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

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

• ISBN13: 9780130655806
• ISBN10: 0130655805
• Edition: 8th
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Pearson College Div

Summary

For two-term, or condensed one-term, freshman/sophomore-level courses in Finite Math and calculus. This mathematically correct, accessible, and student friendly text prepares students for the math they will encounter as they matriculate through a wide range of disciplines. The text's optional graphing calculator material is presented thoughtfully and makes Barnett ideal in course employing the graphing calculator. The emphasis throughout is on computational skills, ideas, and problem solving-rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed.

Table of Contents

Preface	xi
Part One A Library of Elementary Functions	1	(128)
A Beginning Library of Elementary Functions	3	(76)
Functions	3	(20)
Elementary Functions: Graphs and Transformations	23	(13)
Linear Functions and Straight Lines	36	(17)
Quadratic Functions	53	(26)
Important Terms and Symbols	68	(1)
Review Exercise	69	(5)
Group Activity 1: Introduction to Regression Analysis	74	(1)
Group Activity 2: Mathematical Modeling in Business	75	(4)
Additional Elementary Functions	79	(50)
Polynomial and Rational Functions	79	(17)
Exponential Functions	96	(14)
Logarithmic Functions	110	(19)
Important Terms and Symbols	122	(1)
Review Exercise	122	(3)
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions	125	(1)
Group Activity 2: Comparing Regression Models	125	(4)
Part Two Finite Mathematics	129	(380)
Mathematics of Finance	131	(46)
Simple Interest	132	(6)
Compound Interest	138	(13)
Future Value of an Annuity; Sinking Funds	151	(8)
Present Value of an Annuity; Amortization	159	(18)
Important Terms and Symbols	171	(1)
Review Exercise	171	(3)
Group Activity 1: Reducing Interest Payments on a Home Mortgage	174	(1)
Group Activity 2: Yield to Maturity and Internal Rate of Return	175	(2)
Systems of Linear Equations; Matrices	177	(88)
Review:Systems of Linear Equations in Two Variables	178	(13)
Systems of Linear Equations and Augmented Matrices	191	(10)
Gauss-Jordan Elimination	201	(14)
Matrices: Basic Operations	215	(14)
Inverse of a Square Matrix	229	(11)
Matrix Equations and Systems of Linear Equations	240	(10)
Leontief Input-Output Analysis	250	(15)
Important Terms and Symbols	258	(1)
Review Exercise	259	(3)
Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit	262	(1)
Group Activity 2: Direct and Indirect Operating Costs	263	(2)
Linear Inequalities and Linear Programming	265	(100)
Systems of Linear Inequalities in Two Variables	265	(15)
Linear Programming in Two Dimensions: Geometric Approach	280	(15)
Geometric Introduction to the Simplex Method	295	(8)
The Simplex Method: Maximization with Problem Constraints of the Form ≤	303	(19)
Dual Problem: Minimization with Problem Constraints of the Form ≥	322	(16)
Maximization and Minimization with Mixed Problem Constraints	338	(27)
Important Terms and Symbols	357	(1)
Review Exercise	358	(3)
Group Activity 1: The Two-Phase Method (An Alternative to the Big M Method)	361	(2)
Group Activity 2: Production Scheduling	363	(2)
Probability	365	(96)
Basic Counting Principles	366	(10)
Permutations and Combinations	376	(13)
Sample Sapces, Events, and Probability	389	(15)
Union, Intersection, and Complement of Events; Odds	404	(14)
Conditional Probability, Intersection, and Independence	418	(16)
Bayes' Formula	434	(7)
Random Variable, Probability Distribution, and Expected Value	441	(20)
Important Terms and Symbols	451	(1)
Review Exercise	451	(5)
Group Activity 1: Car and Crying Towels	456	(2)
Group Activity 2: Simulation: Draft Lottery for Professional Sports	458	(3)
Markov Chains	461	(48)
Properties of Markov Chains	461	(13)
Regular Markov Chains	474	(12)
Absorbing Markov Chains	486	(23)
Important Terms and Symbols	501	(1)
Review Exercise	502	(3)
Group Activity 1: Social Mobility	505	(1)
Group Activity 2: Gambler's Ruin	506	(3)
Part Three Calculus	509	(506)
The Derivative	511	(98)
Introduction to Limits	512	(16)
Limits and Continuity	528	(17)
