For each date, there is required reading from sections in the textbook and sections in the course reader. You are to read the material before the lecture.

### Textbook

Simmons, George F. *Calculus with Analytic Geometry*. 2nd ed. New York, NY: McGraw-Hill, October 1, 1995. ISBN: 0070576424.

Readings in the textbook are listed by section numbers (e.g., § 2.1-2.4 means read sections 2.1 through 2.4.)

### Course Reader

MIT students will be provided with a copy of the Course Reader: Jerison, D., and A. Mattuck. _Calculus_1. Readings in the Course Reader are listed as “Notes”. (Not available to OCW users.)

ses # | TOPICS | readings |
---|---|---|

1 | Velocity and Rates of Change | § 2.1-2.4. |

2 | Slope and Derivative Limits and Continuity | Notes C. |

3 | Differentiation Formulas: Products and Quotients | § 3.1-3.2. |

4 | Chain Rule and Implicit Differentiation | § 3.3, 3.5-3.6, and 8.1-8.2. |

5 | The Derivatives of Exponential and Logarithm Functions | § 8.3-8.4. |

6 | The Derivatives of Trigonometric Functions | § 9.1-9.2, and 9.4. |

7 | Review for Exam 1 | |

Unit 1 Exam | ||

8 | Approximations Mean Value Theorem | Notes A, MVT. |

9 | Curve Sketching | § 4.1-4.2. |

10 | Max-Min Problems | § 4.3-4.4. |

11 | Related Rates | § 4.5. |

12 | Inequalities, Zeros, and Newton’s Method | § 4.6 and 2.6, pp. 76-77. |

Unit 2 Exam | ||

13 | Differentials and Indefinite Integrals | § 5.1-5.3. |

14 | Definite Integrals | § 6.1-6.4. |

15 | The Fundamental Theorem of Calculus | § 6.5-6.6. |

16 | Properties of Definite Integrals | Notes PI, Notes FT, and § 6.7. |

17 | Differential Equations and Separation of Variables | § 5.4 and 8.5. |

18 | Numerical Integration and Review of Unit 3 | § 10.9. |

Unit 3 Exam | ||

19 | Areas between Curves, Volumes of Revolutions, and Slicing | § 7.1-7.3. |

20 | Volumes by Shells and Average Values | Notes AV, § 7.4. |

21 | Parametric Equations and Arc Length | § 17.1 and 7.5. |

22 | Surface Area and Polar Coordinate Graphs | § 7.6 and 16.1-16.3. |

23 | Area and Arc Length in Polar Coordinates | § 16.4-16.5. |

Unit 4 Exam | ||

24 | Inverse Trigonometric Functions and Hyperbolic Functions | Notes G.7-G.9, § 9.5 and 9.7. |

25 | Integration by Inverse Substitution | § 10.4-10.5. |

26 | Integration by Partial Fractions | Notes F, § 10.6. |

27 | Integration by Parts | § 10.7-10.8. |

Unit 5 Exam | ||

28 | Indeterminate Forms and L’Hospital’s Rule | § 12.1-12.3. |

29 | Improper Integrals | Notes INT, § 12.4. |

30 | Infinite Series | § 13.1-13.3. |

31 | Power Series | § 14.1 and 14.4. |

32-33 | Final Review |