Preliminaries | |

Polynomials and Rational Functions | |

Graphing Calculators and Computer Algebra Systems | |

Inverse Functions | |

Trigonometric and Inverse Trigonometric Functions | |

Exponential and Logarithmic Functions Hyperbolic Functions Fitting a Curve to Data | |

Transformations of Functions | |

Limits and Continuity | |

A Brief Preview of Calculus: Tangent Lines and the Length of a Curve | |

The Concept of Limit | |

Computation of Limits | |

Continuity and its Consequences The Method of Bisections | |

Limits Involving Infinity Asymptotes | |

Formal Definition of the Limit Exploring the Definition of Limit Graphically | |

Limits and Loss-of-Significance Errors Computer Representation of Real Numbers | |

Differentiation | |

Tangent Lines and Velocity | |

The Derivative Numerical Differentiation | |

Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration | |

The Product and Quotient Rules | |

The Chain Rule | |

Derivatives of the Trigonometric Functions | |

Derivatives of the Exponential and Logarithmic Functions | |

Implicit Differentiation and Inverse Trigonometric Functions | |

The Mean Value Theorem | |

Applications of Differentiation | |

Linear Approximations and Newton’s Method | |

Indeterminate Forms and L’Hopital’s Rule | |

Maximum and Minimum Values | |

Increasing and Decreasing Functions | |

Concavity and the Second Derivative Test | |

Overview of Curve Sketching | |

Optimization | |

Related Rates | |

Rates of Change in Economics and the Sciences | |

Integration | |

Antiderivatives | |

Sums and Sigma Notation Principle of Mathematical Induction | |

Area | |

The Definite Integral Average Value of a Function | |

The Fundamental Theorem of Calculus | |

Integration by Substitution | |

Numerical Integration Error Bounds for Numerical Integration | |

The Natural Logarithm as an Integral The Exponential Function as the Inverse of the Natural Logarithm | |

Applications of the Definite Integral | |

Area Between Curves | |

Volume: Slicing, Disks, and Washers | |

Volumes by Cylindrical Shells | |

Arc Length and Surface Area | |

Projectile Motion | |

Applications of Integration to Physics and Engineering | |

Probability | |

Integration Techniques | |

Review of Formulas and Techniques | |

Integration by Parts | |

Trigonometric Techniques of Integration Integrals Involving Powers of Trigonometric Functions Trigonometric Substitution | |

Integration of Rational Functions Using Partial Fractions Brief Summary of Integration Techniques | |

Integration Tables and Computer Algebra Systems | |

Improper Integrals A Comparison Test | |

First-Order Differential Equations | |

Modeling with Differential Equations Growth and Decay Problems Compound Interest | |

Separable Differential Equations Logistic Growth | |

Direction Fields and Euler's Method | |

Systems of First-Order Differential Equations Predator-Prey Systems | |

Infinite Series | |

Sequences of Real Numbers | |

Infinite Series | |

The Integral Test and Comparison Tests | |

Alternating Series Estimating the Sum of an Alternating Series | |

Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Tests | |

Power Series | |

Taylor Series Representations of Functions as Series Proof of Taylor’s Theorem | |

Applications of Taylor Series The Binomial Series | |

Fourier Series | |

Parametric Equations and Polar Coordinates | |

Plane Curves and Parametric Equations | |

Calculus and Parametric Equations | |

Arc Length and Surface Area in Parametric Equations | |

Polar Coordinates | |

Calculus and Polar Coordinates | |

Conic Sections | |

Conic Sections in Polar Coordinates | |

Vectors and th | |

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