**This book is ideal for one- or two-semester or two- or three-quarter courses covering topics in college algebra, finite mathematics, and calculus for students in business, economics, and the life and social sciences.**

Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for students to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises–including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize manageability for teachers and learning for students. The table of contents covers a wide range of topics efficiently, enabling instructors to tailor their courses to meet student needs.

**Personalize Learning with Pearson MyLab Math**

MyLab Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them better absorb course material and understand difficult concepts.

## Features

**Personalize Learning with Pearson MyLab Math**

MyLab Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them better absorb course material and understand difficult concepts.

**Pedagogy and Hallmark Features**

**Applications: **An abundance and variety of applications for the intended audience appear throughout the book so that students see frequently how the mathematics they are learning can be used. These applications cover such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology. Many of these applications are drawn from literature and are documented by references, sometimes from the Web. In some, the background and context are given in order to stimulate interest. However, the text is self-contained, in the sense that it assumes no prior exposure to the concepts on which the applications are based. (See, for example, Chapter 15, Section 7, Example 2.)

**Now Work Problem N: **Throughout the text we have retained the popular *Now Work Problem N *feature. The idea is that after a worked example, students are directed toan end of section problem (labeled with a colored exercise number) that reinforces theideas of the worked example. This gives students an opportunity to practice what theyhave just learned. Because the majority of these keyed exercises are odd-numbered, studentscan immediately check their answer in the back of the book to assess their level ofunderstanding. The complete solutions to the odd-numbered exercises can be found inthe Student Solutions Manual.

**Cautions: **Cautionary warnings are presented in very much the same way an instructor would warn students in class of commonly-made errors. These appear in the margin, along with other explanatory notes and emphases.

**Definitions, key concepts, and important rules and formulas: **These are clearly stated and displayed as a way to make the navigation of the book that much easier for the student. (See, for example, the Definition of Derivative in Section 11.1)

**Review material: **Each chapter has a review section that contains a list of important terms and symbols, a chapter summary, and numerous review problems. In addition, key examples are referenced along with each group of important terms and symbols.

**Inequalities and slack variables: **In Section 1.2, when inequalities are introduced we point out that *a *_ *b *is equivalent to “there exists a non-negative number *s *such that *a *C *s *D *b*”. The idea is not deep but the pedagogical point is that *slack variables*, key to implementing the simplex algorithm in Chapter 7, should be familiar and not distract from the rather technical material in linear programming.

**Absolute value: **It is common to note that j*a *¿� *b*j provides the distance from *a *to *b*. In Example 4e of Section 1.4 we point out that “*x *is less than _ units from _” translates as j*x *¿� _j < _. In Section 1.4 this is but an exercise with the notation, as it should be, but the point here is that later (in Chapter 9) _ will be the mean and _ the standard deviation of a random variable. Again we have separated, in advance, a simple idea from a more advanced one. Of course Problem 12 of Problems 1.4, which asks the student to set up j*f*.*x*/ ¿� *L*j < _, has a similar agenda for Chapter 10 on limits.

**Early treatment of summation notation: **This topic is necessary for study of the definite integral in Chapter 14 but it is *useful *long before that. Since it is a notation that is new to most students at this level, but no more than a notation, we get it out of the way in Chapter 1. By using it when convenient, *before coverage of the definite integral*, it is not a distraction from that challenging concept.

**Section 1.6 on sequences: **This section provides several pedagogical advantages. The very definition is stated in a fashion that paves the way for the more important and more basic definition of function in Chapter 2. In summing the terms of a sequence we are able to practice the use of summation notation introduced in the preceding section. The most obvious benefit though is that “sequences” allows us a better organization in the annuities section of Chapter 5. Both the present and the future values of an annuity are obtained by summing (finite) geometric sequences. Later in the text, sequences arise in the definition of the number *e *in Chapter 4, in Markov chains in Chapter 9, and in Newton’s method in Chapter 12, so that a helpful unifying reference is obtained.

