http://www.math.yale.edu/users/steve/305b.html

Tuesday-Thursday, 1 - 2:15 pm, Prof. Stephen Miller

Final: Thursday May 7th, 1998, 9 am (exam group 26).

Course number **49305**, no CR/D/F.

Office hours: Tuesday, Wednesday 10:15-11:15, rm. 421 DL or by appointment (432-7048).

The notes are now available at Minitprint, 27 Whitney.

The topics will consist of:

- Lebesgue Integration.
- Fourier Series.
- Applications to
- differential equations,
- probability theory.

The grading scheme will be as follows:

- Each midterm exam will account for 20% of the grade. There
will be two midterms:
- February 17th (in class),
- Spring break (take-home exam, due in class on March 31) download it here in postscript format.

- Weekly homeworks will total 20% of the grade, with the lowest homework from each half of the course dropped. Homeworks are assigned in class on Thursdays and due the following Thursday afternoon (before 5 pm to either my office, mail box, or reader Youngson Yoon's box).
- The final exam will be 40% of the grade.
- If a student's performance on the final is significantly better than their performance on the midterms then I will count the final as 80% of their grade (i.e. removing the midterm grades entirely).

This web-page was last updated on **February 2, 1997** and will be
updated
often. If you are interested in taking the course or have any other
questions please contact me below. Thanks for your interest,

- E-mail:
`steve@math.yale.edu` - Phone: (203)432-7048
- Office: 421 Dunham Labs

Week | Section | Topics |

January 13,15 | Lebesgue 1-3 | Basics of Integration and "Lebesgue Outer Measure." (Beals) |

January 20,22 | Lebesgue 4-8 | Measurable Sets and Functions. |

January 27,29 | Lebesgue 8-10 | Lebesgue Integration and its Convergence Theorems. |

February 3,5 | Lebesgue 11-13 | Null sets, Riemann Integration Revisited, Vector Spaces of Functions. |

February 10,12 | Lebesgue 14-15, Fourier 1 | Inner Products of Functions, Fundamental Theorem of Calculus. |

February 17,19 | Fourier 1-3 | MIDTERM, Fourier Series and Coefficients. |

February 24,26 | Fourier 4-7 | Convergence of Fourier Series, Riesz-Fischer Theorem. |

March 3,5 | Fourier Applications | Convolutions, some Number Theory. |

SPRING BREAK, TAKE-HOME MIDTERM | ||

March 24,26 | Fourier Applications | Music: The Fast Fourier Transform and Instruments. |

March 31, April 2 | Fourier Applications | The Heisenberg Uncertainty Principle via Fourier Analysis. |

April 7,9 | ODE 1-3 | Ordinary Differential Equations and Matrices. |

April 14,16 | ODE 4-6 | Existence and Uniqueness Theorems for ODE's. |

April 21,23 | Wrap-up | Finish off some loose ends or do more applications. |

steve@math.yale.edu