Student Study Guide to accompany Applied Calculus, 2nd Edition

by Deborah Hughes-Hallett (Harvard Univ.); Ansie Meiring

• ISBN13: 9780471213611
• ISBN10: 0471213616
• Edition: 2nd
• Format: Paperback
• Copyright: 2002-10-01
• Publisher: Wiley

Summary

Work more effectively and gauge your progress along the way! This Student Study Guide is designed to accompany Hughes-Hallett's Applied Calculus, 2nd Edition. It is a step-by-step guide that walks students through the text as they read it and work problems while supporting the discovery approach. Achieving a fine balance between the concepts and procedures of calculus, Applied Calculus, 2nd Edition provides readers with the solid background they need in the subject with a thorough understanding of its applications in a wide range of fields - from biology to economics.

Table of Contents

Functions and Change	p. 1
What is a Function?	p. 2
Linear Functions	p. 4
Rates of Change	p. 6
Applications of Functions to Economics	p. 8
Exponential Functions	p. 11
The Natural Logarithm	p. 14
Exponential Growth and Decay	p. 17
New Functions From Old	p. 20
Proportionality, Power Functions and Polynomials	p. 21
Periodic Functions	p. 24
Review of Chapter 1	p. 26
Focus on Modeling	p. 29
Fitting Formulas to Data	p. 29
Compound Interest and the Number e	p. 31
Focus on Theory	p. 33
Limits to Infinity and end Behavior	p. 33
Rate of Change: The Derivative	p. 35
Instantaneous Rate of Change	p. 36
The Derivative Function	p. 40
Interpretations of the Derivative	p. 42
The Second Derivative	p. 45
Marginal Cost and Revenue	p. 48
Review of Chapter 2	p. 50
Focus on Theory	p. 52
Limits, Continuity, and the Definition of the Derivative	p. 52
Short-Cuts to Differentiation	p. 55
Derivative Formulas for Powers and Polynomials	p. 56
Exponential and Logarithmic Functions	p. 58
The Chain Rule	p. 60
The Product and Quotient Rules	p. 62
Derivatives of Periodic Functions	p. 63
Review of Chapter 3	p. 64
Focus on Theory	p. 66
Establishing Derivative Formulas	p. 66
Focus on Practice	p. 67
Differentiation	p. 67
Using the Derivative	p. 69
Local Maxima and Minima	p. 70
Inflection Points	p. 73
Global Maxima and Minima	p. 75
Profit, Cost, and Revenue	p. 77
Average Cost	p. 79
Elasticity of Demand	p. 81
Logistic Growth	p. 83
The Surge Function and Drug Concentration	p. 86
Review of Chapter 4	p. 88
Accumulated Change: The Definite Integral	p. 91
Accumulated Change	p. 92
The Definite Integral	p. 94
The Definite Integral as Area	p. 97
Interpretations of the Definite Integral	p. 100
The Fundamental Theorem of Calculus	p. 102
Review of Chapter 5	p. 103
Focus on Theory	p. 105
Theorems About Definite Integrals	p. 105
Using the Integral	p. 107
Average Value	p. 108
Consumer and Producer Surplus	p. 109
Present and Future Value	p. 111
Relative Growth Rates	p. 113
Review of Chapter 6	p. 115
Antiderivatives	p. 117
Constructing Antiderivatives Analytically	p. 118
Integration by Substitution	p. 120
Using the Fundamental Theorem to Find Definite Integrals	p. 121
Analyzing Antiderivatives Graphically and Numerically	p. 122
Review of Chapter 7	p. 124
Probability	p. 125
Density Functions	p. 126
Cumulative Distribution Functions and Probability	p. 127
The Median and the Mean	p. 129
Review of Chapter 8	p. 131
Functions of Several Variables	p. 133
Understanding Functions of Two Variables	p. 134
Contour Diagrams	p. 135
Partial Derivatives	p. 138
Computing Partial Derivatives Algebraically	p. 140
Critical Points and Optimization	p. 141
Constrained Optimization	p. 143
Review of Chapter 9	p. 146
Focus on Theory	p. 148
Deriving the Formula for a Regression Line	p. 148
Mathematical Modeling Using Differential Equations	p. 149
Math Modeling: Setting Up a Differential Equation	p. 150
Solutions of Differential Equations	p. 151
Slope Fields	p. 152
Exponential Growth and Decay	p. 154
Applications and Modeling	p. 155
Modeling the Interaction of Two Populations	p. 157
Modeling the Spread of a Disease	p. 159
Review of Chapter 10	p. 160
Focus on Theory	p. 161
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