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

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

• ISBN13: 9780073040189
• ISBN10: 0073040185
• Edition: 7th
• Format: Hardcover
• Copyright: 1999-10-04
• Publisher: McGraw-Hill Higher Education

Summary

This text is written for students preparing for a career in business, economics, psychology, sociology, architecture, or the life, social, environmental, or physical sciences. It is assumed that these students have completed high school algebra. This text's primary goal is to teach the techniques of differential and integral calculus that students are likely to encounter in undergraduate courses in their majors and in subsequent professional activities. The exposition is designed to provide a sound, intuitive understanding of the basic concepts of calculus without sacrificing mathematical accuracy. Thus, the main results are stated carefully and completely, and whenever possible, explanations are intuitive or geometric.

Table of Contents

Preface	ix
Functions, Graphs, and Limits
Functions	2	(14)
The Graph of a Function	16	(13)
Linear Functions	29	(17)
Functional Models	46	(15)
Limits	61	(13)
Continuity	74	(24)
Summary and Review Problems	84	(14)
Differentiation: Basic Concepts
The Derivative: Slope and Rates	98	(11)
Techniques of Differentiation	109	(13)
The Product and Quotient Rules	122	(11)
Marginal Analysis: Approximation by Increments	133	(15)
The Chain Rule	148	(13)
The Second Derivative	161	(9)
Implicit Differentiation and Related Rates	170	(26)
Summary and Review Problems	183	(13)
Additional Applications of the Derivative
Increasing and Decreasing Functions	196	(15)
Concavity	211	(15)
Limits Involving Infinity: Asymptotes	226	(18)
Optimization	244	(17)
Practical Optimization	261	(37)
Summary and Review Problems	283	(15)
Exponential and Logarithmic Functions
Exponential Functions	298	(16)
Logarithmic Functions	314	(17)
Differentiation of Logarithmic and Exponential Functions	331	(12)
Additional Exponential Models	343	(29)
Summary and Review Problems	357	(15)
Integration
Antidifferentiation: The Indefinite Integral	372	(14)
Integration by Substitution	386	(12)
Introduction to Differential Equations	398	(12)
Integration by Parts	410	(18)
Summary and Review Problems	417	(11)
Further Topics in Integration
Definite Integration	428	(14)
Applications to Business and Economics	442	(18)
Additional Applications of Definite Integration	460	(12)
Improper Integrals	472	(30)
Summary and Review Problems	488	(14)
Calculus of Several Variables
Functions of Several Variables	502	(17)
Partial Derivatives	519	(14)
Optimizing Functions of Two Variables	533	(18)
Constrained Optimization: The Method of Lagrange Multipliers	551	(18)
Double Integrals over Rectangular Regions	569	(22)
Summary and Review Problems	580	(11)
Appendix
A1 Algebra Review	591	(14)
A2 Factoring Polynomials and Solving Systems of Equations	605	(16)
Tables
I Powers of e	621	(1)
II The Natural Logarithm (Base e)	622	(1)
III Trigonometric Functions	623	(1)
Add to Odd-numbered Problems and Review Problems	624	(89)
Index	713