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Tables of Contents for Applied Calculus With Infotrac
Chapter/Section Title
Page #
Page Count
Chapter 1 FUNCTIONS AND LINEAR MODELS
2
78
1.1 Functions from the Numerical and Algebraic Viewpoints
3
14
1.2 Functions from the Graphical Viewpoint
17
13
1.3 Linear Functions
30
11
1.4 Linear Models
41
18
1.5 Linear Regression
59
15
Case Study: Modeling Spending on Internet Advertising
74
6
Optional Internet Topic:
New functions from Old: Scaled and Shifted Functions
Chapter 2 NONLINEAR MODELS
80
58
2.1 Quadratic Functions and Models
81
13
2.2 Exponential Functions and Models
94
16
2.3 Logarithmic Functions and Models
110
11
2.4 Logistic Functions and Models
121
12
Case Study: Checking Up on Malthus
133
5
Optional Internet Topics:
Inverse Functions
Linear and Exponential Regression
Using and Deriving Algebraic Properties of Logarithms
Chapter 3 INTRODUCTION TO THE DERIVATIVE
138
102
3.1 Average Rate of Change
139
15
3.2 The Derivative: Numerical and Graphical Viewpoints
154
23
3.3 The Derivative: Algebraic Viewpoint
177
9
3.4 Derivatives of Powers, Sums, and Constant Multiples
186
12
3.5 A First Application: Marginal Analysis
198
11
3.6 Limits: Numerical & Graphical Approaches (Optional)
209
10
3.7 Limits and Continuity (Optional)
219
6
3.8 Limits and Continuity: Algebraic Approach (Optional)
225
10
Case Study: Reducing Sulfur Emissions
235
5
Optional Internet Topics:
Proof of the Power Rule
Sketching the Graph of the Derivative Continuity and Differentiability
Chapter 4 TECHNIQUES OF DIFFERENTATION
240
50
4.1 The Product and Quotient Rules
241
10
4.2 The Chain Rule
251
10
4.3 Derivatives of Logarithmic and Exponential Functions
261
12
4.4 Implicit Differentiation
273
7
Case Study: Projecting Market Growth
280
10
Optional Internet Topic:
Linear Approximation and Error Estimation
Chapter 5 APPLICATIONS OF THE DERIVATIVE
290
62
5.1 Maxima and Minima
291
13
5.2 Applications of Maxima and Minima
304
13
5.3 The Second Derivative and Analyzing Graphs
317
12
5.4 Related Rates
329
8
5.5 Elasticity
337
9
Case Study: Production Lot-Size Management
346
6
Chapter 6 THE INTEGRAL
352
56
6.1 The Indefinite Integral
353
11
6.2 Substitution
364
9
6.3 The Definite Integral as a Sum: A Numerical Approach
373
11
6.4 The Definite Integral as Area: A Geometric Approach
384
7
6.5 The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus
391
12
Case Study: Wage Inflation
403
5
Optional Internet Topic:
Numerical Integration
Chapter 7 FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL
408
58
7.1 Integration by Parts
409
7
7.2 Area between Two Curves and Applications
416
14
7.3 Averages and Moving Averages
430
8
7.4 Continuous Income Streams
438
4
7.5 Improper Integrals and Applications
442
8
7.6 Differential Equations and Applications
450
8
Case Study: Estimating Tax Revenues
458
8
Chapter 8 FUNCTIONS OF SEVERAL VARIABLES
466
72
8.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints
467
12
8.2 Three-Dimensional Space and the Graph of a Function of Two Variables
479
11
8.3 Partial Derivatives
490
8
8.4 Maxima and Minima
498
10
8.5 Constrained Maxima and Minima and Applications
508
10
8.6 Double Integrals
518
9
Case Study: Modeling Household Income
527
11
Chapter 9 TRIGONOMETRIC MODELS
538
 
9.1 Trigonometric Functions, Models, and Regression
539
16
9.2 Derivatives of Trigonometric Functions and Applications
555
8
9.3 Integrals of Trigonometric Functions and Applications
563
6
Case Study: Predicting Cocoa inventories
569
3080623
Chapter S CALCULUS APPLIED TO PROBABILITY AND STATISTICS OPTIONAL INTERNET TOPIC
S.1 Continuous Random Variables and Histograms
S.2 Probability Density Functions: Uniform, Exponential, Normal, and Beta
S.3 Mean, Median, Variance and Standard Deviation
Case Study: Creating a Family Trust
Appendix A ALGEBRA REVIEW
A1
 
A.1 Real Numbers
A1
 
A.2 Exponents and Radicals
A6
 
A.3 Multiplying and Factoring Algebraic Equations
A16
 
A.4 Rational Expressions
A20
 
A.5 Solving Polynomial Equations
A22
 
A.6 Solving Miscellaneous Equations
A28
 
ANSWERS TO SELECTED EXERCISES
A33
 
INDEX
A65