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

by Barnett, Raymond A.; Ziegler, Michael R.; Byleen, Karl E.

• ISBN13: 9780131432093
• ISBN10: 0131432095
• Edition: 10th
• Format: Hardcover
• Copyright: 2008-01-01
• Publisher: Prentice Hall

Summary

Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.This book features a collection of important topics from mathematics of finance, linear algebra, linear programming, probability, and statistics, with an emphasis on cross-discipline principles and practices.For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.

Table of Contents

Preface	ix
Student and Instructor Resources	xv
Part One A Library of Elementary Functions	1	(128)
A Beginning Library of Elementary Functions	2	(76)
Functions	3	(18)
Elementary Functions: Graphs and Transformations	21	(14)
Linear Functions and Straight Lines	35	(18)
Quadratic Functions	53	(25)
Important Terms, Symbols, and Concepts	68	(2)
Review Exercise	70	(5)
Group Activity 1: Introduction to Regression Analysis	75	(1)
Group Activity 2: Mathematical Modeling in Business	76	(2)
Additional Elementary Functions	78	(51)
Polynomial and Rational Functions	79	(16)
Exponential Functions	95	(14)
Logarithmic Functions	109	(20)
Important Terms, Symbols, and Concepts	122	(1)
Review Exercise	123	(3)
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions	126	(1)
Group Activity 2: Comparing Regression Models	126	(3)
Part Two Finite Mathematics	129	(840)
Mathematics of Finance	130	(50)
Simple Interest	131	(8)
Compound Interest	139	(13)
Future Value of an Annuity; Sinking Funds	152	(9)
Present Value of an Annuity; Amortization	161	(19)
Important Terms, Symbols, and Concepts	174	(1)
Review Exercise	175	(3)
Group Activity 1: Reducing Interest Payments on a Home Mortgage	178	(1)
Group Activity 2: Yield to Maturity and Internal Rate of Return	178	(2)
Systems of Linear Equations; Matrices	180	(94)
Review: Systems of Linear Equations in Two Variables	182	(14)
Systems of Linear Equations and Augmented Matrices	196	(9)
Gauss--Jordan Elimination	205	(15)
Matrices: Basic Operations	220	(14)
Inverse of a Square Matrix	234	(11)
Matrix Equations and Systems of Linear Equations	245	(10)
Leontief Input-Output Analysis	255	(19)
Important Terms, Symbols, and Concepts	264	(3)
Review Exercise	267	(4)
Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit	271	(1)
Group Activity 2: Direct and Indirect Operating Costs	272	(2)
Linear Inequalities and Linear Programming	274	(100)
Systems of Linear Inequalities in Two Variables	275	(14)
Linear Programming in Two Dimensions: Geometric Approach	289	(14)
Geometric Introduction to the Simplex Method	303	(8)
Simplex Method: Maximization with Problem Constraints of the Form ≤	311	(19)
Dual Problem: Minimization with Problem Constraints of the Form ≥	330	(16)
Maximization and Minimization with Mixed Problem Constraints	346	(28)
Important Terms, Symbols, and Concepts	364	(4)
Review Exercise	368	(3)
Group Activity 1: Two-Phase Method: Alternative to the Big M Method	371	(2)
Group Activity 2: Production Scheduling	373	(1)
Logic, Sets, and Counting	374	(46)
Logic	375	(10)
Sets	385	(6)
Basic Counting Principles	391	(10)
Permutations and Combinations	401	(19)
Important Terms, Symbols, and Concepts	414	(1)
Review Exercise	415	(2)
Group Activity 1: Combinations with Repetition Allowed	417	(1)
Group Activity 2: Subset Lattices of Finite Sets	418	(2)
Probability	420	(72)
Sample Spaces, Events, and Probability	422	(15)
Union, Intersection, and Complement of Events; Odds	437	(14)
Conditional Probability, Intersection, and Independence	451	(16)
Bayes' Formula	467	(7)
Random Variable, Probability Distribution, and Expected Value	474	(18)
