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

This accessible text is organized into three parts: (1) A Library of Elementary Functions (Chapters 1-2), (2) Finite Mathematics (Chapters 3-9), and (3) Calculus (Chapters 10-15). The bookrs"s overall approach addresses the challenges of teaching and learning when readersrs" prerequisite knowledge varies greatly. Reader-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for todayrs"s readers. A Library of Elementary Functions: Linear Equations and Graphs; Functions and Graphs.Finite Mathematics:Mathematics of Finance;Systems of Linear Equations; Matrices;Linear Inequalities and Linear Programming; Linear Programming: Simplex Method; Logic, Sets, and Counting; Probability; Markov Chains.Calculus: Limits and the Derivative; Additional Derivative Topics; Graphing and Optimization; Integration; Additional Integration Topics; Multivariable Calculus. For all readers interested in college mathematics for business, economics, life sciences, and social sciences.

Raymond A. Barnett, a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern University; Charles Burke, City College of San Francisco; John Fuji, Merritt College; and Karl Byleen, Marquette University.

 

Michael R. Ziegler (late) received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he held the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler published over a dozen research articles in complex analysis and co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.

 

Karl E. Byleen received his B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.

 

Part One: A Library of Elementary Functions

 

Chapter 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

 

Chapter 2: Functions and Graphs

2-1 Functions

2-2 Elementary Functions: Graphs and Transformations

2-3 Quadratic Functions

2-4 Polynomial and Rational Functions

2-5 Exponential Functions

2-6 Logarithmic Functions

Chapter 2 Review

Review Exercise

 

Part Two: Finite Mathematics

 

Chapter 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

 

Chapter 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 4 Review

Review Exercise

 

Chapter 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

 

Chapter 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; Minimization with Problem Constraints of the form ≥

6-4 Maximization and Minimization with Mixed Problem Constraints

Chapter 6 Review

Review Exercise

 

Chapter 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

 

Chapter 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 Variables, Probability Distribution, and Expected Value

Chapter 8 Review

Review Exercise

 

Chapter 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 Three: Calculus

 

Chapter 10: Limits and the Derivative

10-1 Introduction to Limits

10-2 Infinite Limits and Limits at Infinity

10-3 Continuity

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

 

Chapter 11: Additional Derivative Topics

11-1 The Constant e and Continuous Compound Interest

11-2 Derivatives of Logarithmic and Exponential Functions

11-3 Derivatives of Products and Quotients

11-4 The Chain Rule

11-4 Implicit Differentiation

11-5 Related Rates

11-7 Elasticity of Demand

Chapter 11 Review

Review Exercise

 

Chapter 12: Graphing and Optimization

12-1 First Derivative and Graphs

12-2 Second Derivative and Graphs

12-3 L'Hopitals's Rule

12-4 Curve Sketching Techniques

12-5 Absolute Maxima and Minima

12-6 Optimization

Chapter 12 Review

Review Exercise

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Appendixes

 

Appendix 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

 

Appendix B: Special Topics

B-1 Sequences, Series, and Summation Notation

B-2 Arithmetic and Geometric Sequences

B-3 Binomial Theorem

 

Appendix C: Tables

Table I  Area Under the Standard Normal Curve

Table II  Basic Geometric Formulas

 

Answers

Index

Applications Index

A Library of Elementary Functions