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A Library Of Functions | |
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Functions and Change | |
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Exponential Functions | |
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New Functions from Old | |
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Logarithmic Functions | |
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Trigonometric Functions | |
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Powers, Polynomials, and Rational Functions | |
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Introduction to Continuity | |
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Limits | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Matching Functions to Data, Which Way Is the Wind Blowing? | |
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Key Concept: The Derivative | |
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How Do We Measure Speed? | |
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The Derivative at a Point | |
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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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Differentiability | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Hours of Daylight as a Function of Latitude, US Population | |
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Short-Cuts To Differentiation | |
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Powers and Polynomials | |
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The Exponential Function | |
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The Product and Quotient Rules | |
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The Chain Rule | |
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The Trigonometric Functions | |
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The Chain Rule and Inverse Functions | |
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Implicit Functions | |
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Hyperbolic Functions | |
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Linear Approximation and the Derivative | |
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Theorems about Differentiable Functions | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Rule of 70, Newton� s Method | |
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Using The Derivative | |
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Using First and Second Derivatives | |
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Optimization | |
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Families of Functions | |
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Optimization, Geometry, and Modeling | |
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Applications to Marginality | |
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Rates and Related Rates | |
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L� hopital� s Rule, Growth, and Dominance | |
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Parametric Equations | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks | |
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Key Concept: The Definite Integral | |
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How Do We Measure Distance Traveled? | |
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The Definite Integral | |
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The Fundamental Theorem and Interpretations | |
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Theorems about Definite Integrals | |
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Review Problems | |
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Check Your Understanding | |
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Projects: The Car and the Truck, An Orbiting Satellite | |
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Constructing Antiderivatives | |
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Antiderivatives Graphically and Numerically | |
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Constructing Antiderivatives Analytically | |
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Differential Equations | |
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Second Fundamental Theorem of Calculus | |
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The Equations of Motion | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields | |
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Integration | |
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Integration by Substitution | |
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Integration by Parts | |
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Tables of Integrals | |
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Algebraic Identities and Trigonometric Substitutions | |
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Approximating Definite Integrals | |
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Approximation Errors and Simpson� s Rule | |
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Improper Integrals | |
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Comparison of Improper Integrals | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Taylor Polynomial Inequalities | |
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Using The Definite Integral | |
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Areas and Volumes | |
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Applications to Geometry | |
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Area and Arc Length in Polar Coordinates | |
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Density and Center of Mass | |
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Applications to Physics | |
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Applications to Economics | |
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Distribution Functions | |
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Probability, Mean, and Median | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwell� s Distribution of Molecular Velocities | |
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Sequences And Series | |
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Sequences | |
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Geometric Series | |
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Convergence of Series | |
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Tests for Convergence | |
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Power Series and Interval of Convergence | |
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Review Problems | |
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Check Your Understanding | |
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Projects: A Definition of e, Probability of Winning in Sports, Prednisone | |
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Approximating Functions Using Series | |
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Taylor Polynomials | |
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Taylor Series | |
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Finding and Using Taylor Series | |
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The Error in Taylor Polynomial Approximations | |
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Fourier Series | |
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Review Problems | |
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Check Your Understanding | |
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Projects: Shape of Planets, Machin� s Formula and the Value of pi, Approximation the Derivative | |
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Differential Equations | |
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What Is a Differential Equation? | |
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Slope Fields | |
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Euler� s Method | |
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Separation of Variables | |
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Growth and Decay | |
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Applications and Modeling | |
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The Logistic Model | |
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Systems of Differential Equations | |
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Analyzing the Phase Plane | |
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Second-Order Differential Equations: Oscillations | |
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Linear Second-Order Differential Equations | |
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Review Problems | |
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Check Your Understanding | |
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Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Pareto� s Law, Vibrations in a Molecule | |