SES # | TOPICS | READINGS AND ASSIGNMENTS |
---|---|---|

1 | Monotone sequences; completeness; inequalities | |

2 | Estimations; limit of a sequence | Assignment 1 readings and problems (PDF) |

3 | Examples of limits | Assignment 2 readings and problems (PDF) |

4 | Error term; limit theorems | |

5 | Subsequences, cluster points | Assignment 3 readings and problems (PDF) |

6 | Nested intervals, Bolzano-Weierstrass theorem, Cauchy sequences | Assignment 4 readings and problems (PDF) |

7 | Completeness property for sets | |

8 | Infinite series | Assignment 5 readings and problems (PDF) |

9 | Infinite series (cont.) | |

10 | Power series | Assignment 6 readings and problems (PDF) |

11 | Functions; local and global properties | Assignment 7 readings and problems (PDF) |

12 | Exam 1 (open book) | |

13 | Continuity | Assignment 8 readings and problems (PDF) |

14 | Continuity (cont.) | Assignment 9 readings and problems (PDF) |

15 | Intermediate-value theorem | Assignment 10 readings and problems (PDF) |

16 | Continuity theorems | Assignment 11 readings and problems (PDF) |

17 | Uniform continuity | |

18 | Differentiation: local properties | Assignment 12 readings and problems (PDF) |

19 | Differentiation: global properties | Assignment 13 readings and problems (PDF) |

20 | Convexity; Taylor's theorem (skip proofs) | |

21 | Integrability | Assignment 14 readings and problems (PDF) |

22 | Riemann integral | Assignment 15 readings and problems (PDF) |

23 | Fundamental theorems of calculus | |

24 | Improper integrals, convergence, Gamma function | Assignment 16 readings and problems (PDF) |

25 | Stirling's formula; conditional convergence | Assignment 17 readings and problems (PDF) |

26 | Exam 2 (open book) | |

27 | Uniform convergence of series | |

28 | Continuity of sum; integration term-by-term | Assignment 18 readings and problems (PDF) |

29 | Differentiation term-by-term; analyticity | Assignment 19 readings and problems (PDF) |

30 | Continuous functions on the plane | Assignment 20 readings and problems (PDF) |

31 | Quantifiers and Negation | Assignment 21 readings and problems (PDF) |

32 | Plane point-set topology | Assignment 22 readings and problems (PDF) |

33 | Compact sets and open sets | |

34 | Differentiating integrals with respect to a parameter | Assignment 23 readings and problems (PDF) |

35 | Leibniz and Fubini theorems | Assignment 24 readings and problems (PDF) |

36 | Improper integrals with a parameter | |

37 | Differentiating and integrating improper integrals | Assignment 25 readings and problems (PDF) |

38 | Countability; sets of measure zero | |

39 | Introduction to Lebesgue integral; review | Assignment 26 readings and problems (PDF) |

40 | Three-hour final exam during finals week (open book) |