# Information

Instructor | Jean-Baptiste (JB) Campesato |

campesat [@t) math.toronto.edu | |

Schedule | Monday, 4pm to 5pm |

Wednesday, 4pm to 6pm | |

Room MP202 (1st term) | |

Room MP102 | |

MAT137 Website | http://uoft.me/MAT137 |

# My archives

Some documents I wrote for this course. They may differ from the version on the website of the course.

# 1. Introduction to mathematical logic, quantifiers, definitions and proofs

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Sep 10 | Introduction | --- | --- | slides - notes about slide 8 |

Wed, Sep 12 | Sets and quantifiers | 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 | 1.1, 1.2, 1.3 | slides - printable |

Mon, Sep 17 | Conditional statements | 1.7, 1.8, 1.9 | 1.3 | slides - printable |

Wed, Sep 19 | Definitions, proofs and induction | 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 | 1.4 | slides - printable |

# 2. Limits and continuity

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Sep 24 | Absolute value, distance and inequalities | 2.4 | 1.2, 1.8 | slides - printable |

Wed, Sep 26 | Limits | 2.1, 2.2, 2.3, 2.5, 2.6 | 2.1, 2.2 | slides - printable |

Mon, Oct 1 | Proofs using the definition of limits | 2.7, 2.8, 2.9 | 2.2 | slides - printable - notes about slide 6 |

Wed, Oct 3 | Limit laws | 2.10, 2.11, 2.12, 2.13 | 2.3 | slides - printable - notes about slide 8 |

Wed, Oct 10 | Continuity | 2.14, 2.15, 2.16, 2.17, 2.18 | 2.4 | slides - printable |

Mon, Oct 15 | Some limit computations | 2.19, 2.20 | 2.1, 2.3, 2.4 | slides - printable |

Wed, Oct 17 (1st part) | IVT and EVT | 2.21, 2.22 | 2.5 | slides - printable |

# 3. Derivatives

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Oct 17 (2nd part) | Definition of a derivative | 3.1, 3.2, 3.3 | 3.1 | slides - printable |

Mon, Oct 22 | Differentiation rules | 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 | 3.1, 3.2, 3.3 | slides - printable |

Wed, Oct 24 | The chain rule + more on differentiation rules | 3.10 | 3.5 + 3.1, 3.2, 3.3 | slides - printable |

Mon, Oct 29 | Trig derivatives, implicit differentiation | 3.11, 3.12 | 3.4, 3.7 | slides - printable |

Wed, Oct 31 | Related rates + derivatives of exponentials and logarithms | 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20 | 3.4, 3.6, 3.7, 4.7 | slides - printable |

You have to watch a lot of videos for Wednesday, Oct 31. Even if they are short, you shouldn't wait for the last time to watch them.

# 4. Inverse functions and inverse trigonometric functions

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Nov 12 | Inverse functions | 4.1, 4.2 | 1.5, 1.7 | slides - printable |

Wed, Nov 14 | One-to-one functions and inverse trig functions | 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 | 1.7, 3.5, 3.6 | slides - printable |

# 5. The Mean Value Theorem and applications

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Nov 19 | Local extrema | 5.1, 5.2, 5.3, 5.4 | 4.1 | slides - printable - notes about slide 4 |

Wed, Nov 21 | Rolle's Theorem and the MVT | 5.5, 5.6, 5.7, 5.8, 5.9 | 4.2 | slides - printable - notes about slide 7 |

Mon, Nov 26 | Monotonicity | 5.10, 5.11, 5.12 | 4.3 | slides - printable |

# 6. Applications of the derivative

Warning: I modified the order of the two first lectures.

