utilities for the classroom. Tools support everything from graphing and evaluating functions and matrix operations to solving linear programming problems both graphically and with the simplex method. Use interactive and game tutorials to encourage class participation. Learning and practice modules with built-in, adaptive practice are also available. An online interactive text and exercises explore topics beyond the printed book.

• INNOVATIVE PEDAGOGY APPEALS TO STUDENTS. Learning features such as Question-and-Answer Dialogues, End-of-Section FAQs and "Before We Go On" engage learners. Informal question-and-answer dialogues anticipate student questions and guide students through new concepts. "Before We Go On" discussions follow most examples and offer a check on the answer, a discussion of the feasibility and significance of a solution or an in-depth look at what the solution means. Quick Examples in the Key Concept boxes include quick, straightforward examples to solidify students' understanding of each new concept.

• MARGIN TECHNOLOGY NOTES AND END-OF-CHAPTER TECHNOLOGY GUIDES PROVIDE LEARNING SUPPORT. Brief marginal technology notes outline the use of graphing calculator, spreadsheet and website technology in appropriate examples. When necessary, notes refer the reader to more detailed discussion in an end-of-chapter Technology Guide. These optional Guides provide detailed instruction on using TI-83/84 Plus and spreadsheets. You can use this material or not, as you prefer. Exercise sets throughout this edition clearly indicate when the use of technology is suggested or required.

• COMMUNICATION AND REASONING EXERCISES STRENGTHEN SKILLS IN WRITING AND DISCUSSION. These exercises, which often have no single correct answer, are designed to broaden students’ grasp of the mathematical concepts and strengthen their modeling skills. Some exercises ask students to provide their own examples to illustrate a point or design an application for a given solution. Exercises also include "fill-in-the-blank," discussion and debate and practice that requires students to identify common errors.

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