A Library Of Functions | |

Functions and Change | |

Exponential Functions | |

New Functions from Old | |

Logarithmic Functions | |

Trigonometric Functions | |

Powers, Polynomials, and Rational Functions | |

Introduction to Continuity | |

Limits | |

Review Problems | |

Check Your Understanding | |

Projects: Matching Functions to Data, Which Way Is the Wind Blowing? | |

Key Concept: The Derivative | |

How Do We Measure Speed? | |

The Derivative at a Point | |

The Derivative Function | |

Interpretations of the Derivative | |

The Second Derivative | |

Differentiability | |

Review Problems | |

Check Your Understanding | |

Projects: Hours of Daylight as a Function of Latitude, US Population | |

Short-Cuts To Differentiation | |

Powers and Polynomials | |

The Exponential Function | |

The Product and Quotient Rules | |

The Chain Rule | |

The Trigonometric Functions | |

The Chain Rule and Inverse Functions | |

Implicit Functions | |

Hyperbolic Functions | |

Linear Approximation and the Derivative | |

Theorems about Differentiable Functions | |

Review Problems | |

Check Your Understanding | |

Projects: Rule of 70, Newtonâ s Method | |

Using The Derivative | |

Using First and Second Derivatives | |

Optimization | |

Families of Functions | |

Optimization, Geometry, and Modeling | |

Applications to Marginality | |

Rates and Related Rates | |

Lâ hopitalâ s Rule, Growth, and Dominance | |

Parametric Equations | |

Review Problems | |

Check Your Understanding | |

Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks | |

Key Concept: The Definite Integral | |

How Do We Measure Distance Traveled? | |

The Definite Integral | |

The Fundamental Theorem and Interpretations | |

Theorems about Definite Integrals | |

Review Problems | |

Check Your Understanding | |

Projects: The Car and the Truck, An Orbiting Satellite | |

Constructing Antiderivatives | |

Antiderivatives Graphically and Numerically | |

Constructing Antiderivatives Analytically | |

Differential Equations | |

Second Fundamental Theorem of Calculus | |

The Equations of Motion | |

Review Problems | |

Check Your Understanding | |

Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields | |

Integration | |

Integration by Substitution | |

Integration by Parts | |

Tables of Integrals | |

Algebraic Identities and Trigonometric Substitutions | |

Approximating Definite Integrals | |

Approximation Errors and Simpsonâ s Rule | |

Improper Integrals | |

Comparison of Improper Integrals | |

Review Problems | |

Check Your Understanding | |

Projects: Taylor Polynomial Inequalities | |

Using The Definite Integral | |

Areas and Volumes | |

Applications to Geometry | |

Area and Arc Length in Polar Coordinates | |

Density and Center of Mass | |

Applications to Physics | |

Applications to Economics | |

Distribution Functions | |

Probability, Mean, and Median | |

Review Problems | |

Check Your Understanding | |

Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwellâ s Distribution of Molecular Velocities | |

Sequences And Series | |

Sequences | |

Geometric Series | |

Convergence of Series | |

Tests for Convergence | |

Power Series and Interval of Convergence | |

Review Problems | |

Check Your Understanding | |

Projects: A Definition of e, Probability of Winning in Sports, Prednisone | |

Approximating Functions Using Series | |

Taylor Polynomials | |

Taylor Series | |

Finding and Using Taylor Series | |

The Error in Taylor Polynomial Approximations | |

Fourier Series | |

Review Problems | |

Check Your Understanding | |

Projects: Shape of Planets, Machinâ s Formula and the Value of pi, Approximation the Derivative | |

Differential Equations | |

What Is a Differential Equation? | |

Slope Fields | |

Eulerâ s Method | |

Separation of Variables | |

Growth and Decay | |

Applications and Modeling | |

The Logistic Model | |

Systems of Differential Equations | |

Analyzing the Phase Plane | |

Second-Order Differential Equations: Oscillations | |

Linear Second-Order Differential Equations | |

Review Problems | |

Check Your Understanding | |

Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Paretoâ s Law, Vibrations in a Molecule | |

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