The instructor is Professor Yanyan Li.

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Principles of Mathematical Analysis, by Walter Rudin, Third Edition
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Wed. 10:20--11:40am*

* Homework 25% ;
Midterm 35%;
Final Exam 40% (The in class part is 35%, and the take home part is 5%)
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(No late homework, drop two lowest for homework)

Date | Section | Homework | |
---|---|---|---|

Jan. 24 | Chapter 7, Sequences of Functions: Examples, Issues, and Uniform Convergence | Homework to be handed in: Page 165, #2,3, 4,6. Homework not handed in: Page 176, #1,5,7. | |

Jan. 28 | Chapter 7, Uniform convergence and continuity, Uniform convergence and integration, | Homework to be handed in: Page 166-167, #8, 9, 11, 12. Homework not handed in: P167, #10. | |

Jan. 31 | Chapter 7, Uniform convergence and differentiation | Homework to be handed in: Page 166, #7, 10, and two more assigned by Professor Han in class. | |

Feb. 4 | Chapter 7, Equicontinuity | Homework to be handed in: Page 167-168, #13, 15, 16, 17. | |

Feb. 7 | Chapter 7, Equicontinuity and Stone-Weisstrass Theorem | Homework to be handed in: page 168-169, #19, 20, 23, and one more assigned by Professor Han in class. | |

Feb. 11 | Chapter 8, Power Series, Abel's theorem, | Homework to be handed in: Page 196, #1, 2, 3. | |

Feb. 14 | Chapter 8, Exponential and Logarithmic functions, Trigonomic functions | Homework to be handed in: Page 196, 4a, 4c, 5a, 5c; Page 197, #6, 7, 9. Homework not handed in: Page 197, #4b, 4d, 5b, 5d; #8. | |

Feb. 18 | Chapter 8, Algebraic completeness of the complex field, Fourier Series | Homework to be handed in: Page 197-198, #10, 11, 12(a), 12(b). | |

Feb. 21 | Chapter 8, Fourier Series | Homework to be handed in: Page 198, #12(c), 12(d), 12(e), Page 199, #14, 15. | |

Feb. 25 | Chapter 6, Riemann-Stieltjes integrals, definition and existence of the integral | Homework to be handed in: Page 138, #1, 3, 5, 7. Homework not handed in: Page 138, #2, 4. | |

Feb. 28 | Chapter 6, Properties of the integral | Homework to be handed in: Page 138, #6, 8, 9, 10. | |

March 4 | Class canceled due to weather | Class canceled due to weather | |

March 7 | Exam 1 | ||

March 11 | Chapter 6, Properties of integrals | Homework to be handed in: Page 140, #11, 12; Page 138, #2, 4. | |

March 14 | Chapter 6, Integration and differentiation, Rectifiable curves | Homework to be handed in: Page 141-142, #13, 15, 17, 18. Homework not handed in: Page 141, #16, 19. | |

March 25 | Chapter 9, Linear transformations and Differentiation | Homework to be handed in: Page 239, #8-11. Homework not handed in: Page 239, #1-7. | |

March 28 | Chapter 9, Differentiation | Homework to be handed in: Page 239-240, # 12, 13, 14, 15. | |

April 1 | Chapter 9, The contraction principle, the Inverse Function Theorem | Homework to be handed in: Page 241-242, #17, 19, 21, 23. Homework not handed in: Page 241, #16. | |

April 4 | Chapter 9, Derivatives of higher order, Differential of integrals | Homework to be handed in: Page 241-242, #18, 24, 27, 28. Homework not handed in: Page 241-242, #22, 26. | |

April 8 | Chapter 9 | Homework to be handed in: Page 141, #16, 19; Page 197-198, #8, 13. | |

April 11 | Chapter 10. Integration, Primitive Mappings | Homework to be handed in: Page 288-289, #1-4. | |

April 15 | Chapter 10, Partition of Unity, Change of Variables, Differential Forms | Homework to be handed in: Page 290, #9-12. | |

April 18 | Chapter 10, Differential Forms | Homework to be handed in: Page 289-291, #5, 6, 13, 15. | |

April 22 | Chapter 10, Simplexes and Chains, Stokes' Theorem, Closed Forms and Exact Forms | Homework to be handed in: Page 293-294, #16, 18, 20, 21. | |

April 25 | Chapter 10, Closed Forms and Exact Forms, Poincare Lemma | Homework to be handed in: Page 290-292, #22, 24, 27, 28. | |

April 29 | Chapter 10, Vector Analysis | Homework handed in: Page 297, #23, 25, 26, 31. | |

May 2 | Chapter 10, Vector Analysis, partial review | Homework not handed in: Page 296-297, #30. Prepare for the Final Exam | |

May 6 | Partial review | Prepare for the Final Exam | |