This is a very rapid plan of study. A great deal of energy and
determination will be needed to keep up with it. Modifications may be
necessary. Please send comments to the lecturer. Periodic assignments
(Maple labs, workshops, etc.) may be due at times, and additional
problems may be suggested.
The text is the fifth edition of Stewart's , Brooks/Cole, 1999,
ISBN 0-534-39321-7. Calculus: Early
TranscendentalsA calendar of spring semester dates correlated with the syllabus follows the "plan of study". The calendar may be helpful. |

Syllabus and suggested textbook homework problems for 640:251:05-10 | |||
---|---|---|---|

Lecture | Topic(s) | Relevant text sections | Suggested problems |

1 | R^{3} and vectors |
12.1 12.2 |
12.1: 3, 4, 7, 8, 23, 26, 27, 29, 32 12.2: 5, 7, 12, 19, 20, 23, 26, 29, 31 |

2 | Dot product Cross product |
12.3 12.4 | 12.3: 1, 3, 7, 11, 15, 20, 24, 27, 36, 37, 41, 42, 45, 51 12.4: 2, 13, 23, 30, 34, 41, 42 |

3 | Lines & places | 12.5 | 12.5: 3, 8, 12, 13, 19, 23, 26, 28, 35, 39, 46, 47, 67 |

4 | Vector functions, curves Derivatives, integrals | 13.1 13.2 | 13.1: 1, 5, 9, 10, 12, 19, 20, 21 13.2: 5, 8, 9, 11, 12, 15, 18, 23, 26, 33, 38, 51 |

5 | Arc length; curvature Motion |
13.3 13.4 | 13.3: 1, 2, 3, 4, 11, 13, 14, 15, 16, 27, 29a, 56a 13.4: 13, 16, 19, 23, 35 (13.4 to Kepler's laws) |

6 | Several variable functions Limits; continuity |
14.1 14.2 [12.6] | 14.1: 29, 41, 43, 53 14.2: 5, 7 [12.6: 4, 7, 13, 27] |

7 | Partial derivatives Tan. planes, lin. approx. |
14.3 14.4 | 14.3: 14, 15, 17, 21, 26, 36, 47, 48, 67ad 14.4: 16, 17, 32, 37 |

8 | The Chain Rule | 14.5 | 14.5: 3, 17, 35, 46 |

9 | Directional derivs Gradient | 14.6 | 14.6: 7, 10, 11, 13, 21, 24, 39 |

10 | Max/min | 14.7 | 14.7: 2, 3, 5, 7, 8, 12, 14, 27, 28, 36, 43, 47, 48 |

11 | Lagrange multipliers | 14.8 | 14.8: 3, 5, 8, 9, 18, 38 |

12 | Exam 1 (timing approximate!) | ||

13 | Double & iterated ints | 15.1 15.2 |
15.2: 1, 3, 12, 13, 21 |

14 | More double integrals & in polar coordinates | 15.3 15.4 | 15.3: 1, 3, 7, 9, 14, 24, 26, 37, 38, 43, 44 15.4: 9, 10, 11, 12 |

15 | Some applications Changing variables | 15.5 15.9 |
15.5: 3, 7, 12 15.9: 3,11 (15.9 for double integrals) |

16 | Triple integrals | 15.7 | 15.7: 3,5,9,10,32,36,37 |

17 | Cyl. & sph. coordinates Triple integrals | 12.7 15.8 |
12.7:35, 37, 39, 43, 55 15.8: 3,5,9,12,18,29,33,35 |

18 | Vector fields Line integrals |
16.1 16.2 | 16.1: 5, 11, 13, 15, 17 16.2: 9, 12, 13, 16, 31 |

19 | More line integrals | ||

20 | FTC for line integrals | 16.3 | 16.3: 3, 4, 5, 6, 11, 12, 27, 28 |

21 | Green's Theorem | 16.4 | 16.4: 1, 8, 10, 15 |

22 | Exam 2 (timing approximate!) | ||

23 | Curl & divergence | 16.5 | 16.5: 4, 12hijkl, 19, 33 |

24 | Parametric surfaces Surface area | 15.6 16.6 |
15.6: 4, 9 16.6: 21 |

25 | Surface integrals | 16.7 | 16.7: 5, 14, 19, 24, 41 |

26 | Stokes Theorem | 16.8 | 16.8: 1, 2, 9, 15 |

27 | Divergence Theorem | 16.9 | 16.9: 5, 15, 19 |

28 | Catch-up; a discussion of the {heat|diffusion} equation if there is time & interest. |

Important spring semester dates, with useful (?) references to the lectures |
---|

Spring semester begins: Tuesday, January 17 |

Sunday, January 29, 2006: Chinese New Year (Bing-Xu) [after #4] |

Tuesday, January 31, 2006: Islamic New Year 1427 [#5 on this day] |

Thursday, February 2, 2006: Groundhog Day [before #6] |

Tuesday, February 14, 2006: Valentine's Day [#9 on this day] |

Monday, February 20, 2006: President's Day [before #11] |

Wednesday, March 1, 2006: Ash Wednesday [after #13] |

Spring recess begins: Saturday, March 11 [after #16] |

Friday, March 17, 2006: St. Patrick's Day |

Spring recess ends: Sunday, March 19 |

Monday, March 20, 2006: Vernal Equinox 1:25pm (EST) [before #17] |

Saturday, April 1, 2006: April Fools' Day [after #20] |

Sunday, April 2, 2006: Daylight savings time begins at 2:00 AM |

Thursday, April 13, 2006: Passover [before #24] |

Friday, April 14, 2006: Good Friday [#24 on this day] |

Sunday, April 16, 2006: Easter Sunday |

Regular classes end: Monday, May 1 [after #28] |

Reading days: Tuesday, May 2; Wednesday, May 3 |

Spring exams begin: Thursday, May 4 |

Final exam, sections 05-07: Friday, May 5, 12-3 |

Final exam, sections 08-10: Wednesday, May 10, 8-11 |

Spring exams end: Wednesday, May 10 |

**
Maintained by
greenfie@math.rutgers.edu and last modified 1/16/2006.
**