Functions and Models | |

Four Ways to Represent a Function | |

Mathematical Models | |

New Functions from Old Functions | |

Graphing Calculators and Computers | |

Exponential Functions | |

Inverse Functions and Logarithms | |

Parametric Curves | |

Review | |

Principles of Problem Solving | |

Limits and Derivatives | |

The Tangent and Velocity Problems | |

The Limit of a Function | |

Calculating Limits Using the Limit Laws | |

Continuity | |

Limits Involving Infinity | |

Tangents, Velocities, and Other Rates of Change | |

Derivatives | |

The Derivative as a Function | |

Linear Approximations | |

What does f' say about f? | |

Review | |

Focus on Problem Solving | |

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 | |

Derivatives of Logarithmic Functions | |

Linear Approximations and Differentials | |

Review | |

Focus on Problem Solving | |

Applications of Differentiation | |

Related Rates | |

Maximum and Minimum Values | |

Derivatives and the Shapes of Curves | |

Graphing with Calculus and Calculators | |

Indeterminate Forms and l'Hospital's Rule | |

Optimization Problems | |

Applications to Economics | |

Newton's Method | |

Antiderivatives | |

Review | |

Focus on Problem Solving | |

Integrals | |

Areas and Distances | |

The Definite Integral | |

Evaluating Definite Integrals | |

The Fundamental Theorem of Calculus | |

The Substitution Rule | |

Integration by Parts | |

Additional Techniques of Integration | |

Integration Using Tables and Computer Algebra Systems | |

Approximate Integration | |

Improper Integrals | |

Review | |

Focus on Problem Solving | |

Applications of Integration | |

More about Areas | |

Volumes | |

Arc Length | |

Average Value of a Function | |

Applications to Physics and Engineering | |

Applications to Economics and Biology | |

Probability | |

Review | |

Focus on Problem Solving | |

Differential Equations | |

Modeling with Differential Equations | |

Direction Fields and Euler's Method | |

Separable Equations | |

Exponential Growth and Decay | |

The Logistic Equation | |

Predator-Prey Systems | |

Review | |

Focus on Problem Solving | |

Infinite Sequences and Series | |

Sequences | |

Series | |

The Integral and Comparison Tests | |

Estimating Sums | |

Other Convergence Tests | |

Power Series | |

Representation of Functions as Power Series | |

Taylor and Maclaurin Series | |

The Binomial Series | |

Applications of Taylor Polynomials | |

Review | |

Focus on Problem Solving | |

Vectors and the Geometry of Space | |

Three Dimensional Coordinate Systems | |

Vectors | |

The Dot Product | |

The Cross Product | |

Equations of Lines and Planes | |

Functions and Surfaces | |

Cylindrical and Spherical Coordinates | |

Review | |

Focus on Problem Solving | |

Vector Functions | |

Vector Functions and Space Curves | |

Derivatives and Integrals of Vector Functions | |

Arc Length and Curvature | |

Motion in Space | |

Parametric Surfaces | |

Review | |

Focus on Problem Solving | |

Partial Derivatives | |

Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives | |

Tangent Planes and Linear Approximations | |

The Chain Rule | |

Directional Derivatives and the Gradient Vector | |

Maximum and Minimum Values | |

Lagrange Multipliers | |

Review | |

Focus on Problem Solving | |

Multiple Integrals | |

Double Integrals over Rectangles | |

Interated Integrals | |

Double Integrals over General Regions | |

Double Integrals in Polar Coordinates | |

Applications of Double Integrals | |

Surface Area | |

Triple Integrals | |

Triple Integrals in Cylindrical and Spherical Coordinates | |

Change of Variables in Multiple Integrals | |

Review | |

Focus on Problem Solving | |

Vector Calculus | |

Vector Fields | |

Line Integrals | |

The Fundamental Theorem for Line Integrals | |

Green's Theorem | |

Curl and Divergence | |

Surface Integrals | |

Stokes' Theorem | |

The Divergence Theorem | |

Summary | |

Review | |

Focus on Problem Solving | |

Intervals, Inequalities, And Absolute Values | |

Coordinate Geometry | |

Trigonometry | |

Precise Definitions Of Limits | |

A Few Proofs | |

Sigma Notation | |

Integration Of Rat | |

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