Xuxing Chen (sec 03): xuxing@math.ucdavis.edu

Zachary Ibarra (sec 01, 02): zribarra@ucdavis.edu

Xuxing 3:00 to 4:00 pm Thurs in MSB 3219.

Ibarra 12:00 to 1:00 Tues and 4:00 to 5:00 Fri in MSB 2202.

**Course Outline:** Following the department syllabus from *Analysis on Manifolds* by James Munkres chapters 1-4 (sections 1-20).

This stack exchange thread discusses other good references.

Banach-Tarski Theorem: Why only some sets can get measures.

Dehn Theorem and Hilberrt's third problem: Why cube disections do not give all polyhedra.

**This table** is a rough outline of when topics will be covered and will be edited as the term progresses. The first chapter is meant to be mostly review and will be covered only briefly. The exam scheduling will not change. Homework problems will be added.

Day | Date | Section(#s) covered | Homework |

Mon | Apr 1 | Linear Algebra: 1.1 | HW1 part 1 Due Apr 12. |

Wed | Apr 3 | Matrix Inverse: 1.2 | HW1 parts 1-2 Due Apr 12. |

Fri | Apr 5 | Topology: 1.3 | HW1 Due Apr 12. |

Mon | Apr 8 | Compacta: 1.4 | |

Wed | Apr 10 | Derivatives: 2.5 | HW2Due April 26. |

Fri | Apr 12 | Differentiable: 2.5 | |

Mon | Apr 15 | Continuously Differentiable: 2.6 | |

Wed | Apr 17 | Review | |

Fri | Apr 19 | Midterm I | Solutions, More |

Mon | Apr 22 | Chain Rule Use: 2.7 | HW3 Due April 26. |

Wed | Apr 24 | Chain Rule Proof: 2.7 | |

Fri | Apr 26 | Inverse Fn Thm: 2.8 | |

Mon | Apr 29 | Integrals: 3.10 | HW4 Due May 3. |

Wed | May 1 | Int Existence: 3.11 | |

Fri | May 3 | Int Evaluation: 3.12 | |

Mon | May 6 | Int Evaluation: 3.12 | HW5 Due May 10. |

Wed | May 8 | Int Bounded: 3.13 | |

Fri | May 10 | Int Bounded: 3.13 | |

Mon | May 13 | Rectifiable Sets: 3.14 | HW6 Due May 24 |

Wed | May 15 | review | |

Fri | May 17 | Midterm II | PracticeAnswers covers 2.5 - 3.14 |

Mon | May 20 | Int- Improper: 3.15 | |

Wed | May 22 | Partitioning Unity: 4.16 | |

Fri | May 24 | Change Variables: 4.17 | |

Mon | May 27 | Memorial Day: no class | HW7 Due May 31 |

Wed | May 29 | Diffeomorphism: 4.18 | |

Fri | May 31 | Var Chng Proof: 4.19 | |

Mon | Jun 3 | Var Chng Appl: 4.20 | |

Wed | Jun 5 | review | |

Wed | Jun 12 | Final 6-8pm. |