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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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| 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 | |