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

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

• ISBN13: 9780130797681
• ISBN10: 0130797685
• Edition: 8th
• Format: Hardcover
• Copyright: 1998-12-01
• Publisher: Prentice Hall

Summary

This text is a compilation of Calculus and Finite Mathematics by Barnett/Ziegler. One or two semester format.

Table of Contents

Preface	ix
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS	1	(126)
Chapter 1 A Beginning Library of Elementary Functions	3	(74)
1-1 Functions	3	(20)
1-2 Elementary Functions: Graphs and Transformations	23	(13)
1-3 Linear Functions and Straight Lines	36	(16)
1-4 Quadratic Functions	52	(15)
Important Terms and Symbols	67	(1)
Review Exercise	68	(4)
Group Activity 1: Introduction to Regression Analysis	72	(2)
Group Activity 2: Mathematical Modeling in Business	74	(3)
Chapter 2 Additional Elementary Functions	77	(50)
2-1 Polynomial and Rational Functions	77	(16)
2-2 Exponential Functions	93	(14)
2-3 Logarithmic Functions	107	(13)
Important Terms and Symbols	120	(1)
Review Exercise	120	(3)
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions	123	(1)
Group Activity 2: Comparing Regression Models	124	(3)
PART TWO FINITE MATHEMATICS	127	(384)
Chapter 3 Mathematics of Finance	129	(46)
3-1 Simple Interest	129	(6)
3-2 Compound Interest	135	(14)
3-3 Future Value of an Annuity; Sinking Funds	149	(7)
3-4 Present Value of an Annuity; Amortization	156	(12)
Important Terms and Symbols	168	(1)
Review Exercise	168	(3)
Group Activity 1: Reducing Interest Payments on a Home Mortgage	171	(1)
Group Activity 2: Yield to Maturity and Internal Rate of Return	172	(3)
Chapter 4 Systems of Linear Equations: Matrices	175	(90)
4-1 Review: Systems of Linear Equations in Two Variables	176	(13)
4-2 Systems of Linear Equations and Augmented Matrices	189	(10)
4-3 Gauss-Jordan Elimination	199	(15)
4-4 Matrices: Basic Operations	214	(13)
4-5 Inverse of a Square Matrix	227	(12)
4-6 Matrix Equations and Systems of Linear Equations	239	(11)
4-7 Leontief Input-Output Analysis	250	(8)
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)
Chapter 5 Linear Inequalities and Linear Programming	265	(100)
5-1 Systems of Linear Inequalities in Two Variables	265	(14)
5-2 Linear Programming in Two Dimensions--A Geometric Approach	279	(15)
5-3 A Geometric Introduction to the Simplex Method	294	(8)
5-4 The Simplex Method: Maximization with Problem Constraints of the Form less than or equal to	302	(20)
5-5 The Dual; Minimization with Problem Constraints of the Form greater than or equal to	322	(17)
5-6 Maximization and Minimization with Mixed Problem Constraints	339	(19)
Important Terms and Symbols	358	(1)
Review Exercise	359	(2)
Group Activity 1: The Two-Phase Method (An Alternative to the Big M Method)	361	(3)
Group Activity 2: Production Scheduling	364	(1)
Chapter 6 Probability	365	(98)
6-1 Basic Counting Principles	366	(10)
6-2 Permutations and Combinations	376	(13)
6-3 Sample Spaces, Events, and Probability	389	(16)
6-4 Union, Intersection, and Complement of Events; Odds	405	(15)
6-5 Conditional Probability, Intersection, and Independence	420	(16)
6-6 Bayes' Formula	436	(7)
6-7 Random Variable, Probability Distribution, and Expected Value	443	(10)
Important Terms and Symbols	453	(1)
Review Exercise	454	(5)
Group Activity 1: Car and Crying Towels	459	(1)
Group Activity 2: Simulation-A Draft Lottery for Professional Sports	460	(3)
Chapter 7 Markov Chains	463	(48)
7-1 Properties of Markov Chains	463	(13)
7-2 Regular Markov Chains	476	(12)
7-3 Absorbing Markov Chains	488	(16)
Important Terms and Symbols	504	(1)
Review Exercise	504	(4)
Group Activity 1: Social Mobility	508	(1)
Group Activity 2: Gambler's Ruin	509	(2)
