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

ISBN: 9780130831293 | 0130831298
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 8/1/1999

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SummaryTable of Contents
Designed for students majoring in business, economics, social sciences, or life sciences, this mathematically correct, accessible, and student-friendly introduction to applied calculus prepares students to deal with calculus topics when they are encountered in other areas. The emphasis throughout is on computational skills, ideas, and problem solvingrather than on mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept, and general concepts and results are usually presented only after particular cases have been discussed.
Prefaceix
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS1(126)
Chapter 1 A Beginning Library of Elementary Functions
3(74)
1-1 Function... MORE
3(20)
1-2 Elementary Functions: Graphs and Transformations
23(13)
1-3 Linear Functions and Straight Lines
36(16)
1-4 Quadratic Functions
52(15)
Important Terms and Symbols
67(1)
Review Exercise
68(4)
Group Activity 1: Introduction to Regression Analysis
72(2)
Group Activity 2: Mathematical Modeling in Business
74(3)
Chapter 2 Additional Elementary Functions
77(50)
2-1 Polynomial and Rational Functions
77(16)
2-2 Exponential Functions
93(14)
2-3 Logarithmic Functions
107(13)
Important Terms and Symbols
120(1)
Review Exercise
120(3)
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions
123(1)
Group Activity 2: Comparing Regression Models
124(3)
PART TWO CALCULUS127(604)
Chapter 3 The Derivative
129(92)
3-1 Rate of Change and Slope
130(13)
3-2 Limits
143(17)
3-3 The Derivative
160(13)
3-4 Derivatives of Constants, Power Forms, and Sums
173(13)
3-5 Derivatives of Products and Quotients
186(8)
3-6 Chain Rule: Power Form
194(8)
3-7 Marginal Analysis in Business and Economics
202(11)
Important Terms and Symbols
213(1)
Summary of Rules of Differentiation
214(1)
Review Exercise
214(5)
Group Activity 1: Minimal Average Cost
219(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility
220(1)
Chapter 4 Graphing and Optimization
221(90)
4-1 Continuity and Graphs
222(16)
4-2 First Derivative and Graphs
238(17)
4-3 Second Derivative and Graphs
255(16)
4-4 Curve Sketching Techniques: Unified and Extended
271(16)
4-5 Optimization; Absolute Maxima and Minima
287(16)
Important Terms and Symbols
303(1)
Review Exercise
304(4)
Group Activity 1: Maximizing Profit
308(1)
Group Activity 2: Minimizing Construction Costs
308(3)
Chapter 5 Additional Derivative Topics
311(50)
5-1 The Constant e and Continuous Compound Interest
311(8)
5-2 Derivatives of Logarithmic and Exponential Functions
319(12)
5-3 Chain Rule: General Form
331(12)
5-4 Implicit Differentiation
343(7)
5-5 Related Rates
350(6)
Important Terms and Symbols
356(1)
Additional Rules of Differentiation
356(1)
Review Exercise
357(2)
Group Activity 1: Elasticity of Demand
359(1)
Group Activity 2: Point of Diminishing Returns
360(1)
Chapter 6 Integration
361(84)
6-1 Antiderivatives and Indefinite Integrals
361(15)
6-2 Integration by Substitution
376(12)
6-3 Differential Equations--Growth and Decay
388(12)
6-4 A Geometric-Numeric Introduction to the Definite Integral
400(16)
6-5 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus
416(19)
Important Terms and Symbols
435(1)
Integration Formulas and Properties
435(1)
Review Exercise
435(5)
Group Activity 1: Simpson's Rule
440(3)
Group Activity 2: Bell-Shaped Curves
443(2)
Chapter 7 Additional Integration Topics
445(46)
7-1 Area between Curves
445(12)
7-2 Applications in Business and Economics
457(13)
7-3 Integration by Parts
470(7)
7-4 Integration Using Tables
477(8)
Important Terms and Symbols
485(1)
Review Exercise
485(2)
Group Activity 1: Analysis of Income Concentration from Raw Data
487(2)
Group Activity 2: Grain Exchange
489(2)
Chapter 8 Multivariable Calculus
491(68)
8-1 Functions of Several Variables
491(10)
8-2 Partial Derivatives
501(10)
8-3 Maxima and Minima
511(9)
8-4 Maxima and Minima Using Lagrange Multipliers
520(10)
8-5 Method of Least Squares
530(11)
8-6 Double Integrals Over Rectangular Regions
541(11)
Important Terms and Symbols
552(1)
Review Exercise
552(3)
Group Activity 1: City Planning
555(1)
Group Activity 2: Numerical Integration of Multivariable Functions
556(3)
Chapter 9 Differential Equations
559(46)
9-1 Basic Concepts
559(12)
9-2 Separation of Variables
571(12)
9-3 First-Order Linear Differential Equations
583(12)
Important Terms and Symbols
595(1)
Review Exercise
595(2)
Group Activity 1: Torricelli's Law
597(2)
Group Activity 2: Euler's Method
599(6)
Chapter 10 Taylor Polynomials and Infinite Series
605(52)
10-1 Taylor Polynomials
605(15)
10-2 Taylor Series
620(11)
10-3 Operations on Taylor Series
631(9)
10-4 Approximations Using Taylor Series
640(11)
Important Terms and Symbols
651(1)
Review Exercise
651(2)
Group Activity 1: L'Hopital's Rule
653(2)
Group Activity 2: Taylor Series Solutions to Differential Equations
655(2)
Chapter 11 Probability and Calculus
657(48)
11-1 Improper Integrals
657(8)
11-2 Continuous Random Variables
665(13)
11-3 Expected Value, Standard Deviation, and Median
678(10)
11-4 Special Probability Distributions
688(12)
Important Terms and Symbols
700(1)
Review Exercise
700(3)
Group Activity 1: Beta Distributions
703(1)
Group Activity 2: Chi-Square Distributions
704(1)
Chapter 12 Trigonometric Functions
705(26)
12-1 Trigonometric Functions Review
706(9)
12-2 Derivatives of Trigonometric Functions
715(6)
12-3 Integration of Trigonometric Functions
721(5)
Important Terms and Symbols
726(1)
Review Exercise
727(1)
Group Activity 1: Seasonal Business Cycles
728(1)
Group Activity 2: Heating Degree Days
729(2)
Appendix A Basic Algebra Review
731(68)
Self-Test on Basic Algebra
731(2)
A-1 Sets
733(6)
A-2 Algebra and Real Numbers
739(7)
A-3 Operations on Polynomials
746(7)
A-4 Factoring Polynomials
753(6)
A-5 Operations on Rational Expressions
759(7)
A-6 Integer Exponents and Scientific Notation
766(6)
A-7 Rational Exponents and Radicals
772(7)
A-8 Linear Equations and Inequalities in One Variable
779(10)
A-9 Quadratic Equations
789(10)
Appendix B Special Topics
799(48)
B-1 Sequences, Series, and Summation Notation
799(6)
B-2 Arithmetic and Geometric Sequences
805(8)
B-3 The Binomial Theorem
813(4)
B-4 Increments and Differentials
817(8)
B-5 L'Hopital's Rule
825(11)
B-6 Double Integrals Over More General Regions
836(11)
Appendix C Tables
847
Table I Basic Geometric Formulas
847(2)
Table II Integration Formulas
849(4)
Table III Area Under the Standard Normal Curve
853
AnswersA-1
IndexI-1
Library of Elementary FunctionsInside front cover
Applications IndexInside back cover

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