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

by Hoffmann, Laurence D.; Bradley, Gerald L.

• ISBN13: 9780071143110
• ISBN10: 0071143114
• Format: Paperback
• Copyright: 2000-04-01
• Publisher: McGraw-Hill

Table of Contents

Index of Selected Applications	xi
Preface	xv
Functions, Graphs, and Limits
Functions	2	(13)
The Graph of a Function	15	(16)
Linear Functions	31	(15)
Functional Models	46	(18)
Limits and Continuity	64	(17)
Limits Involving Infinity; Asymptotes	81	(16)
Chapter Summary and Review Problems	88	(9)
Differentiation: Basic Concepts
The Derivative	97	(13)
Techniques of Differentiation	110	(11)
The Derivative as a Rate of Change	121	(12)
Approximation by Differentials; Marginal Analysis	133	(11)
The Chain Rule	144	(12)
Implicit Differentiation and Related Rates	156	(12)
Higher-Order Derivatives	168	(18)
Chapter Summary and Review Problems	176	(10)
Additional Applications of the Derivative
Relative Extrema; Curve Sketching with the First Derivative	186	(14)
More on Curve Sketching; Concavity and the Second Derivative Test	200	(17)
Absolute Maxima and Minima	217	(14)
Practical Optimization Problems	231	(15)
Applications to Business and Economics	246	(29)
Chapter Summary and Review Problems	266	(9)
Exponential and Logarithmic Functions
Exponential Functions	275	(12)
Exponential Models	287	(9)
The Natural Logarithm	296	(14)
Differentiation of Logarithmic and Exponential Functions	310	(17)
Applications Involving Compound Interest	327	(26)
Chapter Summary and Review Problems	340	(13)
Integration
Antidifferentiation: The Indefinite Integral	353	(19)
Integration by Substitution	372	(14)
Area and the Definite Integral	386	(12)
Applications to Business and Economics	398	(15)
Integration by Parts; Integral Tables	413	(29)
Chapter Summary and Review Problems	429	(13)
Further Topics in Integration
The Definite Integral as the Limit of a Sum	442	(17)
Improper Integrals	459	(10)
Probability Density Functions	469	(16)
Numerical Integration	485	(22)
Chapter Summary and Review Problems	497	(10)
Functions of Two Variables
Functions of Two Variables; Surfaces and Level Curves	507	(15)
Partial Derivatives	522	(11)
The Chain Rule; Approximation by the Total Differential	533	(14)
Relative Maxima and Minima	547	(12)
Lagrange Multipliers	559	(16)
The Method of Least Squares	575	(10)
Double Integrals	585	(12)
Applications of Double Integrals	597	(26)
Chapter Summary and Review Problems	609	(14)
Infinite Series and Taylor Approximation
Infinite Series	623	(10)
Additional Applications of Series; The Cobweb Model	633	(15)
Taylor Approximation	648	(22)
Chapter Summary and Review Problems	660	(10)
Trigonometric Functions
The Trigonometric Functions	670	(17)
Differentiation and Integration of Trigonometric Functions	687	(10)
Additional Applications Involving Trigonometric Functions	697	(27)
Chapter Summary and Review Problems	713	(11)
APPENDIX: ALGEBRA REVIEW
A1. A Brief Review of Algebra	724	(12)
A2. Factoring Polynomials and Solving Systems of Equations	736	(14)
TABLES
I. Powers of e	750	(1)
II. The Natural Logarithm (Base e)	751	(1)
III. Trigonometric Functions	752	(1)
Answers to Odd-numbered Problems and Review Problems	753	(85)
Index	838