Mathematical Applications for Management

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

• ISBN13: 9780395961421
• ISBN10: 0395961424
• Edition: 6th
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Cengage Learning

Table of Contents

Preface	xiii
Algebraic Concepts	1	(63)
Sets	2	(7)
The Real Numbers	9	(7)
Integral Exponents	16	(6)
Radicals and Rational Exponents	22	(9)
Operations with Algebraic Expressions	31	(10)
Factoring	41	(6)
Algebraic Fractions	47	(17)
Key Terms and Formulas	55	(2)
Review Exercises	57	(2)
Chapter Test	59	(2)
Extended Applications/Group Projects:	61	(3)
Linear Equations and Functions	64	(82)
Warm-up	64	(2)
Solution of Linear Equations in One Variable	66	(9)
Functions	75	(16)
Linear Functions	91	(11)
Graphs and Graphing Utilities	102	(9)
Solutions of Systems of Linear Equations	111	(12)
Applications of Functions in Business and Economics	123	(23)
Key Terms and Formulas	135	(2)
Review Exercises	137	(4)
Chapter Test	141	(2)
Extended Applications/Group Projects:	143	(3)
Special Functions	146	(66)
Warm-up	146	(2)
Quadratic Equations	148	(10)
Quadratic Functions; Parabolas	158	(9)
Business Applications of Quadratic Functions	167	(9)
Special Functions and Their Graphs	176	(14)
Modeling; Fitting Curves to Data with Graphing Utilities (optional)	190	(22)
Key Terms and Formulas	202	(1)
Review Exercises	203	(3)
Chapter Test	206	(3)
Extended Applications/Group Projects:	209	(3)
Matrices	212	(84)
Warm-up	212	(2)
Matrices	214	(13)
Multiplication of Matrices	227	(15)
Gauss-Jordan Elimination: Solving Systems of Equations	242	(16)
Inverse of a Square Matrix; Matrix Equations	258	(14)
Applications of Matrices: Leontief Input-Output Models	272	(24)
Key Terms and Formulas	287	(1)
Review Exercises	288	(3)
Chapter Test	291	(2)
Extended Applications/Group Projects:	293	(3)
Inequalities and Linear Programming	296	(82)
Warm-up	296	(2)
Linear Inequalities in One Variable	298	(7)
Linear Inequalities in Two Variables	305	(9)
Linear Programming: Graphical Methods	314	(14)
The Simplex Method: Maximization	328	(18)
The Simplex Method: Duality and Minimization	346	(10)
The Simplex Method with Mixed Constraints	356	(22)
Key Terms and Formulas	367	(1)
Review Exercises	367	(3)
Chapter Test	370	(2)
Extended Applications/Group Projects:	372	(6)
Exponential and Logarithmic Functions	378	(50)
Warm-up	378	(2)
Exponential Functions	380	(13)
Logarithmic Functions and Their Properties	393	(14)
Solution of Exponential Equatios; Applications of Exponential and Logarithmic Functions	407	(21)
Key Terms and Formulas	419	(1)
Review Exercises	419	(3)
Chapter Test	422	(3)
Extended Applications/Group Projects	425	(3)
Mathematics of Finance	428	(68)
Warm-up	428	(2)
Simple Interest; Sequences	430	(9)
Compound Interest; Geometric Sequences	439	(17)
Future Value of Annuities	456	(11)
Present Value of Annuities	467	(11)
Loans and Amortization	478	(18)
Key Terms and Formulas	487	(1)
Review Exercises	488	(3)
Chapter Test	491	(2)
Extended Applications/Group Projects	493	(3)
Introduction to Probability	496	(74)
Warm-up	496	(2)
Probability; Odds	498	(11)
Unions and Intersections of Events; One-Trial Experiments	509	(9)
Conditional Probability; The Product Rule	518	(12)
Probability Trees and Bayes' Formula	530	(11)
Counting; Permutations and Combinations	541	(6)
