Mathematics 305b

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:

The grading scheme will be as follows:

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

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.
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.