Chutong Wu, Email: ctwu@ucdavis.edu, Office: MSB 2129

**Course Outline:** Following the department syllabus and department outline

from *Analysis on Manifolds* by James Munkres chapters 1-4 (sections 1-20).

This stack exchange thread discusses other good references.

More fun math: Directed Reading Program

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 and optimistic outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will be added.

Chain Rule: 2.7

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

Wednesday | September 22 | Linear Algebra:1.1 | 1.1.1, 1.1.4. (Due Fri Oct 1). |

Friday | September 24 | Matrices: 1.2 | 1.2.1, 1.2.2, 1.2.4. (Due Fri Oct 1). |

Monday | September 27 | Inverses: 1.2 | 1.1.2, 1.2.6. (Due Fri Oct 8). |

Wednesday | September 29 | Topology: 1.3 | 1.3.1, 1.3.2. (Due Fri Oct 8). |

Friday | October 1 | Closure: 1.3 | 1.3.3, 1.3.4, 1.3.9. (Due Fri Oct 8.) |

Monday | October 4 | Continuity: 1.3 | 1.3.6, 1.3.7. (Due Mon Oct 18) |

Wednesday | October 6 | Continuity: 1.3 | 1.3.5, 1.3.8. (Due Mon Oct 18). |

Friday | October 8 | Compacta: 1.4 | 1.4.1.a, 1.4.2. (Due Mon Oct 18) |

Monday | October 11 | Derivatives: 2.5 | 2.5.2, 2.5.3. (Due Mon Oct 18) |

Wednesday | October 13 | Review | Office Hours Today |

Friday | October 15 | Midterm I Answers and Practice Exam Answers | |

Monday | October 18 | Continuously Differentiable: 2.6 | 2.5.4, 2.6.5 (Due Friday Oct 29). |

Wednesday | October 20 | Continuously Differentiable: 2.6 | 2.6.4, 2.6.6 (Due Friday Oct 29). |

Friday | October 22 | Multiple Derivatives 2.6 | 2.6.9, 2.6.10 (Due Friday Oct 29). |

Monday | October 25 | Chain Rule: 2.7 | 2.6.3, 2.6.7. (Due Friday Nov 5). |

Wednesday | October 27 | 2.7.1 , 2.7.2, 2.7.3. (Due Friday Nov 5). | |

Friday | October 29 | Inverse Function Thm: 2.8 | 2.8.1, 2.8.2. (Due Friday Nov 5). |

Monday | November 1 | Inverse Function Thm: 2.8 | 2.8.3, 2.8.4. (Due Monday Nov 15). |

Wednesday | November 3 | Inverse Function Thm: 2.8 | 2.8.5. (Due Monday Nov 15). |

Friday | November 5 | Riemann Integral: 3.10 | |

Monday | November 8 | Lebesgue Condition: 3.11 | 3.10.5, 3.11.5 (Due Friday Nov 19). |

Wednesday | November 10 | Review | |

Friday | November 12 | Midterm II Answers. | Practice Exam and Answers |

Monday | November 15 | Fubini Thm: 3.12 | 3.12.1, 3.12.3 (Due Monday Nov 29). |

Wednesday | November 17 | Integration over Bounded Sets: 3.13 | 3.12.4, 3.13.1, 3.13.5 (Due Monday Nov 29). |

Friday | November 19 | Rectifiable Sets: 3.14 | 3.14.2, 3.14.6, 3.14.7 (Due Monday Nov 29). |

Monday | November 22 | Improper Integrals: 3.15 | 3.15.1, 3.15.2, 3.15.4. (Due Monday Nov 29) |

Wednesday | November 24 | Change of Variables: 4 | 4.17.3, 4.17.5 (Due Friday Dec 3). |

Friday | November 26 | No Class | |

Monday | November 29 | Change of Variables: 4 | |

Wednesday | December 1 | Change of Variables: 4 | |

Friday | December 3 | Change of Variables: 4 | |

Tuesday | December 7 | Final 1-3pm |