The Derivative	545	(15)
Derivatives of Constants, Power Forms, and Sums	560	(14)
Derivatives of Products and Quotients	574	(8)
Chain Rule: Power Form	582	(7)
Marginal Analysis in Business and Economics	589	(20)
Important Terms and Symbols	601	(1)
Summary of Rules of Differentiation	602	(1)
Review Exercise	602	(5)
Group Activity 1: Minimal Average Cost	607	(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility	608	(1)
Graphing and Optimization	609	(74)
First Derivative and Graphs	610	(17)
Second Derivative and Graphs	627	(16)
Curve Sketching Techniques: Unified and Extended	643	(17)
Optimization; Absolute Maxima and Minima	660	(23)
Important Terms and Symbols	676	(1)
Review Exercise	676	(4)
Group Activity 1: Maximizing Profit	680	(1)
Group Activity 2: Minimizing Construction Costs	680	(3)
Additional Derivative Topics	683	(48)
The Constant e and Continuous Compound Interest	683	(7)
Derivatives of Logarithmic and Exponential Functions	690	(12)
Chain Rule: General Form	702	(11)
Implicit Differentiation	713	(7)
Related Rates	720	(11)
Important Terms and Symbols	726	(1)
Additional Rules of Differentiation	726	(1)
Review Exercise	726	(2)
Group Activity 1: Elasticity of Demand	728	(1)
Group Activity 2: Point of Diminishing Returns	729	(2)
Integration	731	(82)
Antiderivatives and Indefinite Integrals	731	(15)
Integration by Substitution	746	(12)
Differential Equations; Growth and Decay	758	(11)
Geometric-Numeric Introduction to the Definite Integral	769	(16)
Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus	785	(28)
Important Terms and Symbols	803	(1)
Integration Formulas and Properties	804	(1)
Review Exercise	804	(4)
Group Activity 1: Simpson's Rule	808	(3)
Group Activity 2: Bell-Shaped Curves	811	(2)
Additional Integration Topics	813	(44)
Area Between Curves	813	(11)
Applications in Business and Economics	824	(13)
Integration by Parts	837	(8)
Integration Using Tables	845	(12)
Important Terms and Symbols	852	(1)
Review Exercise	853	(2)
Group Activity 1: Analysis of Income Concentration from Raw Data	855	(1)
Group Activity 2: Grain Exchange	856	(1)
Multivariable Calculus	857	(68)
Functions of Several Variables	857	(11)
Partial Derivatives	868	(9)
Maxima and Minima	877	(9)
Maxima and Minima Using Lagrange Multipliers	886	(10)
Method of Least Squares	896	(11)
Double Integrals Over Rectangular Regions	907	(18)
Important Terms and Symbols	917	(1)
Review Exercise	918	(3)
Group Activity 1: City Planning	921	(1)
Group Activity 2: Numerical Integration of Multivariable Functions	922	(3)
Differential Equations	925	(42)
Basic Concepts	925	(11)
Separation of Variables	936	(12)
First-Order Linear Differential Equations	948	(19)
Important Terms and Symbols	959	(1)
Review Exercise	959	(2)
Group Activity 1: Torricelli's Law	961	(2)
Group Activity 2: Euler's Method	963	(4)
Probability and Calculus	967	(48)
Improper Integrals	967	(8)
Continuous Random Variables	975	(13)
Expected Value, Standard Deviation, and Median	988	(9)
Special Probability Distributions	997	(18)
Important Terms and Symbols	1008	(1)
Review Exercise	1009	(3)
Group Activity 1: Beta Distributions	1012	(1)
Group Activity 2: Chi-Square Distributions	1012	(3)
APPENDIX A Basic Algebra Review	1015	(68)
Self-Test on Basic Algebra	1015	(2)
A-1 Sets	1017	(6)
A-2 Algebra and Real Numbers	1023	(7)
A-3 Operations on Polynomials	1030	(7)
A-4 Factoring Polynomials	1037	(6)
A-5 Operations on Rational Expressions	1043	(6)
A-6 Integer Exponents and Scientific Notation	1049	(6)
A-7 Rational Exponents and Radicals	1055	(7)
A-8 Linear Equations and Inequalities in One Variable	1062	(10)
A-9 Quadratic Equations	1072	(11)
APPENDIX B Special Topics	1083	(62)
B-1 Sequences, Series, and Summation Notation	1083	(7)
B-2 Arithmetic and Geometric Sequences	1090	(8)
B-3 The Binomial Theorem	1098	(3)
B-4 Increments and Differentials	1101	(8)
B-5 L'Hopital's Rule	1109	(11)
B-6 Double Integrals over More General Regions	1120	(9)
B-7 Interpolating Polynomials and Divided Differences	1129	(16)
APPENDIX C Tables	1145	(1)
Table I Basic Geometric Formulas	1145	(2)
Table II Integration Formulas	1147	(3)
Table III Area under the Standard Normal Curve	1150
Answers	1	(1)
Index	1