https://classes.yale.edu/math305b
Final: Tuesday May 1st, 2001, 9 am (exam group 26).
Course number 49305, no CR/D/F.
Office hours: Tuesday, Thursday 10:15-11:15,
rm. 421 DL or by appointment (432-7048).
The topics will consist of:
Week | Section | Topics |
January 13,15 | Lebesgue 1-3 | Basics of Integration and "Lebesgue Outer Measure." |
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. |