Applied Calculus / Edition 6

Applied Calculus / Edition 6

ISBN-10:
0135732131
ISBN-13:
9780135732137
Pub. Date:
08/28/1996
Publisher:
Prentice Hall Professional Technical Reference

Hardcover

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Overview

Applied Calculus / Edition 6

This user-friendly survey of applied calculus prepares readers to deal with the calculus they may encounter while working in business, economics, life sciences, or social sciences. The emphasis throughout is on computational skills, ideas, and problem solving—rather than on mathematical theory. It features numerous worked, annotated, step-by-step examples and an abundance of applications, problems, and exercises for practice. The use of graphing calculators and computers is addressed throughout and web references lead readers to sites where they will find sources of real data for applications, further discussion of applications, further examples of topics, etc. A Beginning Library of Elementary Functions. Additional Elementary Functions. The Derivative. Graphing and Optimization. Additional Derivative Topics. Integration. Additional Integration Topics. Multivariable Calculus. Differential Equations. Taylor Polynomials and Infinite Series. Probability and Calculus. Trigonometric Functions. Basic Algebra Review. Special Topics. For anyone needing a solid introduction to the mathematics used in business, economics, life science, and social sciences.

Product Details

ISBN-13: 9780135732137
Publisher: Prentice Hall Professional Technical Reference
Publication date: 08/28/1996
Edition description: Older Edition
Pages: 839
Product dimensions: 8.26(w) x 9.50(h) x 1.41(d)

Table of Contents

Preface xi
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS 1(120)
A Beginning Library of Elementary Functions
3(72)
Functions
3(19)
Elementary Functions: Graphs and Transformations
22(11)
Linear Functions and Straight Lines
33(18)
Quadratic Functions
51(24)
Group Activity: Mathematical Modeling in Business
68(1)
Review
69(6)
Additional Elementary Functions
75(46)
Polynomial and Relational Functions
75(15)
Exponential Functions
90(14)
Logarithmic Functions
104(17)
Group Activity: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions
116(1)
Review
117(4)
PART TWO CALCULUS 121(632)
The Derivative
123(102)
Rate of Change and Slope
124(14)
Limits
138(20)
The Derivative
158(14)
Derivatives of Constants, Power Forms, and Sums
172(15)
Derivatives of Products and Quotients
187(9)
Chain Rule: Power Form
196(8)
Marginal Analysis in Business and Economics
204(21)
Group Activity: Minimal Average Cost
216(2)
Review
218(7)
Graphing and Optimization
225(98)
Continuity and Graphs
225(18)
First Derivative and Graphs
243(20)
Second Derivative and Graphs
263(18)
Curve Sketching Techniques: Unified and Extended
281(19)
Optimization; Absolute Maxima and Minima
300(23)
Group Activity: Maximizing Profit
317(1)
Review
317(6)
Additional Derivative Topics
323(52)
The Constant e and Continuous Compound Interest
323(8)
Derivatives of Logarithmic and Exponential Functions
331(12)
Chain Rule: General Form
343(13)
Implicit Differentiation
356(7)
Related Rates
363(12)
Group Activity: Increasing Production of Cellular Phones
370(1)
Review
371(4)
Integration
375(90)
Antiderivatives and Indefinite Integrals
375(16)
Integration by Substitution
391(13)
Differential Equations---Growth and Decay
404(14)
A Geometric--Numeric Introduction to the Definite Integral
418(18)
Definite Integrals as a Limit of a Sum; Fundamental Theorem of Calculus
436(29)
Group Activity: Bell-Shaped Curves
456(2)
Review
458(7)
Additional Integration Topics
465(46)
Area between Curves
465(12)
Applications in Business and Economics
477(14)
Integration by Parts
491(7)
Integration Using Tables
498(13)
Group Activity: Analysis of Income Concentration from Raw Data
506(1)
Review
507(4)
Multivariable Calculus
511(68)
Functions of Several Variables
511(10)
Partial Derivatives
521(10)
Maxima and Minima
531(9)
Maxima and Minima Using Lagrange Multipliers
540(11)
Method of Least Squares
551(11)
Double Integrals Over Rectangular Regions
562(17)
Group Activity: City Planning
574(1)
Review
574(5)
Differential Equations
579(44)
Basic Concepts
579(12)
Separation of Variables
591(13)
First-Order Linear Differential Equations
604(19)
Group Activity: Euler's Method
616(3)
Review
619(4)
Taylor Polynomials and Infinite Series
623(54)
Taylor Polynomials
623(16)
Taylor Series
639(12)
Operations on Taylor Series
651(11)
Approximations Using Taylor Series
662(15)
Group Activity: L'Hopital's Rule
672(2)
Review
674(3)
Probability and Calculus
677(50)
Improper Integrals
677(8)
Continuous Random Variables
685(14)
Expected Value, Standard Deviation, and Median
699(11)
Special Probability Distributions
710(17)
Group Activity: Beta Distributions
722(1)
Review
723(4)
Trigonometric Functions
727(26)
Trigonometric Functions Review
728(10)
Derivatives of Trigonometric Functions
738(6)
Integration of Trigonometric Functions
744(9)
Group Activity: Seasonal Business Cycles
749(1)
Review
750(3)
APPENDIX A Tables 753(1)
Table I Basic Geometric Formulas
753(3)
Table II Integration Formulas
756(5)
Table III Under the Standard Normal Curve
761(1)
Answers A-1(1)
Index I-1

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