# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 21D: Vector Analysis

**Approved:**2007-04-01 (revised 2013-01-01, J. DeLoera)

**ATTENTION:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1 |
15.1 |
Double and Iterated Integrals Over Rectangles |

1.5 |
15.2 |
Double Integrals Over General Regions |

0.5 |
15.3 |
Area by Double Integration |

1 |
15.4 |
Double Integrals in Polar Form |

1 |
15.5 |
Triple Integrals in Rectangular Coordinates |

1 |
15.6 |
Moments and Centers of Mass |

1 |
15.7 |
Triple Integrals in Cylindrical and Spherical Coordinates |

2 |
15.8 |
Substitutions in Multiple Integrals |

1 |
12, 13.1, 13.2 |
Review of Vectors |

1 |
13.3 |
Arc Length in Space |

1.5 |
13.4 |
Curvature and Normal Vectors of a Curve |

0.5 |
13.5 |
Tangential and Normal Components of Acceleration |

1 |
16.1 |
Line Integrals |

2 |
16.2 |
Vector Fields and Line Integrals: Work, Circulation, and Flux |

1 |
16.3 |
Path Independence, Conservative Fields. Potential Functions |

2 |
16.4 |
Green’s Theorem in the Plane |

2 |
16.5 |
Surfaces and Area |

1 |
16.6 |
Surface Integrals |

2 |
16.7 |
Stokes’ Theorem |

2 |
16.8 |
The Divergence Theorem and a Unified Theory |

**Additional Notes:**

**Learning Goals:**

Students will master both integral and differential multivariable calculus, with special emphasis placed on two and three dimensions. By this stage, students are expected to be experts at “word problems” requiring them to convert real world problems into mathematics. The course begins with multiple integrals and then introduces the main differential operators in two and three dimensions. These themes are unified by Stoke's theorem at the end of the course.

By the end of this course, students will have the mathematical skills to succeed in a wide range of science classes, especially those involving motions and flows in the three dimensional world surrounding us.

Note: Care should be taken in this course to teach students how to produce simple yet meaningful sketches of the three dimensional geometric objects studied. Use appropriate visualization technology.

**Assessment:**