## MAT 371: Advanced Calculus I

## Spring 2019

Class Time | Tu,Th 1:30pm – 2:45pm |

Class Location | Tempe – WXLRA 108 |

Instructor | Sébastien Motsch |

Office | WXLRA 836 |

smotsch@asu[dot]edu | |

Office Hours | Wed 9:30am – 10:30am, Th 3:00pm – 4:00pm, |

Class webpage | www.seb-motsch.com/teaching |

## Textbook

- Stephen Abbott,
*Understanding Analysis*(2nd edition)

### Course description

- set theory, topology
*(Chap. 1-3)* - functions
*(Chap. 4-5)* - series and integrale
*(Chap. 6-7)*

The first mid-term will be held **Thursday Feb. 14**. The second mid-term will be held **Thursday Mar. 28**. The **final** will be on *Thursday May 2nd* (12:10-2:00).

### Class Schedule

Jan 8 – 10 | Presentation course – real numbers (chap. 1.1-1.2) |

Jan 15 – 17 | Completeness, cardinality (chap. 1.3-1.5) |

Jan 22 – 24 | Cantor’s theorem, sequences (chap. 1.6, 2.1-2.2) |

Jan 29 – 31 | Sequences, Monotone convergence (chap. 2.2-2.5) |

Feb 05 – 07 | Cauchy criteria, Series (chap. 2.6-2.8) |

Feb 12 – 14 | Revision (solution practice mid-term 1), Mid-term 1 (solution) |

Feb 19 – 21 | Open, closed sets (chap. 3.1-3.3) |

Feb 26 – 28 | Connected sets, Baire theorem (chap. 3.4-3.5) |

Mar 5 – 7 | Continuous functions (chap. 4.2-4.3) |

Mar 12 – 14 | Continuity and compact sets (chap. 4.4) |

Mar 19 – 21 | Continuity and connected sets (chap. 4.5) |

Mar 26 – 28 | Revision (solution practice mid-term 2), Mid-term 2 (solution) |

Apr 02 – 04 | Derivatives (chap. 5.2-5.3) |

Apr 09 – 11 | Limit sequence of functions (chap. 6.2-6.4) |

Apr 16 – 18 | Power series, Integral (chap. 6.5-6.6, 7.2) |

### Class homework

Jan 15 | chap 1.2: 3, 4, 5, 7, 8, 9, solution |

Jan 22 | chap 1.3: 8,9, 11, chap 1.4: 3,4, chap 1.5: 4,5, (extra 9), solution |

Jan 29 | chap 1.6: 3, 4, (extra 9), chap 2.2: 1, 2, 4, 5, solution |

Feb 5 | chap 2.2: 7, chap 2.3: 2, 3, 5, 9, 11, chap 2.4: 1, solution |

Feb 12 | chap 2.5: 1, 5, chap 2.6: 2, 4, chap 2.7: 2, solution |

Feb 26 | chap 3.2: 2, 3, 6, 8, 11, 14, chap 3.3: 2, solution |

Mar 12 | chap 3.3.: 4, 8, chap 3.4: 1, 7, chap 3.5: 5, 9, chap 4.2: 2, solution |

Mar 21 | chap 4.2.: 5, 9, chap 4.3: 6, 9, solution |

Apr 9 | chap 5.2.: 2, 5, 6, chap 5.3: 1, 2, 6, 7, solution |

Apr 16 | chapter 6.2: 1, 3, 9, chapter 6.3: 1, 2, 3, chapter 6.4: 2, solution |

Apr 23 | chap. 6.5: 2, 4, 7, 8, chap. 6.6: 2, 7, chap. 7.2: 2 solution |