# Mathematics with Applications for the Management, Life, and Social Sciences

## 2nd Edition

**Authors:**Howard Anton Bernard Kolman

**eBook ISBN:**9781483264370

**Imprint:**Academic Press

**Published Date:**1st January 1982

**Page Count:**864

## Description

Mathematics with Applications for the Management, Life, and Social Sciences, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given.

Comprised of 16 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus.

This monograph is intended for students and instructors of applied mathematics.

## Table of Contents

Preface

One Set Theory

1.1 Introduction to Sets

1.2 Union and Intersection of Sets

1.3 Complementation and Cartesian Product of Sets

Key Ideas for Review

Two Coordinate Systems and Graphs

2.1 Coordinate Systems

2.2 The Straight Line

2.3 Linear Systems of Two Equations in Two Unknowns

2.4 Applications of Linear Equations

2.5 Linear Inequalities and Their Graphs

Key Ideas for Review

Three Linear Programming (A Geometric Approach)

3.1 What Is Linear Programming?

3.2 Solving Linear Programming Problems Geometrically

Key Ideas for Review

Four Matrices and Linear Systems

4.1 Linear Systems

4.2 Gauss-Jordan Elimination

4.3 Matrices; Matrix Addition and Scalar Multiplication

4.4 Matrix Multiplication

4.5 Inverses of Matrices

Key Ideas for Review

Five Linear Programming (An Algebraic Approach)

5.1 Introduction; Slack Variables

5.2 The Key Ideas of the Simplex Method

5.3 The Simplex Method

5.4 Nonstandard Linear Programming Problems; Duality

Key Ideas for Review

Six Counting Techniques; Permutations and Combinations

6.1 Counting Elements in Sets

6.2 Permutations and Combinations

Key Ideas for Review

Seven Probability

7.1 Introduction; Sample Space and Events

7.2 Probability Models for Finite Sample Spaces

7.3 Basic Theorems of Probability

7.4 Solving Probability Problems

7.5 Conditional Probability; Independence

7.6 Bayes' Formula

Key Ideas for Review

Eight Statistics

8.1 Introduction; Random Variables

8.2 Expected Value of a Random Variable

8.3 Variance of a Random Variable

8.4 Chebyshev's Inequality; Applications of Mean and Variance

8.5 Binomial Random Variables

8.6 The Normal Approximation of the Binomial

8.7 Hypothesis Testing; The Chi-Square Test

Key Ideas for Review

Nine Applications

9.1 Applications of Probability and Expected Value to Life Insurance and Mortality

9.2 Introduction to Game Theory and Applications

9.3 Games with Mixed Strategies

9.4 An Application of Probability to Genetics; The Hardy-Weinberg Stability Principle

9.5 An Application of Conditional Probability to Medical Diagnosis

9.6 Markov Chains and Applications

Key Ideas for Review

Ten Mathematics of Finance

10.1 Simple and Compound Interest

10.2 Effective Rate of Interest; Simple Discount

10.3 Annuities and Sinking Funds

10.4 Present Value

10.5 Mortgages and Amortization Schedules

Key Ideas for Review

Eleven Functions, Limits, and Rates of Change

11.1 Introduction

11.2 Functions

11.3 Limits

11.4 Limits at Infinity

11.5 Continuity

11.6 Average and Instantaneous Rate of Change

Key Ideas for Review

Twelve The Derivative

12.1 The Derivative

12.2 The Chain Rule

12.3 Applications of the Derivative

12.4 Derivatives of the Exponential and Logarithmic Functions

Key Ideas for Review

Thirteen Applications of Differentiation

13.1 Applications of Differentiation to Optimization

13.2 First and Second Derivative Tests

13.3 More Applications to Optimization

13.4 Sketching Graphs of Polynomial Functions

13.5 Applications to Exponential Growth and Decay Models

Key Ideas for Review

Fourteen Integration

14.1 Antiderivatives and Indefinite Integrals

14.2 The Definite Integral

14.3 Properties of the Definite Integral

14.4 Techniques of Integration

14.5 Improper Integrals

Key Ideas for Review

Fifteen Applications of Integration

15.1 Integrating Rates of Change

15.2 Differential Equations

15.3 Applications of Integration in Probability

Key Ideas for Review

Sixteen Functions of Several Variables

16.1 Functions of Two Variables; Coordinate Systems in Three Dimensions

16.2 Partial Derivatives

16.3 Applications of Partial Derivatives to Optimization

Key Ideas for Review

Algebra Review

A.1 Real Numbers

A.2 Algebraic Notation and the Basic Rules of Algebra

A.3 Solving Equations; Linear Equations

A.4 Exponents and Radicals

A.5 Polynomials and Factoring

A.6 Rational Expressions

A.7 Quadratic Equations

A.8 Logarithms

Appendix/Tables

Answers to Odd-Numbered Exercises

Index

## Details

- No. of pages:
- 864

- Language:
- English

- Copyright:
- © Academic Press 1982

- Published:
- 1st January 1982

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483264370

## About the Author

### Howard Anton

### Bernard Kolman

### Affiliations and Expertise

Drexel University