## Study Guides

The Study Guides include pre-tests, photographs of every chalkboard used in the videotapes, reading assignments in the supplementary notes and textbook, and exercises with solutions.

LEC # | TOPICS | PHOTOS, READINGS, and EXERCISES | SOLUTIONS |
---|---|---|---|

Part I: Vector Arithmetic |
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1 | The "Game" of Mathematics | (PDF - 1.8MB) | (PDF - 3.7MB) |

2 | Three-Dimensional Vectors | (PDF) | (PDF - 2.8MB) |

3 | Three-Dimensional Vectors | (PDF) | (PDF - 2.1MB) |

4 | The Dot Product | (PDF) | (PDF - 2.9MB) |

5 | The Cross Product | (PDF) | (PDF - 2.1MB) |

6 | Equations of Lines & Planes | (PDF) | (PDF - 2.9MB) |

Part II: Vector Calculus |
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1 | Vector Functions of a Scalar Variable | (PDF) | (PDF - 2.4MB) |

2 | Tangential & Normal Vectors | (PDF) | (PDF - 2.8MB) |

3 | Polar Coordinates | (PDF) | (PDF - 2.6MB) |

4 | Vectors in Polar Coordinates | (PDF) | (PDF - 4.7MB) |

Part III: Partial Derivatives |
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1 | n-Dimensional Vector Spaces | (PDF - 1.1MB) | (PDF - 4.2MB) |

2 | Calculus of Several Variables | (PDF) | (PDF - 3.6MB) |

3 | Directional Derivatives | (PDF) | (PDF - 4.2MB) |

4 | The Chain Rule | (PDF) | (PDF - 2.7MB) |

5 | Integrals Involving Parameters | (PDF) | (PDF - 3.0MB) |

6 | Exact Differentials | (PDF) | (PDF - 4.2MB) |

Part IV: Matrix Algebra |
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1 | Linearity Revisited | (PDF) | (PDF - 2.3MB) |

2 | The "Game" of Matrices | (PDF) | (PDF - 3.1MB) |

3 | Inverting a Matrix | (PDF) | (PDF - 2.9MB) |

4 | Inverting More General Systems of Equations | (PDF) | (PDF - 1.5MB) |

5 | Maxima and Minima in Several Variables | (PDF) | (PDF - 3.8MB) |

Part V: Multiple Integration |
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1 | Double Multiple Sums | (PDF - 1.1MB) | (PDF - 2.3MB) |

2 | The Fundamental Theorem | (PDF) | (PDF 2.3MB) |

3 | Multiple Integration and the Jacobian | (PDF) | (PDF - 4.2MB) |

4 | Introduction to Line Integrals | (PDF) | (PDF - 2.2MB) |

5 | Green's Theorem | (PDF) | (PDF - 1.7MB) |

## Supplementary Notes for Multivariable Calculus, Parts I through V

The Supplementary Notes include prerequisite materials, detailed proofs, and deeper treatments of selected topics.

- Chapter 1: An Introduction to Mathematical Structure (PDF - 3.4MB)
- Chapter 2: An Introduction to Vector Arithmetic (PDF - 2.1MB)
- Chapter 3: An Introduction to Vector Calculus (PDF - 2.6MB)
- Chapter 4: An Introduction to Functions of Several Real Variables (PDF - 5.4MB)
- Chapter 5: Derivatives in n-Dimensional Spaces (PDF - 3.0MB)
- Chapter 6: Matrix Algebra in the Study of Functions of Several Variables (PDF - 7.6MB)
- Chapter 7: Applications of Linear Algebra to Non-Linear Functions (PDF - 2.1MB)

**Textbook:** The course makes reference to the out-of-print textbook cited below, but any newer textbook will suffice to expand on topics covered in the video lectures.

Thomas, George B. *Calculus and Analytic Geometry*. Addison-Wesley, 1968. ISBN: 9780201075250.