Applied Mathematics: For Business, Economics, Life Sciences, and Social Sciences

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

• ISBN13: 9780130831200
• ISBN10: 0130831204
• Edition: 7th
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Pearson College Div

Summary

Written in a student-friendly format, this text prepares students to understand finite mathematics and calculus used in a wide range of disciplines. Covering relevant topics from finance, linear algebra, programming, and probability, the Seventh Edition places emphasis on computational skills, ideas, and problem solving. Other highlights include a rich variety of applications and integration of graphing calculators.

Table of Contents

Preface	ix
Part One A Library Of Elementary Functions	1	(126)
A Beginning Library of Elementary Functions	3	(74)
Functions	3	(20)
Elementary Functions: Graphs and Transformations	23	(13)
Linear Functions and Straight Lines	36	(16)
Quadratic Functions	52	(25)
Important Terms and Symbols	67	(1)
Review Exercise	68	(4)
Introduction to Regression Analysis	72	(2)
Mathematical Modeling in Business	74	(3)
Additional Elementary Functions	77	(50)
Polynomial and Rational Functions	77	(16)
Exponential Functions	93	(14)
Logarithmic Functions	107	(20)
Important Terms and Symbols	120	(1)
Review Exercise	120	(3)
Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions	123	(1)
Comparing Regression Models	124	(3)
Part Two Finite Mathematics	127	(384)
Mathematics of Finance	129	(46)
Simple Interest	129	(6)
Compound Interest	135	(14)
Future Value of an Annuity; Sinking Funds	149	(7)
Present Value of an Annuity; Amortization	156	(19)
Important Terms and Symbols	168	(1)
Review Exercise	168	(3)
Reducing Interest Payments on a Home Mortgage	171	(1)
Yield to Maturity and Internal Rate of Return	172	(3)
Systems of Linear Equations; Matrices	175	(90)
Review: Systems of Linear Equations in Two Variables	176	(13)
Systems of Linear Equations and Augmented Matrices	189	(10)
Gauss--Jordan Elimination	199	(15)
Matrices: Basic Operations	214	(13)
Inverse of a Square Matrix	227	(12)
Matrix Equations and Systems of Linear Equations	239	(11)
Leontief Input--Output Analysis	250	(15)
Important Terms and Symbols	258	(1)
Review Exercise	259	(3)
Using Matrices to Find Cost, Revenue, and Profit	262	(1)
Direct and Indirect Operating Costs	263	(2)
Linear Inequalities and Linear Programming	265	(100)
Systems of Linear Inequalities in Two Variables	265	(14)
Linear Programming in Two Dimensions---A Geometric Approach	279	(15)
A Geometric Introduction to the Simplex Method	294	(8)
The Simplex Method: Maximization with Problem Constraints of the Form ≥	302	(20)
The Dual; Minimization with Problem Constraints of the Form≥	322	(17)
Maximization and Minimization with Mixed Problem Constraints	339	(26)
Important Terms and Symbols	358	(1)
Review Exercise	359	(2)
The Two-Phase Method (An Alternative to the Big M Method)	361	(3)
Production Scheduling	364	(1)
Probability	365	(98)
Basic Counting Principles	366	(10)
Permutations and Combinations	376	(13)
Sample Spaces, Events, and Probability	389	(16)
Union, Intersection, and Complement of Events; Odds	405	(15)
Conditional Probability, Intersection, and Independence	420	(16)
Bayes' Formula	436	(7)
Random Variable, Probability Distribution, and Expected Value	443	(20)
Important Terms and Symbols	453	(1)
Review Exercise	454	(5)
Car and Crying Towels	459	(1)
Simulation---A Draft Lottery for Professional Sports	460	(3)
Markov Chains	463	(48)
Properties of Markov Chains	463	(13)
Regular Markov Chains	476	(12)
Absorbing Markov Chains	488	(23)