Permutations, Combinations, and Probability	547	(7)
Markov Chains	554	(16)
Key Terms and Formulas	562	(1)
Review Exercises	563	(2)
Chapter Test	565	(2)
Extended Applications/Group Projects	567	(3)
Further Topics in Probability; Statistics	570	(52)
Warm-up	570	(2)
Binomial Probability Experiments	572	(5)
Discrete Probability Distributions; Decision Making	577	(8)
The Binomial Distribution	585	(6)
Descriptive Statistics	591	(13)
Normal Probability Distribution	604	(18)
Key Terms and Formulas	613	(1)
Review Exercises	614	(2)
Chapter Test	616	(3)
Extended Applications/Group Projects	619	(3)
Derivatives	622	(110)
Warm-up	622	(2)
Limits	624	(18)
Continuous Functions; Limits at Infinity	642	(14)
The Derivative; Rates of Change; Tangent to a Curve	656	(15)
Derivative Formulas	671	(13)
Product and Quotient Rules	684	(9)
The Chain Rule and Power Rule	693	(9)
Using Derivative Formulas	702	(6)
Higher-Order Derivatives	708	(8)
Applications of Derivatives in Business and Economics	716	(16)
Key Terms and Formulas	724	(1)
Review Exercises	725	(3)
Chapter Test	728	(1)
Extended Applications/Group Projects	729	(3)
Applications of Derivatives	732	(78)
Warm-up	732	(2)
Relative Maxima and Minima; Curve Sketching	734	(17)
Concavity; Points of Inflection	751	(14)
Optimization in Business and Economics	765	(13)
Applications of Maxima and Minima	778	(10)
Asymptotes; More Curve Sketching	788	(22)
Key Terms and Formulas	801	(1)
Review Exercises	801	(4)
Chapter Test	805	(2)
Extended Applications/Group Projects	807	(3)
Derivatives Continued	810	(52)
Warm-up	810	(2)
Derivatives of Logarithmic Functions	812	(8)
Derivatives of Exponential Functions	820	(8)
Implicit Differentiation	828	(10)
Related Rates	838	(7)
Applications in Business and Economics	845	(17)
Key Terms and Formulas	855	(1)
Review Exercises	856	(2)
Chapter Test	858	(1)
Extended Applications/Group Projects	859	(3)
Indefinite Integrals	862	(58)
Warm-up	862	(2)
The Indefinite Integral	864	(9)
The Power Rule	873	(10)
Integrals Involving Logarithmic and Exponential Functions	883	(10)
Applications of the Indefinite Integral in Business and Economics	893	(9)
Differential Equations	902	(18)
Key Terms and Formulas	913	(1)
Review Exercises	914	(2)
Chapter Test	916	(1)
Extended Applications/Group Projects	917	(3)
Definite Integrals; Techniques of Integration	920	(76)
Warm-up	920	(2)
Area Under a Curve	922	(10)
The Definite Integral; The Fundamental Theorem of Calculus	932	(10)
Area Between Two Curves	942	(12)
Applications of Definite Integrals in Business and Economics	954	(12)
Using Tables of Integrals	966	(5)
Integration by Parts	971	(7)
Improper Integrals and Their Applications	978	(18)
Key Terms and Formulas	987	(2)
Review Exercises	989	(1)
Chapter Test	990	(3)
Extended Applications/Group Projects	993	(3)
Functions of Two or More Variables	996
Warm-up	996	(2)
Functions of Two or More Variables	998	(7)
Partial Differentiation	1005	(11)
Applications of Functions of Two Variables in Business and Economics	1016	(8)
Maxima and Minima	1024	(11)
Maxima and Minima of Functions Subject to Constraints; Lagrange Multipliers	1035
Key Terms and Formulas	1043	(1)
Review Exercises	1043	(3)
Chapter Test	1046	(1)
Extended Applications/Group Projects	1047
Appendix: Areas Under the Standard Normal Curve	AP-1	(1)
Answers	A-1	(1)
Index	I-1	(1)
Credits	I-1