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Nov 28 | Indeterminate forms and L'Hôpital's Rule | (6.3), 6.4, 6.5, (6.6), 6.7, 6.8, (6.9), 6.10 | 4.4, 4.5, 4.6 | slides - printable |

Mon, Dec 3 | Applied optimization | 6.1, 6.2 | 4.8 | slides - printable |

Wed, Dec 5 | Concavity and asymptotes | 6.11, 6.12, 6.13, 6.14, 6.15, 6.16 | 2.1, 4.9 | slides |

Thu, Dec 6 Thanksgiving make up |
Curve sketching | ∅ | 4.9 | slides - printable |

# 7. Integral: a definition and first properties

Date | Topics | Required videos | Lecture slides |
---|---|---|---|

Mon, Jan 7 | Summation and the Σ notation | 7.1, 7.2 | slides - printable |

Wed, Jan 9 | Integrable functions | 7.3, 7.4, 7.5, 7.6, 7.7 | slides - printable - notes about slide 6 |

Mon, Jan 14 | Integrable functions (continuation) | 7.8, 7.9 | slides - printable - notes about slides 4 and 5 |

Wed, Jan 16 (1st part) | Properties of the integral | 7.10, 7.11, 7.12 | slides - printable - Recap of the notations |

# 8. The fundamental theorem of calculus

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Jan 16 (2nd part) | Antiderivatives and indefinite integrals | 8.1, 8.2 | 5.5, 5.6 | slides - printable |

Mon, Jan 21 | FTC - 1 | 8.3, 8.4 | 5.6 | slides - printable |

Wed, Jan 23 (1st part) | FTC - 2 | 8.5, 8.6, 8.7 | 5.6 | slides - printable |

# 9. Integration methods

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Jan 23 (2nd part) | Integration by substitution | 9.1, (9.2), (9.3), (9.4) | 6.1 | slides - printable |

Mon, Jan 28 | Integration by parts | (9.5), 9.6, (9.7), (9.8), (9.9) | 6.2 | slides - printable |

Wed, Jan 30 | Trigonometric and rational functions | 9.10, (9.11), (9.12), 9.15, (9.16), (9.17) | 6.3, 6.5 | slides - printable |

# 10. Volumes

Date | Topics | Required videos | Lecture slides |
---|---|---|---|

Mon, Feb 4 | Volumes: slicing method | 10.1 | slides - printable |

Wed, Feb 6 (1st part) Fri, Feb 8, 3-4pm Room: MP203 |
Volumes: shell method | 10.2 | slides |

# 11. Sequences

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Feb 6 (2nd part) Mon, Feb 11, 4-6pm Room: MP102 |
Sequences: definition and first properties |
11.1, 11.2, 11.3, 11.4 | 8.1, 8.2 | slides - printable |

Wed, Feb 13 | Theorems about sequences | 11.5, 11.6, 11.7, 11.8 | 8.2 | slides - printable |

# 12. Improper integrals

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Feb 25 | Improper integrals | 12.1, (12.2), (12.3), 12.4, (12.5), (12.6) | 7.8, 7.9 | slides - printable |

Wed, Feb 27 | BCT and LCT for integrals | 12.7, 12.8, 12.9, 12.10 | 7.8, 7.9 | slides - some notes |

# 13. Series

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Mon, Mar 4 | Definition of series | (13.1), 13.2, 13.3, 13.4 | 8.3 | slides - printable - notes about slide 7 |

Wed, Mar 6 | Properties of series | 13.5, 13.6, 13.7, 13.8, 13.9 | 8.3, 8.4 | slides - printable |

Mon, Mar 11 | Integral and comparison tests | 13.10, 13.11, 13.12 | 8.5, 8.7 | slides |

Wed, Mar 13 | Absolute convergence and alternating series | 13.13, 13.14, 13.15, (13.16), (13.17) | 8.6 | slides - printable |

Mon, Mar 18 | Ratio test | 13.18, 13.19 | 8.7 | slides - printable |

# 14. Power series and Taylor series

Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|

Wed, Mar 20 | Power series and Taylor polynomials | 14.1, 14.2, 14.3, 14.4 | 9.1, 9.2, 9.3 | slides - printable |

Mon, Mar 25 | Taylor series | 14.5, 14.6 | 9.1, 9.2, 9.3 | slides - printable |

Wed, Mar 27 | Analytic functions | 14.7, 14.8, 14.9, 14.10 | 9.1, 9.2, 9.3 | slides - printable |

Mon, Apr 1 | Applications | 14.12, 14.14 | 9.1, 9.2, 9.3, 9.4 | slides (with recap) |

Wed, Apr 3 | Applications | 14.11, 14.13, 14.15 | 9.1, 9.2, 9.3, 9.4 | slides - printable - Slide 6 solutions |