- Chapter 1: Vectors
- Section 1.1: Vectors in Two and Three Dimensions
- Section 1.2: More About Vectors
- Section 1.3: The Dot Product
- Section 1.4: The Cross Product
- Section 1.5: Equations for Planes; Distance Problems
- Section 1.6: Some
*n*-dimensional Geometry - Section 1.7: New Coordinate Systems

- Chapter 2: Differentiation in Several Variables
- Section 2.1: Functions of Several Variables; Graphing Surfaces
- Section 2.2: Limits
- Section 2.3: The Derivative
- Section 2.4: Properties; Higher-order Partial Derivatives
- Section 2.5: The Chain Rule
- Section 2.6: Directional Derivatives and the Gradient
- Section 2.7: Newton's Method (Optional)

- Chapter 3: Vector-Valued Functions
- Section 3.1: Parametrized Curves and Kepler's Laws
- Section 3.2: Arclength and Differential Geometry
- Section 3.3: Vector Fields: An Introduction
- Section 3.4: Gradient, Divergence, Curl, and the Del Operator

- Chapter 4: Maxima and Minima in Several Variables
- Section 4.1: Differentials and Taylor's Theorem
- Section 4.2: Extrema of Functions
- Section 4.3: Lagrange Multipliers
- Section 4.4: Some Applications of Extrema

- Chapter 5: Multiple Integrals
- Section 5.1: Introduction: Areas and Volume
- Section 5.2: Double Integrals
- Section 5.3: Changing the Order of Integration
- Section 5.4: Triple Integrals
- Section 5.5: Change of Variables
- Section 5.6: Applications of Integration
- Section 5.7: Numerical Approximations of Multiple Integrals (optional)

- Chapter 6: Line Integrals
- Section 6.1: Scalar and Vector Line Integrals
- Section 6.2: Green's Theorem
- Section 6.3: Conservative Vector Fields

- Chapter 7: Surface Integrals and Vector Analysis
- Section 7.1: Parametrized Surfaces
- Section 7.2: Surface Integrals
- Section 7.3: Stokes's and Gauss's Theorems
- Section 7.4: Further Vector Analysis; Maxwell's Equations

- Chapter 8: Vector Analysis in Higher Dimensions
- Section 8.1: An Introduction to Differential Forms
- Section 8.2: Manifolds and Integrals of
*k*-forms - Section 8.3: The Generalized Stokes's Theorem

Section 1.1 | Section 1.2 | Section 1.3 | ||||
---|---|---|---|---|---|---|

Exercise 1 | Exercise 19 | Exercise 1 | Exercise 19 | Exercise 37 | Exercise 1 | Exercise 19 |

Exercise 2 | Exercise 20 | Exercise 2 | Exercise 20 | Exercise 38 | Exercise 2 | Exercise 20 |

Exercise 3 | Exercise 21 | Exercise 3 | Exercise 21 | Exercise 39 | Exercise 3 | Exercise 21 |

Exercise 4 | Exercise 22 | Exercise 4 | Exercise 22 | Exercise 40 | Exercise 4 | Exercise 22 |

Exercise 5 | Exercise 23 | Exercise 5 | Exercise 23 | Exercise 41 | Exercise 5 | Exercise 23 |

Exercise 6 | Exercise 24 | Exercise 6 | Exercise 24 | Exercise 42 | Exercise 6 | Exercise 24 |

Exercise 7 | Exercise 25 | Exercise 7 | Exercise 25 | Exercise 43 | Exercise 7 | Exercise 25 |

Exercise 8 | Exercise 26 | Exercise 8 | Exercise 26 | Exercise 44 | Exercise 8 | Exercise 26 |

Exercise 9 | Exercise 27 | Exercise 9 | Exercise 27 | Exercise 45 | Exercise 9 | Exercise 27 |

Exercise 10 | Exercise 10 | Exercise 28 | Exercise 46 | Exercise 10 | Exercise 28 | |

Exercise 11 | Exercise 11 | Exercise 29 | Exercise 47 | Exercise 11 | Exercise 29 | |

Exercise 12 | Exercise 12 | Exercise 30 | Exercise 12 | Exercise 30 | ||

Exercise 13 | Exercise 13 | Exercise 31 | Exercise 13 | Exercise 31 | ||

Exercise 14 | Exercise 14 | Exercise 32 | Exercise 14 | Exercise 32 | ||

Exercise 15 | Exercise 15 | Exercise 33 | Exercise 15 | Exercise 33 | ||

Exercise 16 | Exercise 16 | Exercise 34 | Exercise 16 | Exercise 34 | ||

Exercise 17 | Exercise 17 | Exercise 35 | Exercise 17 | Exercise 35 | ||

Exercise 18 | Exercise 18 | Exercise 36 | Exercise 18 | Exercise 36 |