Mathematical Applications for the Management, Life, and Social Sciences

by Harshbarger, Ronald J.; Reynolds, James J.

• ISBN13: 9780547145099
• ISBN10: 0547145098
• Edition: 9th
• Format: Hardcover
• Copyright: 2008-10-24
• Publisher: Brooks Cole

Summary

MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT, LIFE, AND SOCIAL SCIENCES, 9th EDITION is intended for a two-semester applied calculus or combined finite mathematics and applied calculus course. The book's concept-based approach, multiple presentation methods, and interesting and relevant applications keep students who typically take the course—business, economics, life sciences, and social sciences majors—engaged in the material. This edition broadens the book's real-life context by adding a number of environmental science and economic applications. The use of modeling has been expanded, with modeling problems now clearly labeled in the examples. Also included in the Ninth Edition is a brief review of algebra to prepare students with different backgrounds for the material in later chapters.

Table of Contents

Algebraic Concepts

Sets

The Real Numbers

Integral Exponents

Radicals and Rational Expressions

Operations with Algebraic Expressions

Factoring

Algebraic Fractions

Linear Equations and Functions

Solutions of Linear Equations and Inequalities in One Variable

Functions

Linear Functions

Graphs and Graphing Utilities

Solutions of Systems of Linear Equations

Applications of Functions in Business and Economics

Quadratic and Other Special Functions

Quadratic Functions

Quadratic Functions: Parabolas

Business Applications of Quadratic Functions

Special Functions and Their Graphs

Modeling

Fitting Curves to Data with Graphing Utilities (Optional)

Matrices

Matrices

Multiplication of Matrices

Gauss-Jordan Elimination: Solving Systems of Equations

Inverse of a Square Matrix

Matrix Equations

Applications of Matrices: Leontif Input-Output Models

Inequalities and Linear Programming

Linear Inequalities in Two Variables

Linear Programming: Graphical Methods

The Simplex Method: Maximization

The Simplex Method: Duality and Minimization

The Simplex Method with Mixed Constraints

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions and Their Properties

Solutions of Exponential Equations: Applications of Exponential and Logarithmic Functions

Mathematics of Finance

Simple Interest

Sequences

Compound Interest

Geometric Sequence

Future Value of Annuities

Present Value of Annuities

Loans and Amortization

Introduction to Probability

Probability

Odds

Unions and Intersections of Events: One-Trial Experiments

Conditional Probability: The Product Rule

Probability Trees and Bayes' Formula

Counting: Permutations and Combinations

Permutations, Combinations, and Probability

Markov Chains

Further Topics in Probability

Binomial Probability Experiments

Data Descriptions

Discrete Probability Distributions

The Binomial Distribution

Normal Probability Distribution

The Normal Curve Approximation to the Binomial Distribution

Derivatives

Limits

Continuous Functions

Limits at Infinity

Average and Instantaneous Rates of Change: The Derivative

Derivative Formulas

The Product Rule and The Quotient Rule

The Chain Rule and the Power Rule

Using Derivative Formulas

Higher-Order Derivatives

Applications of Derivatives in Business and Economics

Applications of Derivatives

Relative Maxima and Minima: Curve Sketching

Concavity: Points of Inflection

Optimization in Business and Economics

Applications of Maxima and Minima

Rational Functions: More Curve Sketching

Derivatives Continued

Derivatives of Logarithmic Functions

Derivatives of Exponential Functions

Implicit Differentiation

Related Rates

Applications in Business and Economics

Indefinite Integrals

The Indefinite Integral

The Power Rule

Integrals Involving Exponential and Logarithmic Functions

Applications of the Indefinite Integral in Business and Economics

Differential Equations

Definite Integrals: Techniques of Integration

Area Under a Curve

The Definite Integral: The Fundamental Theorem of Calculus

Area Between Two Curves

Applications of Definite Integrals in Business and Economics

Using Tables of Integrals

Integration by Parts

Improper Integrals and Their Applications

Numerical Integration Methods: Trapezoidal Rule and Simpson's Rule

Functions of Two or More Variables

Functions of Two or More Variables

Partial Differentiation

Applications of Functions of Two Variables in Business and Economics

Maxima and Minima

Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers

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