**Real numbers** |

0 | Proof writing and set theory | I 2.1-2.4 | |

1 | Axioms for the real numbers | I 3.1-3.7 | |

2 | Integers, induction, sigma notation | I 4.1-4.6 | Course Notes A |

3 | Least upper bound, triangle inequality | I 3.8-3.10, I 4.8 | Course Notes B |

4 | Functions, area axioms | 1.2-1.10 | |

**The integral** |

5 | Definition of the integral | 1.12-1.17 | |

6 | Properties of the integral, Riemann condition | | Course Notes C |

7 | Proofs of integral properties | 88-90, 113-114 | Course Notes D |

8 | Piecewise, monotonic functions | 1.20-1.21 | Course Notes E |

**Limits and continuity** |

9 | Limits and continuity defined | 3.1-3.4 | Course Notes F |

10 | Proofs of limit theorems, continuity | 3.5-3.7 | |

11 | Hour exam I | | |

12 | Intermediate value theorem | 3.9-3.11 | |

13 | Inverse functions | 3.12-3.14 | Course Notes G |

14 | Extreme value theorem and uniform continuity | 3.16-3.18 | Course Notes H |

**Derivatives** |

15 | Definition of the derivative | 4.3-4.4, 4.7-4.8 | |

16 | Composite and inverse functions | 4.10, 6.20 | Course Notes I |

17 | Mean value theorem, curve sketching | 4.13-4.18 | |

18 | Fundamental theorem of calculus | 5.1-5.3 | Course Notes K |

19 | Trigonometric functions | | Course Notes L |

**Elementary functions; integration techniques** |

20 | Logs and exponentials | 6.3-6.7, 6.12-6.16 | Course Notes M |

21 | IBP and substitution | 5.7, 5.9 | Course Notes N |

22 | Inverse trig; trig substitution | 6.21 | |

23 | Hour exam II | | |

24 | Partial fractions | 6.23 | Course Notes N |

**Taylor's formula and limits** |

25 | Taylor's formula | 7.1-7.2 | |

26 | Proof of Taylor's formula | | Course Notes O |

27 | L'Hopital's rule and infinite limits | 7.12-7.16 | Course Notes P |

**Infinite series** |

28 | Sequences and series; geometric series | 10.1-10.6, 10.8 (first page only) | |

29 | Absolute convergence, integral test | 10.11, 10.13, 10.18 | |

30 | Tests: comparison, root, ratio | 10.12, 10.15 | Course Notes Q |

31 | Hour exam III | | |

32 | Alternating series; improper integrals | 10.17, 10.23 | |

**Series of functions** |

33 | Sequences of functions, convergence | 11.1-11.2 | |

34 | Power series | 11.3-11.4 | Course Notes R |

35 | Properties of power series | | Course Notes R |

36 | Taylor series | 11.9 | Course Notes S |

37 | Fourier series | | Course Notes T |