Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for its application in other areas. Concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.   Features a collection of important topics from mathematics of finance, algebra, linear programming, probability, and descriptive statistics, with an emphasis on cross-discipline principles and practices. For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.

Why We wrote This Book:

This text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible.  We emphasize computational skills, ideas, and problem solving rather than mathematical theory.  Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept.  General concepts and results are usually presented only after particular cases have been discussed.  Graphing calculators and computers are playing an increasing role in mathematics education and in real-world applications of mathematics.  This books deals with the mathematics that is required to use modern technology effectively as an OPTIONAL feature.  In appropriate places in the text, there are clearly identified examples and exercises related to graphing calculators and computers, illustrations of applications of spreadsheets, and sample computer output. All of these may be omitted without loss of continuity.

PART 1 A LIBRARY OF ELEMENTARY FUNCTIONS

1 Linear Equations and Graphs

1-1 Linear Equations and Inequalities

1-2 Graphs and Lines

1-3 Linear Regression

Chapter 1 Review

Review Exercise

2 Functions and Graphs

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Exponential Functions

2-5 Logarithmic Functions

Chapter 2 Review

Review Exercise

PART 2 FINITE MATHEMATICS

3 Mathematics of Finance

3-1 Simple Interest

3-2 Compound and Continuous Compound Interest

3-3 Future Value of an Annuity; Sinking Funds

3-4 Present Value of an Annuity; Amortization

Chapter 3 Review

Review Exercise

4 Systems of Linear Equations; Matrices

4-1 Review: Systems of Linear Equationsin Two Variables

4-2 Systems of Linear Equations and Augmented Matrices

4-3 Gauss—Jordan Elimination

4-4 Matrices: Basic Operations

4-5 Inverse of a Square Matrix

4-6 Matrix Equations and Systems of Linear Equations

4-7 Leontief Input—Output Analysis

Chapter 2 Review

Review Exercise

5 Linear Inequalities and Linear Programming

5-1 Inequalities in Two Variables

5-2 Systems of Linear Inequalities in Two Variables

5-3 Linear Programming in Two Dimensions: A Geometric Approach

Chapter 5 Review

Review Exercise

6 Linear Programming: Simplex Method

6-1 A Geometric Introduction to the Simplex Method

6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≤

6-3 The Dual Problem; Minimization with Problem Constraints of the Form ≥

6-4 Maximization and Minimization with Mixed Problem Constraints

Chapter 6 Review

Review Exercise

7 Logic, Sets, and Counting

7-1 Logic

7-2 Sets

7-3 Basic Counting Principles

7-4 Permutations and Combinations

Chapter 7 Review

Review Exercise

8 Probability

8-1 Sample Spaces, Events, and Probability

8-2 Union, Intersection, and Complement of Events; Odds

8-3 Conditional Probability, Intersection, and Independence

8-4 Bayes’ Formula

8-5 Random Variable, Probability Distribution, and Expected Value

Chapter 8 Review

Review Exercise

9 Markov Chains

9-1 Properties of Markov Chains

9-2 Regular Markov Chains

9-3 Absorbing Markov Chains

Chapter 9 Review

Review Exercise

PART 3 CALCULUS

10 Limits and the Derivative

10-1 Introduction to Limits

10-2 Continuity

10-3 Infinite Limits and Limits at Infinity

10-4 The Derivative

10-5 Basic Differentiation Properties

10-6 Differentials

10-7 Marginal Analysis in Business and Economics

Chapter 10 Review

Review Exercise

11 Additional Derivative Topics

11-1 The Constant e and Continuous Compound Interest

11-2 Derivatives of Exponential and Logarithmic Functions

11-3 Derivatives of Products and Quotients

11-4 The Chain Rule

11-5 Implicit Differentiation

11-6 Related Rates

11-7 Elasticity of Demand

Chapter 11 Review

Review Exercise

12 Graphing and Optimization

12-1 First Derivative and Graphs

12-2 Second Derivative and Graphs

12-3 L’Hôpital’s Rule

12-4 Curve-Sketching Techniques

12-5 Absolute Maxima and Minima

12-6 Optimization

Chapter 12 Review

Review Exercise

13 Integration

13-1 Antiderivatives and Indefinite Integrals

13-2 Integration by Substitution

13-3 Differential Equations; Growth and Decay

13-4 The Definite Integral

13-5 The Fundamental Theorem of Calculus

Chapter 13 Review

Review Exercise

14 Additional Integration Topics

14-1 Area between Curves

14-2 Applications in Business and Economics

14-3 Integration by Parts

14-4 Integration Using Tables

Chapter 14 Review

Review Exercise

15 Multivariable Calculus

15-1 Functions of Several Variables

15-2 Partial Derivatives

15-3 Maxima and Minima

15-4 Maxima and Minima Using Lagrange Multipliers

15-5 Method of Least Squares

15-6 Double Integrals over Rectangular Regions

15-7 Double Integrals over More General Regions

Chapter 15 Review

Review Exercise

A Basic Algebra Review

Self-Test on Basic Algebra

A-1 Algebra and Real Numbers

A-2 Operations on Polynomials

A-3 Factoring Polynomials

A-4 Operations on Rational Expressions

A-5 Integer Exponents and Scientific Notation

A-6 Rational Exponents and Radicals

A-7 Quadratic Equations

B Special Topics

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 The Binomial Theorem

C Tables

Table I Basic Geometric Formulas

Table II Integration Formulas

Answers

Index

Applications Index

A Library of Elementary Functions