18.01 - Syllabus (Fall 2017)

Date (click on date for lecture notes) | Reading (recommended before class) | Topics |

First recitation | Notes G: sections 1 - 4 | graphing |

9-7-17 | Text: 2.1 - 2.4 | derivatives, slope, velocity, rate of change |

9-8-17 | Notes C; Text: 2.5 (bottom pp. 70-73; concentrate on examples, skip the ε - δ definition); Text: 2.6 to pg. 75; learn definition (1) and the proof of "differentiable => continuous" at the end | limits, continuity, trigonometric limits |

9-12-17 | Text: 3.1, 3.2, and 3.4 | derivatives of products, quotients, sine, cosine |

9-14-17 | Text: 3.3 and 3.6 | chain rule, higher derivatives |

9-15-17 | Text: 3.5; Notes G: section 5; Text: 9.5 (bottom pp. 313 - 315) | implicit differentiation, inverses |

9-19-17 | Notes X (Text 8.2 has some of this); Text: 8.3 to middle of pg. 267, Text: 8.4 to top of pg. 271; Text: 9.7 to pg. 326 | exponential and log, logarithmic differentiation, hyperbolic functions |

9-21-17 | Notes A | linear and quadratic approximations |

9-22-17 | Text: 4.1 and 4.2 | curve sketching |

9-26-17 | Text: 4.3 and 4.4 | min-max problems |

9-28-17 | Midterm # 1 | |

9-29-17 | Holiday | Holiday |

10-3-17 | Text: 4.5 | related rates |

10-5-17 | Text: 4.6 (4.7 is optional) | Newton's method and other applications |

10-6-17 | Text: 2.6 to middle of pg. 77; Notes: MVT | mean value theorem, inequalities |

10-10-17 | Holiday | Holiday |

10-12-17 | Text: 5.2 and 5.3 | differentials, antiderivatives |

10-13-17 | Text: 5.4 and 5.8 | differential equations, separation of variables |

10-17-17 | Text: 6.3 though formula (4); skip proofs; Text: 6.4 and 6.5 | definite integrals |

10-19-17 | Review for Midterm #2 | |

10-20-17 | Midterm #2 | |

10-24-17 | Text: 6.6, 6.7 to top of pg. 215 (skip the proof pp. 207-8, which will be discussed in Ses #20) | first fundamental theorem of calculus |

10-26-17 | Notes: PI, pg. 2 [eqn. (7) and example]; Notes: FT | second fundamental theorem of calculus |

10-27-17 | Text: 7.1, 7.2, and 7.3 | applications to logarithms and geometry |

10-31-17 | Text 7.4 | volumes by disks, shells |

11-2-17 | Text: 7.7 to middle of pg. 247; Notes: AV | work, average value, probability |

11-3-17 | Text: 10.9 | numerical integration |

11-7-17 | Text: 10.2 and 10.3 | trigonometric integrals and substitutions |

11-9-17 | Text: 10.4 and 10.5 | integration by inverse substitution, completing the square |

11-10-17 | Holiday | Holiday |

11-14-17 | Review for Midterm # 3 | |

11-16-17 | Midterm # 3 | |

11-17-17 | Text: 10.6; Notes: F | partial fractions |

11-21-17 | Text: 10.7 | integration by parts, reduction formulas |

11-23-17 | Holiday | Holiday |

11-24-17 | Holiday | Holiday |

11-28-17 | Text: 17.1, 7.5, and 7.6 | parametric equations, arclength, surface area |

11-30-17 | Text: 16.1; (Text: 16.2 lightly, for the pictures), Text: 16.3 to top of pg. 570; Text: 16.5 to middle of pg. 581 | polar coordinates, area in polar coordinates |

12-1-17 | Text: 12.2 and 12.3 (examples 1-3, remark 1) | indeterminate forms - L'Hôspital's rule |

12-5-17 | Text: 12.4; Notes: INT | improper integrals |

12-7-17 | Text: pp. 439-442 (top), pp. 451-453 (skip proof in example 3), and pp. 455-457 (top) | infinite series and convergence tests |

12-8-17 | Midterm #4 | |

12-12-17 | Text: 14.4 through p. 498 (bottom); skip everything involving the remainder term Rn (x); Text: 14.3-pg. 490 (top) and examples 1-5 | Taylor's series |