**Sum of an infinite sequence: **In the course of summing the terms of a finite sequence, it is natural to raise the possibility of summing the terms of an infinite sequence. This is a nonthreatening environment in which to provide a first foray into the world of limits. We simply explain how certain infinite geometric sequences have well-defined sums and phrase the results in a way that creates a toehold for the introduction of limits in Chapter 10. These particular infinite sums enable us to introduce the idea of a perpetuity, first informally in the sequence section, and then again in more detail in a separate section in Chapter 5.

**Section 2.8, Functions of Several Variables: **The introduction to functions of several variables appears in Chapter 2 because it is a topic that should appear long before Calculus. Once we have done some calculus there are particular ways to use calculus in the study of functions of several variables, but these aspects should not be confused with the basics that we use throughout the book. For example, “a-sub-n-angle-r” and “s-sub-nangle- r” studied in the Mathematics of Finance, Chapter 5, are perfectly good functions of two variables and Linear Programming seeks to optimize linear functions of several variables subject to linear constraints.

**Leontief’s input-output analysis in Section 6.7: **In this section we have separated various aspects of the total problem. We begin by describing what we call the Leontief matrix *A *as an encoding of the input and output relationships between sectors of an economy. Since this matrix can often be assumed to be constant, for a substantial period of time, we begin by assuming that *A *is a given. The simpler problem is then to determine the production *X *which is required to meet an external demand *D *for an economy whose Leontief matrix is *A*. We provide a careful account of this as the solution of .*I*¿�*A*/*X *D *D*.

Since *A *can be assumed to be fixed while various demands *D *are investigated, there is *some *justification to compute .*I *¿� *A*/¿�1 so that we have *X *D .*I *¿� *A*/¿�1*D*. However, use of a matrix inverse should not be considered an essential part of the solution. Finally, we explain how the Leontief matrix can be found from a table of data that might be available to a planner.

**Birthday probability in Section 8.4: **This is a treatment of the classic problem of determining the probability that at least 2 of *n *people have their birthday on the same day. While this problem is given as an example in many texts, the recursive formula that we give for calculating the probability as a function of *n *is not a common feature. It is reasonable to include it in this book because recursively defined sequences appear explicitly in Section 1.6.

**Markov Chains: **We noticed that considerable simplification to the problem of finding steady state vectors is obtained by writing state vectors as columns rather than rows. This does necessitate that a transition matrix **T **D .*t**ij*¿ have *t**ij *D“probability that next state is *i *given that current state is *j*” but avoids several artificial transpositions.

**Sign Charts for a function in Chapter 10: **The sign charts that we introduced in the 12th edition now make their appearance in Chapter 10. Our point is that these charts can be made for any real-valued function of a real variable and their help in graphing a function begins prior to the introduction of derivatives. Of course we continue to exploit their use in Chapter 13 “Curve Sketching” where, for each function *f*, we advocate making a sign chart for each of *f*, *f*0, and *f*00, interpreted for *f *itself. When this is possible, the graph of the function becomes almost self-evident. We freely acknowledge that this is a blackboard technique used by many instructors, but it appears too rarely in textbooks.

