## COURSE DESCRIPTION

This course will cover the key ideas from chapters 12-15 of Edwards and Penney. This is a subset of the syllabus for 18.02 (Multivariable Calculus). For more detail, see the syllabus.

**Text Book:** *Multivariable Calculus* by Edwards and Penney

# SCHEDULE

Event | Date | Related Documents |
---|---|---|

PSET 1 | Due July 8 | Solutions |

Midterm 1 | July 10 in class | |

PSET 2 | Due July 17 | Solutions |

PSET 3 | Due July 22 | Solutions |

Midterm 2 | July 24 in class | |

PSET 4 | Due July 31 | Solutions |

PSET 5 | Due August 5 | Solutions |

Final | August 8 |

# Lecture Notes

Day | Topics and Notes |
---|---|

Day 1 | Vectors, dot products, geometric proofs. Notes. Summary |

Day 2 | Lines, planes, determinants, cross products. Notes. Summary |

Day 3 | Parameterizations, velocity, acceleration, arc length. Notes. Summary |

Day 4 | Functions of several variables, partial derivatives. Notes. Summary |

Day 5 | Gradient, directional derivatives, chain rule. Notes. Summary |

Day 6 | Constrained optimization and Lagrange multipliers. Notes. Summary |

Day 7 | Double integrals. Notes. Summary |

Day 8 | Double integrals in cartesian and polar coordinates. Notes. Summary |

Day 9 | Triple integrals in cartesian coordinates. Notes. Summary |

Day 10 | Triple integrals in cylidrical and spherical coordinates. Notes. Summary |

Day 11 | Vector fields, line integrals, conservative vector fields. Notes. Summary |

Day 12 | Fundamental theorem of line integrals, Green's theorem. Notes. Summary |