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Mathematics with Applications for the Management, Life, and Social Sciences
- 2nd Edition - May 10, 2014
- Authors: Howard Anton, Bernard Kolman
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 4 3 7 - 0
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… Read more
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Request a sales quoteMathematics 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.
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
- No. of pages: 864
- Language: English
- Edition: 2
- Published: May 10, 2014
- Imprint: Academic Press
- eBook ISBN: 9781483264370
BK
Bernard Kolman
Affiliations and expertise
Drexel UniversityRead Mathematics with Applications for the Management, Life, and Social Sciences on ScienceDirect