Introduction to Analysis II

Syllabus
Note: on the printed syllabus, my office phone was wrong; the correct number is (212) 854-2298.

Jan. 18: Gallagher, lecture 33.

Jan. 23: Gallagher, lecture 34, with Cesaro's Theorem and Hardy's Theorem from lecture 29.

Jan. 25: Gallagher, end of lecture 34 and jump discontinuities from lecture 35.
Homework 1 (due Feb. 1)

Jan. 30: Gallagher, lecture 36.

Feb. 1: Rudin pages 204–215 and 235–236.
Homework 2 (Due Feb. 13)

Feb. 6: Rudin pages 218 (Theorem 9.19) and 220–223

Feb. 8: Rudin pages 223–228

Feb. 13: Rudin pages 231–234 and 245–248
Homework 3 (Due Feb. 20)

Feb. 15: Rudin pages 248–253

Homework 4 (Due Apr. 17)

Homework 5 (Due Apr. 24)

Notes from Professor Gallagher

The lectures are available in PDF or DjVu format. You can get a free software viewer (standalone or plug-in) for Linux or Unix systems, or a plug-in for other platforms.

Lecture 29: Theorems of Abel and Tauber (DJVU)

Lecture 33: Fourier Series: Fejer's Theorem (DJVU)

Lecture 34: Fourier Series: Theorems of Dirichlet and Parseval (DJVU)

Lecture 35: Fourier Series: Dirichlet's Proof, Jump Discontinuities (DJVU)

Lecture 36: Random Walks; Appl. of Fourier Series to Gauss Sums and Fresnel Integrals (DJVU)

Lecture 41: Measure of an Open Set

Lecture 42: Outer Measure, Inner Measure, Measure

Lecture 43: More on Measurable and Non-Measurable Sets

Lecture 44: Measurable Functions, Egorav's Theorem