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Functions and Change | |
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What is a Function? | |
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Linear Functions | |
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Rates of Change | |
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Applications of Functions to Economics | |
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Exponential Functions | |
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The Natural Logarithm | |
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Exponential Growth and Decay | |
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New Functions From Old | |
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Proportionality, Power Functions and Polynomials | |
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Periodic Functions | |
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Review of Chapter 1 | |
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Focus on Modeling | |
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Fitting Formulas to Data | |
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Compound Interest and the Number e | |
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Focus on Theory | |
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Limits to Infinity and end Behavior | |
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Rate of Change: The Derivative | |
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Instantaneous Rate of Change | |
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The Derivative Function | |
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Interpretations of the Derivative | |
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The Second Derivative | |
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Marginal Cost and Revenue | |
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Review of Chapter 2 | |
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Focus on Theory | |
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Limits, Continuity, and the Definition of the Derivative | |
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Short-Cuts to Differentiation | |
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Derivative Formulas for Powers and Polynomials | |
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Exponential and Logarithmic Functions | |
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The Chain Rule | |
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The Product and Quotient Rules | |
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Derivatives of Periodic Functions | |
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Review of Chapter 3 | |
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Focus on Theory | |
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Establishing Derivative Formulas | |
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Focus on Practice | |
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Differentiation | |
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Using the Derivative | |
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Local Maxima and Minima | |
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Inflection Points | |
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Global Maxima and Minima | |
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Profit, Cost, and Revenue | |
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Average Cost | |
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Elasticity of Demand | |
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Logistic Growth | |
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The Surge Function and Drug Concentration | |
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Review of Chapter 4 | |
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Accumulated Change: The Definite Integral | |
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Accumulated Change | |
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The Definite Integral | |
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The Definite Integral as Area | |
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Interpretations of the Definite Integral | |
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The Fundamental Theorem of Calculus | |
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Review of Chapter 5 | |
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Focus on Theory | |
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Theorems About Definite Integrals | |
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Using the Integral | |
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Average Value | |
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Consumer and Producer Surplus | |
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Present and Future Value | |
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Relative Growth Rates | |
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Review of Chapter 6 | |
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Antiderivatives | |
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Constructing Antiderivatives Analytically | |
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Integration by Substitution | |
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Using the Fundamental Theorem to Find Definite Integrals | |
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Analyzing Antiderivatives Graphically and Numerically | |
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Review of Chapter 7 | |
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Probability | |
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Density Functions | |
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Cumulative Distribution Functions and Probability | |
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The Median and the Mean | |
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Review of Chapter 8 | |
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Functions of Several Variables | |
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Understanding Functions of Two Variables | |
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Contour Diagrams | |
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Partial Derivatives | |
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Computing Partial Derivatives Algebraically | |
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Critical Points and Optimization | |
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Constrained Optimization | |
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Review of Chapter 9 | |
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Focus on Theory | |
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Deriving the Formula for a Regression Line | |
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Mathematical Modeling Using Differential Equations | |
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Math Modeling: Setting Up a Differential Equation | |
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Solutions of Differential Equations | |
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Slope Fields | |
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Exponential Growth and Decay | |
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Applications and Modeling | |
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Modeling the Interaction of Two Populations | |
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Modeling the Spread of a Disease | |
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Review of Chapter 10 | |
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Focus on Theory | |