# MATH 255 Honours Analysis 2

## Lecture notes

Subject | Semester |
---|---|

## Wednesday, January 9, 2013Some basic continuous functions results |
Winter 2013 |

## Friday, January 11, 2013Continuous functions on closed, bounded intervals |
Winter 2013 |

## Monday, January 14, 2013Location of roots and the Intermediate Value Theorem |
Winter 2013 |

## Wednesday, January 16, 2013Uniform Continuity |
Winter 2013 |

## Friday, January 18, 2013Lipschitz functions, increasing/decreasing functions |
Winter 2013 |

## Monday, January 21, 2013More on monotonic sequences and a brief introduction to cardinality |
Winter 2013 |

## Wednesday, January 23, 2013Properties of monotone functions |
Winter 2013 |

## Friday, January 25, 2013Differentiability and combinations of differentiable functions |
Winter 2013 |

## Monday, January 28, 2013Carathéodory's Theorem and set-up for the chain rule |
Winter 2013 |

## Wednesday, January 30, 2013The chain rule, derivatives of inverse functions, and relative extrema |
Winter 2013 |

## Friday, February 1, 2013Rolle's Theorem, Mean Value Theorem |
Winter 2013 |

## Monday, February 4, 2013Continuing with the mean value theorem |
Winter 2013 |

## Wednesday, February 6, 2013L'Hospital's Rule |
Winter 2013 |

## Friday, February 8, 2013Taylor's Theorem |
Winter 2013 |

## Friday, February 15, 2013Riemann Criterion, and some results about integrability |
Winter 2013 |

## Monday, February 25, 2013Integrability of function compositions |
Winter 2013 |

## Monday, February 11, 2013Introduction to Riemann sums |
Winter 2013 |

## Wednesday, February 27, 2013Fundamental Theorem of Calculus |
Winter 2013 |

## Wednesday, February 13, 2013Defining the integral |
Winter 2013 |

## Monday, February 18, 2013Linearity of the integral |
Winter 2013 |

## Monday, March 11, 2013Antiderivatives and Integration by Parts |
Winter 2013 |

## Monday, March 18, 2013Cauchy Criterion for function sequences, introduction to the norm |
Winter 2013 |

## Wednesday, February 20, 2013Additivity Theorem for integrals |
Winter 2013 |

## Wednesday, March 20, 2013Distinctions between uniform and pointwise convergence |
Winter 2013 |

## Friday, March 22, 2013Interchange of limits and differentiability |
Winter 2013 |

## Monday, March 25, 2013The exponential function |
Winter 2013 |

## Wednesday, March 27, 2013Introduction to series |
Winter 2013 |

## Wednesday, April 3, 2013Comparison tests, absolute and conditional convergence |
Winter 2013 |

## Friday, April 12, 2013Series of functions |
Winter 2013 |

## Friday, February 22, 2013? |
Winter 2013 |

## Friday, March 1, 2013? |
Winter 2013 |

## Wednesday, March 13, 2013? |
Winter 2013 |

## Friday, March 15, 2013? |
Winter 2013 |

## Friday, April 5, 2013? |
Winter 2013 |

## Monday, April 8, 2013? |
Winter 2013 |

## Wednesday, April 10, 2013? |
Winter 2013 |