Functions And Models | |

Four Ways to Represent a Function | |

Mathematical Models: A Catalog of Essential Functions | |

New Functions from Old Functions | |

Graphing Calculators and Computers | |

Exponential Functions | |

Inverse Functions and Logarithms | |

Review | |

Principles of Problem Solving | |

Limits And Derivatives | |

The Tangent and Velocity Problems | |

The Limit of a Function | |

Calculating Limits Using the Limit Laws | |

The Precise Definition of a Limit | |

Continuity | |

Limits at Infinity | |

Horizontal Asymptotes | |

Tangents, Velocities, and Other Rates of Change | |

Derivatives | |

Writing Project: Early Methods for Finding Tangents | |

The Derivative as a Function | |

Review | |

Problems Plus | |

Differentiation Rules | |

Derivatives of Polynomials and Exponential Functions | |

The Product and Quotient Rules | |

Rates of Change in the Natural and Social Sciences | |

Derivatives of Trigonometric Functions | |

The Chain Rule | |

Implicit Differentiation | |

Higher Derivatives, Applied Project: Where Should a Pilot Start Descent? , Applied Project: Building a Better Roller Coaster | |

Derivatives of Logarithmic Functions | |

Hyperbolic Functions | |

Related Rates | |

Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials | |

Review | |

Problems Plus | |

Applications Of Differentiation | |

Maximum and Minimum Values, Applied Project: The Calculus of Rainbows | |

The Mean Value Theorem | |

How Derivatives Affect the Shape of a Graph | |

Indeterminate Forms and L?Hospital?s Rule, Writing Project: The Origins of L?Hospital?s Rule | |

Summary of Curve Sketching | |

Graphing with Calculus and Calculators | |

Optimization Problems, Applied Project: The Shape of a Can | |

Applications to Business and Economics | |

Newton?s Method | |

Antiderivatives | |

Review | |

Problems Plus | |

Integrals | |

Areas and Distances | |

The Definite Integral, Discovery Project: Area Functions | |

The Fundamental Theorem of Calculus | |

Indefinite Integrals and the Net Change Theorem, Writing Project: Newton, Leibniz and the Invention of Calculus | |

The Substitution Rule | |

The Logarithm Defined as an Integral | |

Review | |

Problems Plus | |

Applications Of Integration | |

Areas between Curves | |

Volume | |

Volumes by Cylindrical Shells | |

Work | |

Average Value of a Function | |

Applied Project: Where to Sit at the Movie | |

Review | |

Problems Plus | |

Techniques Of Integration | |

Integration by Parts | |

Trigonometric Integrals | |

Trigonometric Substitution | |

Integration of Rational Functions by Partial Fractions | |

Strategy for Integration | |

Integration Using Tables and Computer Algebra Systems, Discovery Project: Patterns in Integrals | |

Approximate Integration | |

Improper Integrals | |

Review | |

Problems Plus | |

Further Applications Of Integration | |

Arc Length | |

Discovery Project: Arc Length Contest | |

Area of a Surface of Revolution, Discovery Project: Rotating on a Slant | |

Applications to Physics and Engineering | |

Applications to Economics and Biology | |

Probability | |

Review | |

Problems Plus | |

Differential Equations | |

Modeling with Differential Equations | |

Direction Fields and Euler?s Method | |

Separable Equations, Applied Project: How Fast Does a Tank Drain?, Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay, Applied Project: Calculus and Baseball | |

The Logistic Equation | |

Linear Equations | |

Predator-Prey Systems | |

Review | |

Problems Plus | |

Curves In Parametric, Vector, And Polar Form | |

Curves Defined by Parametric Equations, Laboratory Project: Running Circles around Circles | |

Calculus with Parametric Curves, Laboratory Project: Bezier Curves | |

Vectors in Two Dimensions | |

Vector Functions and Their Derivatives | |

Curvilinear Motions: Velocity and Acceleration | |

Polar Coordinates | |

Areas and Lengths in Polar Coordinates | |

Conic Sections | |

Conic Sections in Polar Coordinates | |

Review | |

Problems Plus | |

Infinite Sequences And Series | |

Sequences, Laboratory Project: Logistic Sequences | |

Series | |

The Integral Test and Estimates of Sums | |

The Comparison Tests | |

Alternating Series | |

Absolute Convergence and the Ratio and Root Tests | |

Strategy for Testing Series | |

Power Series | |

Representation | |

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