Important Terms, Symbols, and Concepts	484	(1)
Review Exercise	485	(4)
Group Activity 1: Car and Crying Towels	489	(1)
Group Activity 2: Simulation: Draft Lottery for Professional Sports	490	(2)
Markov Chains	492	(48)
Properties of Markov Chains	493	(13)
Regular Markov Chains	506	(11)
Absorbing Markov Chains	517	(23)
Important Terms, Symbols, and Concepts	533	(1)
Review Exercise	534	(3)
Group Activity 1: Social Mobility	537	(1)
Group Activity 2: Gambler's Ruin	538	(2)
Part Three Calculus
The Derivative	540	(94)
Introduction to Limits	542	(16)
Continuity	558	(12)
The Derivative	570	(16)
Power Rule and Basic Differentation Properties	586	(10)
Derivatives of Products and Quotients	596	(8)
General Power Rule (Chain Rule)	604	(8)
Marginal Analysis in Business and Economics	612	(22)
Important Terms, Symbols, and Concepts	623	(3)
Review Exercise	626	(5)
Group Activity 1: Minimal Average Cost	631	(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility	632	(2)
Graphing and Optimization	634	(80)
First Derivative and Graphs	635	(18)
Second Derivative and Graphs	653	(16)
Graphing Rational Functions	669	(16)
Absolute Maxima and Minima	685	(7)
Optimization	692	(22)
Important Terms, Symbols, and Concepts	706	(3)
Review Exercise	709	(3)
Group Activity 1: Maximizing Profit	712	(1)
Group Activity 2: Minimizing Construction Costs	712	(2)
Additional Derivative Topics	714	(64)
The Constant e and Continuous Compound Interest	715	(8)
Exponential Functions and Their Derivatives	723	(11)
Logarithmic Functions and Their Derivatives	734	(13)
Chain Rule: Elasticity of Demand	747	(12)
Implicit Differentiation	759	(7)
Related Rates	766	(12)
Important Terms, Symbols, and Concepts	773	(1)
Review Exercise	774	(2)
Group Activity 1: Increasing Production of Cellular Phones	776	(1)
Group Activity 2: Point of Diminishing Returns	777	(1)
Integration	778	(74)
Antiderivatives and Indefinite Integrals	779	(14)
Integration by Substitution	793	(12)
Differential Equations; Growth and Decay	805	(11)
The Definite Integral	816	(11)
The Fundamental Theorem of Calculus	827	(25)
Important Terms, Symbols, and Concepts	841	(2)
Review Exercise	843	(4)
Group Activity 1: Simpson's Rule	847	(3)
Group Activity 2: Bell-Shaped Curves	850	(2)
Additional Integration Topics	852	(46)
Area Between Curves	853	(11)
Applications in Business and Economics	864	(12)
Integration by Parts	876	(7)
Integration Using Tables	883	(15)
Important Terms, Symbols, and Concepts	892	(1)
Review Exercise	893	(2)
Group Activity 1: Analysis of Income Concentration from Raw Data	895	(1)
Group Activity 2: Grain Exchange	896	(2)
Multivariable Calculus	898	(71)
Functions of Several Variables	899	(10)
Partial Derivatives	909	(10)
Maxima and Minima	919	(9)
Maxima and Minima Using Lagrange Multipliers	928	(10)
Method of Least Squares	938	(11)
Double Integrals Over Rectangular Regions	949	(20)
Important Terms, Symbols, and Concepts	960	(2)
Review Exercise	962	(2)
Group Activity 1: City Planning	964	(1)
Group Activity 2: Numerical Integration of Multivariable Functions	965	(4)
Basic Algebra Review	969	(1)
A Self-Test on Basic Algebra	969	(64)
Algebra and Real Numbers	971	(6)
Operations on Polynomials	977	(8)
Factoring Polynomials	985	(7)
Operations on Rational Expressions	992	(6)
Integer Exponents and Scientific Notation	998	(6)
Rational Exponents and Radicals	1004	(7)
Linear Equations and Inequalities in One Variable	1011	(10)
Quadratic Equations	1021	(12)
B Special Topics	1033	(20)
Sequences, Series, and Summation Notation	1033	(7)
Arithmetic and Geometric Sequences	1040	(8)
The Binomial Theorem	1048	(5)
C Tables	1053	(1)
Table I Basic Geometric Formulas	1053	(2)
Table II Integration Formulas	1055
Answers	1	(1)
Index	1