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Note: Each chapter concludes with a Summary, a Concept Check, a Review Test, and one or two Projects. 1. Ingredients of Change: Functions and Models 1.1 Models and Functions 1.2 Linear Functions and Models 1.3 Exponential and Logarithmic Functions and Models 1.4 Logistic Functions and Models 1.5 Polynomial Functions and Models 2. Describing Change: Rates 2.1 Change, Percentage Change, and Average Rates of Change 2.2 Instantaneous Rates of Change 2.3 Derivative Notation and Numerical Estimates 2.4 Algebraically Finding Slopes 3. Determining Change: Derivatives 3.1 Drawing Rate-of-Change Graphs 3.2 Simple Rate-of-Change Formulas 3.3 Exponential and Logarithmic Rate-of-Change Formulas 3.4 The Chain Rule 3.5 The Product Rule 3.6 Limiting Behavior Revisited: L'Hopital's Rule 4. Analyzing Change: Applications of Derivatives 4.1 Approximating Change 4.2 Relative and Absolute Extreme Points 4.3 Inflection Points 4.4 Interconnected Change: Related Rates 5. Accumulating Change: Limits of Sums and the Definite Integral 5.1 Results of Change and Area Approximations 5.2 Accumulation Functions 5.3 The Fundamental Theorem 5.4 The Definite Integral 5.5 Average Value and Average Rate of Change 5.6 Integration by Substitution or Algebraic Manipulation 6. Analyzing Accumulated Change: Integrals in Action 6.1 Perpetual Accumulation and Improper Integrals 6.2 Streams in Business and Biology 6.3 Integrals in Economics 6.4 Probability Distributions and Density Functions 7. Repetitive Change: Cyclic Functions 7.1 Cycles and Sine Functions 7.2 Sine Functions as Models 7.3 Rates of Change and Derivatives 7.4 Extrema and Points of Inflection 7.5 Accumulation in Cycles 8. Dynamics of Change: Differential Equations and Proportionality 8.1 Differential Equations and Slope Fields 8.2 Separable Differential Equations 8.3 Numerically Estimating by Using Differential Equations: Euler's Method 8.4 Second-Order Differential Equations 9. Ingredients of Multivariable Change: Models, Graphs, Rates 9.1 Multivariable Functions and Contour Graphs 9.2 Cross-Sectional Models and Rates of Change 9.3 Partial Rates of Change 9.4 Compensating for Change 10. Analyzing Multivariable Change: Optimization 10.1 Multivariable Critical Points 10.2 Multivariable Optimization 10.3 Optimization Under Constraints 10.4 Least-Squares Optimization
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