Real Analysis: Mathematics 305b, Spring 1998

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,

Stephen Miller

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

Tentative Syllabus

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