Important Terms and Symbols	504	(1)
Review Exercise	504	(4)
Social Mobility	508	(1)
Gambler's Ruin	509	(2)
Part Three Calculus	511	(526)
The Derivative	513	(92)
Rate of Change and Slope	514	(13)
Limits	527	(17)
The Derivative	544	(13)
Derivatives of Constants, Power Forms, and Sums	557	(13)
Derivatives of Products and Quotients	570	(8)
Chain Rule: Power Form	578	(8)
Marginal Analysis in Business and Economics	586	(19)
Important Terms and Symbols	597	(1)
Summary of Rules of Differentiation	598	(1)
Review Exercise	598	(5)
Minimal Average Cost	603	(1)
Numerical Differentiation on a Graphing Utility	604	(1)
Graphing and Optimization	605	(90)
Continuity and Graphs	606	(16)
First Derivative and Graphs	622	(17)
Second Derivative and Graphs	639	(16)
Curve Sketching Techniques: Unified and Extended	655	(16)
Optimization; Absolute Maxima and Minima	671	(24)
Important Terms and Symbols	687	(1)
Review Exercise	688	(4)
Maximizing Profit	692	(1)
Minimizing Construction Costs	692	(3)
Additional Derivative Topics	695	(50)
The Constant e and Continuous Compound Interest	695	(8)
Derivatives of Logarithmic and Exponential Functions	703	(12)
Chain Rule: General Form	715	(12)
Implicit Differentiation	727	(7)
Related Rates	734	(11)
Important Terms and Symbols	740	(1)
Additional Rules of Differentiation	740	(1)
Review Exercise	741	(2)
Elasticity of Demand	743	(1)
Point of Diminishing Returns	744	(1)
Integration	745	(84)
Antiderivatives and Indefinite Integrals	745	(15)
Integration by Substitution	760	(12)
Differential Equations---Growth and Decay	772	(12)
A Geometric-Numeric Introduction to the Definite Integral	784	(16)
Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus	800	(29)
Important Terms and Symbols	819	(1)
Integration Formulas and Properties	819	(1)
Review Exercise	819	(5)
Simpson's Rule	824	(3)
Bell-Shaped Curves	827	(2)
Additional Integration Topics	829	(46)
Area between Curves	829	(12)
Applications in Business and Economics	841	(13)
Integration by Parts	854	(7)
Integration Using Tables	861	(14)
Important Terms and Symbols	869	(1)
Review Exercise	869	(2)
Analysis of Income Concentration from Raw Data	871	(2)
Grain Exchange	873	(2)
Multivariable Calculus	875	(68)
Functions of Several Variables	875	(10)
Partial Derivatives	885	(10)
Maxima and Minima	895	(9)
Maxima and Minima Using Lagrange Multipliers	904	(10)
Method of Least Squares	914	(11)
Double Integrals Over Rectangular Regions	925	(18)
Important Terms and Symbols	936	(1)
Review Exercise	936	(3)
City Planning	939	(1)
Numerical Integration of Multivariable Functions	940	(3)
Differential Equations	943	(46)
Basic Concepts	943	(12)
Separation of Variables	955	(12)
First-Order Linear Differential Equations	967	(22)
Important Terms and Symbols	979	(1)
Review Exercise	979	(2)
Torricelli's Law	981	(2)
Euler's Method	983	(6)
Probability and Calculus	989	(48)
Improper Integrals	989	(8)
Continuous Random Variables	997	(13)
Expected Value, Standard Deviation, and Median	1010	(10)
Special Probability Distributions	1020	(17)
Important Terms and Symbols	1032	(1)
Review Exercise	1032	(3)
Beta Distributions	1035	(1)
Chi-Square Distributions	1036	(1)
Appendix A Special Topics	1037	(48)
A-1 Sequences, Series, and Summation Notation	1037	(6)
A-2 Arithmetic and Geometric Sequences	1043	(8)
A-3 The Binomial Theorem	1051	(4)
A-4 Increments and Differentials	1055	(8)
A-5 L'Hopital's Rule	1063	(11)
A-6 Double Integrals Over More General Regions	1074	(11)
Appendix B Tables	1085
Table I Basic Geometric Formulas	1085	(2)
Table II Integration Formulas	1087	(4)
Table III Area Under the Standard Normal Curve	1091
Answers	A-1	(1)
Index	I-1