Calculus for Business, Economics, Life Sciences, and Social Sciences

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

• ISBN13: 9780130920539
• ISBN10: 0130920533
• Edition: 9th
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Pearson College Div

Summary

This book covers calculus with an emphasis on cross-discipline principles and practices. Designed to be both reader-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Each chapter concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving. Two-part coverage presents a library of elementary functions and calculus. For individuals looking for a view of mathematical ideas and processes, and an illustration of the relevance of mathematics to the real world.

Table of Contents

Preface	xiii
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 Exponental and Polynomial Functions, and Logarithmic and Root Functions	125	(1)
Group Activity 2: Comparing Regression Models	125	(4)
Part Two Calculus	129	(452)
The Derivative	131	(94)
Rate of Change and Slope	132	(12)
Limits	144	(18)
The Derivative	162	(13)
Derivatives of Constants, Power Forms, and Sums	175	(14)
Derivatives of Products and Quotients	189	(8)
Chain Rule: Power Form	197	(7)
Marginal Analysis in Business and Economics	204	(21)
Important Terms and Symbols	216	(1)
Summary of Rules of Differentiation	216	(1)
Review Exercise	217	(4)
Group Activity 1: Minimal Average Cost	221	(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility	222	(3)
Graphing and Optimization	225	(90)
Continuity and Graphs	226	(16)
First Derivative and Graphs	242	(17)
Second Derivative and Graphs	259	(16)
Curve Sketching Techniques: Unified and Extended	275	(17)
Optimization: Absolute Maxima and Minima	292	(23)
Important Terms and Symbols	308	(1)
Review Exercise	309	(4)
Group Activity 1: Maximizing Profit	313	(1)
Group Activity 2: Minimizing Construction Costs	313	(2)
Additional Derivative Topics	315	(48)
The Constant e and Continuous Compound Interest	315	(7)
Derivatives of Logarithmic and Exponential Functions	322	(12)
Chain Rule: General Form	334	(11)
Implicit Differentiation	345	(7)
Related Rates	352	(11)
Important Terms and Symbols	358	(1)
Additional Rules of Differentiation	358	(1)
Review Exercise	358	(2)
Group Activity 1: Elasticity of Demand	360	(1)
Group Activity 2: Point of Diminishing Returns	361	(2)
Integration	363	(82)
Antiderivatives and Indefinite Integrals	363	(15)
Integration by Substitution	378	(12)
Differential Equations; Growth and Decay	390	(11)
Geometric--Numeric Introduction to the Definite Integral	401	(16)
Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus	417	(28)
Important Terms and Symbols	435	(1)
Integration Formulas and Properties	436	(1)
Review Exercise	436	(4)
Group Activity 1: Simpson's Rule	440	(3)
Group Activity 2: Bell-Shaped Curves	443	(2)
Additional Integration Topics	445	(44)
Area Between Curves	445	(11)
Applications in Business and Economics	456	(13)
Integration by Parts	469	(8)
Integration Using Tables	477	(12)
Important Terms and Symbols	484	(1)
Review Exercise	485	(2)
Group Activity 1: Analysis of Income Concentration from Raw Data	487	(1)
Group Activity 2: Grain Exchange	488	(1)
Multivariable Calculus	489	(68)
Functions of Several Variables	489	(11)
Partial Derivatives	500	(9)
Maxima and Minima	509	(9)
Maxima and Minima Using Lagrange Multipliers	518	(10)
Method of Least Squares	528	(11)
Double Integrals over Rectangular Regions	539	(18)
Important Terms and Symbols	549	(1)
Review Exercise	550	(3)
Group Activity 1: City Planning	553	(1)
Group Activity 2: Numerical Integration of Multivariable Functions	554	(3)
Trigonometric Functions	557	(24)
Trigonometric Functions Review	558	(8)
Derivatives of Trigonometric Functions	566	(6)
Integration of Trigonometric Functions	572	(9)
Important Terms and Symbols	577	(1)
Review Exercise	578	(1)
Group Activity 1: Seasonal Business Cycles	579	(1)
Group Activity 2: Heating Degree Days	580	(1)
APPENDIX A Basic Algebra Review	581	(68)
Self-Test on Basic Algebra	581	(2)
A-1 Sets	583	(6)
A-2 Algebra and Real Numbers	589	(7)
A-3 Operations on Polynomials	596	(7)
A-4 Factoring Polynomials	603	(6)
A-5 Operations on Rational Expressions	609	(6)
A-6 Integer Exponents and Scientific Notation	615	(6)
A-7 Rational Exponents and Radicals	621	(7)
A-8 Linear Equations and Inequalities in One Variable	628	(10)
A-9 Quadratic Equations	638	(11)
APPENDIX B Special Topics	649	(20)
B-1 Sequences, Series, and Summation Notation	649	(7)
B-2 Arithmetic and Geometric Sequences	656	(8)
B-3 The Binomial Theorem	664	(5)
APPENDIX C Tables	669	(1)
Table I Basic Geometric Formulas	669	(2)
Table II Integration Formulas	671
Answers	A1
Index	I1