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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