2008 February 15 / E-Mail Me

Introduction To Calculus, Carleton College Math 111, Winter 2008, Prof. Joshua R. Davis

We largely follow the textbook (Stewart, *Calculus: Early Transcendentals*, 6th edition), but we mix the content of the applications sections (3.7, 3.8, 3.9, 4.7, 8.4, 8.5, etc.) into the rest.

- * indicates a question that benefits from a calculator or computer; do the others by hand, if you can.
- ^ indicates a typographical error. In 2.5 #42, change "2 < x < 3" to "2 <= x < 3".

Day | Date | Topic | Reading | Problems | Hand-In Day |
---|---|---|---|---|---|

1 | F 1/4 | introduction, functions | 1.1, 1.2 | 1.1: #2, 10, 16, 20, 24, 26, 28, 36, 42, 46, 48, 52, 54, 64 1.2: #2, 4, 8, 10, 16, 20, 26* | 4 |

2 | M 1/7 | more functions | 1.5, 1.6 (omit Inverse Trig) | 1.5: #16b, 18, 22* 1.6: #14, 18, 22, 26, 30, 36, 46, 50, 58 | 4 |

3 | W 1/9 | operations on functions, tangent lines, velocities | 1.3, 2.1 | 1.3: #2, 4, 10, 12, 28, 34, 44, 54, 56, 66 1.5: #8, 12, 14 1.6: #46 2.1: #2, 4, 6, 8 | 7 |

4 | F 1/11 | limits | 2.2 | 2.2: #6, 10, 12, 16, 24*, 28*, 36*, 40 | 7 |

5 | M 1/14 | limit laws | 2.3 | 2.3: #2, 4, 10, 20, 22, 26, 28, 36, 52, 58, 62 | 7 |

6 | W 1/16 | continuity, derivatives | 2.5, 2.7 | 2.5: #6, 10, 22, 40, 42^, 44, 48, 64c, 65 2.7: #8, 12, 14, 20, 30, 32, 38, 42ab*, 46, 48, 50, 52 | 10 |

7 | F 1/18 | derivative as function | 2.8, 3.7 (omit Ex. 6) | 2.8: #2, 8, 12, 20, 32a, 34*, 44, 48a, 56 3.7: #6, 12a, 16ab | 10 |

8 | M 1/21 | basic differentiation rules | 3.1, 3.2 | 3.1: #4, 8, 12, 15, 24, 30, 36, 42*, 50*, 54, 64, 72, 76a 3.2: #2, 6, 10, 18, 26, 34, 46, 48a, 50a, 54, 56 | 10 |

9 | W 1/23 | exponential growth, decay, cooling | 3.8 | 3.8: #4, 7, 16 3.4: #86* | 13 |

10 | F 1/25 | trigonometry | Appendix D, 3.3 | 3.3: #2, 10, 16, 20, 24, 28a, 34, 36, 38*, 40, 44, 48, 50 | 13 |

11 | M 1/28 | chain rule, related rates | 3.4, 3.9 | 3.4 #8, 14, 20, 48, 62, 66, 76, 82*, 84 3.9 #2, 12, 24, 32, 34, 40 | 13 |

12 | W 1/30 | catch-up, review | |||

13 | F 2/1 | exam 1 | |||

M 2/4 | midterm break | ||||

14 | W 2/6 | implicit differentiation, inverse functions | 3.5 (omit Inverse Trig), 3.6 | 3.5 #2, 22, 36 3.6 #4, 12, 20, 24, 26, 30, 34, 48, 50, 54 | 18 |

15 | F 2/8 | extrema | 4.1 | 4.1 #8, 14, 28, 36, 40, 48, 62, 73 | 18 |

16 | M 2/11 | mean value theorem, asymptotes | 4.2, 2.6 | 4.2 #4, 8, 22, 30, 34, 36 2.6 #6, 14, 18, 22, 38ac*, 48, 58 | 18 |

17 | W 2/13 | monotonicity, concavity, curve sketching | 4.3, 4.5 | 4.3 #6, 16, 22, 26, 30ac, 32, 62, 64 4.5 #22, 38, 40, 54, 56 | 21 |

18 | F 2/15 | optimization | 4.7 | 4.7 #8, 10, 38, 42, 58, 72 | 21 |

19 | M 2/18 | Newton's method | 4.8 | 4.8 #4, 8*, 16*, 30*, 33, 42* | 21 |

20 | W 2/20 | antiderivatives, substitution | 4.9, 5.5 (stop at Def. Integrals) | 4.9 #4, 10, 14, 24, 32, 44, 48, 50, 52, 62, 69, 72 5.5 #4, 6, 10, 12, 24, 30, 46 | 24 |

21 | F 2/22 | sigma notation, areas | 5.1 | 5.1 #2*, 4, 14*, 16*, 18, 20, 22, 26 | 24 |

22 | M 2/25 | integrals | 5.2 | 5.2 #4*, 8*, 12*, 18, 22, 30, 36, 44, 54, 70 | 24 |

23 | W 2/27 | catch-up, review | |||

24 | F 2/29 | exam 2 | |||

25 | M 3/3 | fundamental theorem | 5.3, 5.4, 5.5 (start at Def. Integrals) | 5.3 #2, 6, 14, 22, 26, 36, 40, 44, 58, 60, 64, 66 5.4 #32, 38, 48, 50, 52, 58, 60, 64 5.5 #54, 76, 78 | 27 |

26 | W 3/5 | areas between curves | 6.1 | 6.1 #2, 30, 32, 42*, 44, 50 | never |

27 | F 3/7 | volumes by washers | 6.2 | 6.2 #2, 6, 16, 34, 44, 46*, 60 | never |

28 | M 3/10 | conclusion, evaluations | |||

F 3/14 | final exam, 7:00-9:30 PM |