LEC # | TOPICS | KEY DATES |
---|---|---|

1 | Sets, Set Operations, and Mathematical Induction | |

2 | Cantor’s Theory of Cardinality (Size) | Assignment 1 due |

3 | Cantor’s Remarkable Theorem and the Rationals’ Lack of the Least Upper Bound Property | |

4 | The Characterization of the Real Numbers | Assignment 2 due |

5 | The Archimedian Property, Density of the Rationals, and Absolute Value | |

6 | The Uncountabality of the Real Numbers | Assignment 3 due |

7 | Convergent Sequences of Real Numbers | |

8 | The Squeeze Theorem and Operations Involving Convergent Sequences | Assignment 4 due |

9 | Limsup, Liminf, and the Bolzano-Weierstrass Theorem | |

10 | The Completeness of the Real Numbers and Basic Properties of Infinite Series | Assignment 5 due |

11 | Absolute Convergence and the Comparison Test for Series | |

12 | The Ratio, Root, and Alternating Series Tests | Assignment 6 due |

Midterm Exam | Midterm Exam due | |

13 | Limits of Functions | |

14 | Limits of Functions in Terms of Sequences and Continuity | Assignment 7 due |

15 | The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet’s Function | |

16 | The Min/Max Theorem and Bolzano’s Intermediate Value Theorem | Assignment 8 due |

17 | Uniform Continuity and the Definition of the Derivative | |

18 | Weierstrass’s Example of a Continuous and Nowhere Differentiable Function | Assignment 9 due |

19 | Differentiation Rules, Rolle’s Theorem, and the Mean Value Theorem | |

20 | Taylor’s Theorem and the Definition of Riemann Sums | Assignment 10 due |

21 | The Riemann Integral of a Continuous Function | |

22 | The Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula | Assignment 11 due |

23 | Pointwise and Uniform Convergence of Sequences of Functions | |

24 | Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits | Assignment 12 due |

25 | Power Series and the Weierstrass Approximation Theorem | |

Final Assignment | Final Assignment due |

## Calendar

## Course Info

##### Instructor

##### Departments

##### As Taught In

Fall
2020

##### Level

##### Learning Resource Types

*notes*Lecture Notes

*theaters*Lecture Videos

*grading*Exams

*assignment*Problem Sets