## Course schedule

Lecture | Date | Topic | Notes |
---|---|---|---|

1 | Jan 19 | Natural numbers, mathematical induction | |

2 | Jan 21 | Field axioms and rational numbers | |

3 | Jan 24 | The completeness axiom | |

4 | Jan 26 | Infinity | |

5 | Jan 28 | Sequences, convergence | HW 1 due |

6 | Jan 31 | Properties of sequences | |

7 | Feb 2 | Cauchy sequences | |

8 | Feb 4 | Subsequences | HW 2 due |

9 | Feb 7 | Bolzano–Weierstraß theorem | |

10 | Feb 9 | lim sup and lim inf | |

11 | Feb 11 | Series and convergence properties | HW 3 due |

12 | Feb 14 | Integral tests | |

13 | Feb 16 | Metric spaces: metrics | |

14 | Feb 18 | Metric spaces: set topology | HW 4 due |

Feb 21 | Presidents Day | ||

15 | Feb 23 | Metric spaces: compactness | |

Feb 25 | Midterm 1 | ||

16 | Feb 28 | Continuity | |

17 | Mar 2 | Intermediate Value Theorem | |

18 | Mar 4 | Uniform continuity | HW 5 due See note 1 |

19 | Mar 7 | Limits of functions 1 | |

20 | Mar 9 | Limits of functions 2 | |

21 | Mar 11 | Power series 1 | HW 6 due |

22 | Mar 14 | Uniform convergence | |

23 | Mar 16 | Power series 2 | |

24 | Mar 18 | Weierstraß approximation theorem | HW 7 due |

Mar 21 | Spring Break | ||

Mar 23 | Spring Break | ||

Mar 25 | Spring Break | ||

25 | Mar 28 | Differentiation | |

26 | Mar 30 | Midterm review | |

Apr 1 | Midterm 2 | ||

27 | Apr 4 | Mean Value Theorem / Rolle's theorem | |

28 | Apr 6 | Differentiation of inverses | |

29 | Apr 8 | L'Hôpital's rule | HW 8 due |

30 | Apr 11 | Taylor's theorem | See note 2 |

31 | Apr 13 | Riemann integration | |

32 | Apr 15 | Integration properties | HW 9 due |

33 | Apr 18 | Fundamental theorem of calculus | |

34 | Apr 20 | Fundamental theorem of calculus 2 | |

35 | Apr 22 | Improper integrals | HW 10 due |

36 | Apr 25 | Metric spaces: compactness 2 | See note 3 |

37 | Apr 27 | Metric spaces: continuity | |

38 | Apr 29 | Metric spaces: continuity 2 | HW 11 due |

## Notes

- The lecture on March 4th will be given by Michael VanValkenburgh.
- The lecture on April 11th will be given by Benjamin Stamm.
- The lecture on April 25th will be given by Per-Olof Persson.