## Lecture notes

The schedule of topics for all sections is available in the common page for MATH 100.

Timeline | Topics | Textbook sections | Comments | ||
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Limits and continuity |
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Week 1 |
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09/05 | Imagine Day: no class | ||||

09/07 | Intro. Lecture | Introduction. Motivation and the limit of a function. | 1.1 - 1.3 | Reading assignment: section 1.1 | |

Week 2 |
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09/12 | Lecture | Limits to infinity. Calculating limits with limit laws. | 1.3 and 1.4 | ||

09/14 | Lecture | More on limit laws. Limits at infinity. | 1.5 - 1.6 | Read Theorem 1.5.9 carefully | |

Week 3 |
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09/19 | Lecture | Examples of limits at infinity. Continuity. | 1.6 | ||

09/21 | Quiz 1 | Lecture | Intermediate Value Theorem. Bisection Method. | 1.6 | A video about "the woobly table theorem" |

Week 4 |
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The derivative |
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09/26 | Lecture | The derivative | 2.1 - 2.3 | Two Geogebra apps: for visualizing secant and tangent lines and the derivative as the slope of the tangent . | |

09/28 | Lecture | Arithmetic of derivatives (and some proofs). Derivatives of exponential functions. | 2.3-2.7 | Read the review of logarithms: Section 2.7 in CLP-I. | |

Week 5 |
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10/03 | Lecture/Worksheet | Derivatives of exponential and trigonometric functions | 2.6-2.8 | ||

10/05 | Quiz 2 | Lecture/Worksheet | The chain rule | 2.9 | |

Week 6 |
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10/10 | Lecture/Worksheet | Review of inverse function and logarithms | 0.6, 2.10 | More on the importance of logarithms (in two comic strips): https://xkcd.com/1162/ and https://xkcd.com/482/ | |

10/12 | Lecture/Worksheet | Implicit differentiation. Derivatives of inverse functions: logarithm and trigonometric functions. | 2.10, 2.11, 2.12 | ||

Applications |
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Week 7 |
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10/17 | Lecture/Worksheet | Rates of change. Exponential growth and decay. | 3.1 and 3.3. | A note on acceleration and speeding up | |

10/19 | Quiz 3 | Lecture/Worksheet | Exponential growth and decay. | 3.3 | |

Week 8 |
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10/24 | Lecture/Worksheet | Newton's law of cooling and related rates | 3.3 and 3.2 | ||

10/26 | Lecture/Worksheet | Linear approximation, quadratic approximation and introduction to Taylor polynomials. | 3.4 | ||

Week 9 |
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10/31 | Lecture/Worksheet | Taylor polynomials and remainders | 3.4 | ||

11/02 | Quiz 4 | Lecture | More on Taylor polynomials and remainders. Global maxima and minima. | 3.4 and 3.5 | |

Week 10 |
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11/07 | Lecture/Worksheet | Optimisation: maxima and minima | 3.5 | ||

11/09 | Lecture | Mean Value Theorem | 2.13 | ||

Week 11 |
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11/14 | Lecture/Worksheet | Problems on Mean Value Theorem. Curve sketching: derivatives and the shape of a function. | 2.13 and 3.6 | ||

11/16 | Quiz 5 | Lecture/Worksheet | Curve sketching: concavity | 3.6 | |

Week 12 |
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11/21 | Lecture/Worksheet | Cuve sketching: symmetries and sketching | 3.6 | ||

11/23 | Lecture/Worksheet | L'Hôpital's rule | 3.7 | ||

Week 13 |
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11/28 | Lecture/Worksheet | Optimisation problems | 3.5.3 | ||

11/30 | Lecture/Worksheet | Antiderivatives | 4.1 | ||

Exams. 12/05 - 12/20 |
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Final exam |