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College Mathematics for Business, Economics, Life Sciences & Social Sciences

Raymond A. Barnett, Michael R. Ziegler, and, Karl E. Byleen
Prentice Hall
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The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

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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




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 Equations in 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




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




Applications Index

A Library of Elementary Functions