## Table of Contents

**CHAPTER 0** **Review of Algebra**

0.1 Sets of Real Numbers

0.2 Some Properties of Real Numbers

0.3 Exponents and Radicals

0.4 Operations with Algebraic Expressions

0.5 Factoring

0.6 Fractions

0.7 Equations, in Particular Linear Equations

0.8 Quadratic Equations

Chapter 0 Review

**CHAPTER 1** **Applications and More Algebra**

1.1 Applications of Equations

1.2 Linear Inequalities

1.3 Applications of Inequalities

1.4 Absolute Value

1.5 Summation Notation

1.6 Sequences

Chapter 1 Review

**CHAPTER 2** **Functions and Graphs**

2.1 Functions

2.2 Special Functions

2.3 Combinations of Functions

2.4 Inverse Functions

2.5 Graphs in Rectangular Coordinates

2.6 Symmetry

2.7 Translations and Reflections

2.8 Functions of Several Variables

Chapter 2 Review

**CHAPTER 3** **Lines, Parabolas, and Systems**

3.1 Lines

3.2 Applications and Linear Functions

3.3 Quadratic Functions

3.4 Systems of Linear Equations

3.5 Nonlinear Systems

3.6 Applications of Systems of Equations

Chapter 3 Review

**CHAPTER 4** **Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Logarithmic and Exponential Equations

Chapter 4 Review

**PART II ****FINITE MATHEMATICS**

**CHAPTER 5** **Mathematics of Finance**

5.1 Compound Interest

5.2 Present Value

5.3 Interest Compounded Continuously

5.4 Annuities

5.5 Amortization of Loans

5.6 Perpetuities

Chapter 5 Review

**CHAPTER 6** **Matrix Algebra**

6.1 Matrices

6.2 Matrix Addition and Scalar Multiplication

6.3 Matrix Multiplication

6.4 Solving Systems by Reducing Matrices

6.5 Solving Systems by Reducing Matrices (continued)

6.6 Inverses

6.7 Leontief’s Input–Output Analysis

Chapter 6 Review

**CHAPTER 7** **Linear Programming**

7.1 Linear Inequalities in Two Variables

7.2 Linear Programming

7.3 The Simplex Method

7.4 Artificial Variables

7.5 Minimization

7.6 The Dual

Chapter 7 Review

**CHAPTER 8** **Introduction to Probability and Statistics**

8.1 Basic Counting Principle and Permutations

8.2 Combinations and Other Counting Principles

8.3 Sample Spaces and Events

8.4 Probability

8.5 Conditional Probability and Stochastic Processes

8.6 Independent Events

8.7 Bayes’ Formula

Chapter 8 Review

**CHAPTER 9** **Additional Topics in Probability**

9.1 Discrete Random Variables and Expected Value

9.2 The Binomial Distribution

9.3 Markov Chains

Chapter 9 Review

**PART III ****CALCULUS**

**CHAPTER 10** **Limits and Continuity**

10.1 Limits

10.2 Limits (Continued)

10.3 Continuity

10.4 Continuity Applied to Inequalities

Chapter 10 Review

**CHAPTER 11** **Differentiation**

11.1 The Derivative

11.2 Rules for Differentiation

11.3 The Derivative as a Rate of Change

11.4 The Product Rule and the Quotient Rule

11.5 The Chain Rule

Chapter 11 Review

**CHAPTER 12** **Additional Differentiation Topics**

12.1 Derivatives of Logarithmic Functions

12.2 Derivatives of Exponential Functions

12.3 Elasticity of Demand

12.4 Implicit Differentiation

12.5 Logarithmic Differentiation

12.6 Newton’s Method

12.7 Higher-Order Derivatives

Chapter 12 Review

**CHAPTER 13** **Curve Sketching**

13.1 Relative Extrema

13.2 Absolute Extrema on a Closed Interval

13.3 Concavity

13.4 The Second-Derivative Test

13.5 Asymptotes

13.6 Applied Maxima and Minima

Chapter 13 Review

**CHAPTER 14** **Integration**

14.1 Differentials

14.2 The Indefinite Integral

14.3 Integration with Initial Conditions

14.4 More Integration Formulas

14.5 Techniques of Integration

14.6 The Definite Integral

14.7 The Fundamental Theorem of Calculus

Chapter 14 Review

**CHAPTER 15** **Applications of Integration**

15.1 Integration by Tables

15.2 Approximate Integration

15.3 Area Between Curves

15.4 Consumers’ and Producers’ Surplus

15.5 Average Value of a Function

15.6 Differential Equations

15.7 More Applications of Differential Equations

15.8 Improper Integrals

Chapter 15 Review

**CHAPTER 16** **Continuous Random Variables**

16.1 Continuous Random Variables

16.2 The Normal Distribution

16.3 The Normal Approximation to the Binomial Distribution

Chapter 16 Review

**CHAPTER 17** **Multivariable Calculus**

17.1 Partial Derivatives

17.2 Applications of Partial Derivatives

17.3 Higher-Order Partial Derivatives

17.4 Maxima and Minima for Functions of Two Variables

17.5 Lagrange Multipliers

17.6 Multiple Integrals

Chapter 17 Review

APPENDIX A Compound Interest Tables

APPENDIX B Table of Selected Integrals

APPENDIX C Areas Under the Standard Normal Curve