PART THREE CALCULUS	511	(432)
Chapter 8 The Derivative	513	(92)
8-1 Rate of Change and Slope	514	(13)
8-2 Limits	527	(17)
8-3 The Derivative	544	(13)
8-4 Derivatives of Constants, Power Forms, and Sums	557	(13)
8-5 Derivatives of Products and Quotients	570	(8)
8-6 Chain Rule: Power Form	578	(8)
8-7 Marginal Analysis in Business and Economics	586	(11)
Important Terms and Symbols	597	(1)
Summary of Rules of Differentiation	598	(1)
Review Exercise	598	(5)
Group Activity 1: Minimal Average Cost	603	(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility	604	(1)
Chapter 9 Graphing and Optimization	605	(90)
9-1 Continuity and Graphs	606	(16)
9-2 First Derivative and Graphs	622	(17)
9-3 Second Derivative and Graphs	639	(16)
9-4 Curve Sketching Techniques: Unified and Extended	655	(16)
9-5 Optimization; Absolute Maxima and Minima	671	(16)
Important Terms and Symbols	687	(1)
Review Exercise	688	(4)
Group Activity 1: Maximizing Profit	692	(1)
Group Activity 2: Minimizing Construction Costs	692	(3)
Chapter 10 Additional Derivative Topics	695	(50)
10-1 The Constant e and Continuous Compound Interest	695	(8)
10-2 Derivatives of Logarithmic and Exponential Functions	703	(12)
10-3 Chain Rule: General Form	715	(12)
10-4 Implicit Differentiation	727	(7)
10-5 Related Rates	734	(6)
Important Terms and Symbols	740	(1)
Additional Rules of Differentiation	740	(1)
Review Exercise	741	(2)
Group Activity 1: Elasticity of Demand	743	(1)
Group Activity 2: Point of Diminishing Returns	744	(1)
Chapter 11 Integration	745	(84)
11-1 Antiderivatives and Indefinite Integrals	745	(15)
11-2 Integration by Substitution	760	(12)
11-3 Differential Equations-Growth and Decay	772	(12)
11-4 A Geometric-Numeric Introduction to the Definite Integral	784	(16)
11-5 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus	800	(19)
Important Terms and Symbols	819	(1)
Integration Formulas and Properties	819	(1)
Review Exercise	819	(5)
Group Activity 1: Simpson's Rule	824	(3)
Group Activity 2: Bell-Shaped Curves	827	(2)
Chapter 12 Additional Integration Topics	829	(46)
12-1 Area between Curves	829	(12)
12-2 Applications in Business and Economics	841	(13)
12-3 Integration by Parts	854	(7)
12-4 Integration Using Tables	861	(8)
Important Terms and Symbols	869	(1)
Review Exercise	869	(2)
Group Activity 1: Analysis of Income Concentration from Raw Data	871	(2)
Group Activity 2: Grain Exchange	873	(2)
Chapter 13 Multivariable Calculus	875	(68)
13-1 Functions of Several Variables	875	(10)
13-2 Partial Derivatives	885	(10)
13-3 Maxima and Minima	895	(9)
13-4 Maxima and Minima Using Lagrange Multipliers	904	(10)
13-5 Method of Least Squares	914	(11)
13-6 Double Integrals Over Rectangular Regions	925	(11)
Important Terms and Symbols	936	(1)
Review Exercise	936	(3)
Group Activity 1: City Planning	939	(1)
Group Activity 2: Numerical Integration of Multivariable Functions	940	(3)
Appendix A Basic Algebra Review	943	(68)
Self-Test on Basic Algebra	943	(2)
A-1 Sets	945	(6)
A-2 Algebra and Real Numbers	951	(7)
A-3 Operations on Polynomials	958	(7)
A-4 Factoring Polynomials	965	(6)
A-5 Operations on Rational Expressions	971	(7)
A-6 Integer Exponents and Scientific Notation	978	(6)
A-7 Rational Exponents and Radicals	984	(7)
A-8 Linear Equations and Inequalities in One Variable	991	(10)
A-9 Quadratic Equations	1001	(10)
Appendix B Special Topics	1011	(18)
B-1 Sequences, Series, and Summation Notation	1011	(6)
B-2 Arithmetic and Geometric Sequences	1017	(8)
B-3 The Binomial Theorem	1025	(4)
Appendix C Tables	1029
Table I Basic Geometric Formulas	1029	(2)
Table II Integration Formulas	1031
Answers	A-1
Index	I-1
Library of Elementary Functions	Inside front cover
Applications Index	Inside back cover