Analysis II (Math 131B), Fall 2021

Sweeney Hall 413, MW 12:30-1:45pm (Sec 03, code 50896)

Last update of this page: Tue Dec 07, 10:10am

Ongoing useful links:

Announcements:

FUA (Frequently Used Acronyms):

In the box below are some acronyms that I use all the time, both in class and when grading your work. You are welcome to use them as well.

(list of Frequently Used Abbreviations)

Administrative handouts:

Course greensheet

Course notes:

Course mechanics: Homework in Math 131B, Checkins, Workflow in this class

Course content: Writing proofs, How to do a problem set outline; Problem solving strategies in analysis.

Topics for exams:

Exam 1, Exam 2, Exam 3, Final exam.

Sample exams:

Exam 1, Exam 2, Exam 3, Final exam.

Online lectures:

Click on the link in the "Sections covered" column for a copy of the slides for the day; click on the link in "Extra slides" for other stuff displayed that day; and click on the link(s) in the "Video" column to watch the lecture on YouTube. Or just check out our class playlist here.


Date Sections covered Extra slides Video
Mon Aug 23 1.1-1.2, 2.1 Motivating examples Video 1, Video 2
Wed Aug 25 2.2-2.4 Video
Mon Aug 30 2.4-2.5, 3.1 Video
Wed Sep 01 3.1-3.2 Video
Wed Sep 08 3.3 Video
Mon Sep 13 3.4 Video
Wed Sep 15 3.5 Video
Mon Sep 20 4.1-4.2 Six NOs Video
Sample exam 1 Video
Mon Sep 27 4.3-4.4 Six NOs Video
Wed Sep 29 4.5-4.6 Video
Mon Oct 04 4.6, 5.1, 5.2 Video
Wed Oct 06 5.3, 6.1, 6.2 Video
Mon Oct 11 6.4, 7.1 Video
Wed Oct 13 7.1-7.2 Video
Mon Oct 18 7.2-7.3 Video
Wed Oct 20 7.3-7.4 Video
Sample exam 2 Video
Wed Oct 27 7.4-7.5 Video
Mon Nov 01 7.5-7.6 Video
Wed Nov 03 8.1-8.2 Video
Mon Nov 08 8.3 Dirac kernels, Cesàro sums Video
Wed Nov 10 8.4 Video
Mon Nov 15 12.1 Video
Wed Nov 17 12.2 Gauss kernel Video
Sample exam 3 Video
Mon Nov 29 12.3 Video
Wed Dec 01 12.4 Video
Mon Dec 06 Semester review Video
Sample final exam Video

Problem sets:

HW New definitions Outline due Completion due Last revision due Problems to be turned in
PS00 n/a n/a Wed Aug 25 n/a See handout
PS01 2.1, 2.2, 2.3, 2.4 Wed Aug 25 Mon Aug 30 Mon Sep 20 1.1.2, 2.1.6, 2.2.3, 2.3.2, 2.3.5, 2.4.1, 2.4.10.
PS02 2.5, 3.1, 3.2 Wed Sep 01 Wed Sep 08 Wed Oct 20 2.5.2, 3.1.2, 3.1.4, 3.1.6, 3.1.12, 3.2.4, 3.2.6.
PS03 3.3, 3.4. Mon Sep 13 Wed Sep 15 Wed Oct 20 3.3.2, 3.3.3, 3.3.4, 3.4.2(c), 3.4.3, 3.4.4.
PS04 3.5, 4.1, 4.2, 4.3, 4.4. Wed Sep 29 Mon Oct 04 Mon Dec 06 3.5.2, 4.1.1, 4.2.1, 4.3.5, 4.3.6, 4.4.1.
PS05 4.5, 4.6, 5.1, 5.2, 5.3. Wed Oct 06 Mon Oct 11 Mon Dec 06 4.5.1, 4.5.2, 4.5.4, 4.5.6, 4.6.2, 5.1.1, 5.2.2.
PS06 6.1, 6.2, 6.4, 7.1. Wed Oct 13 Mon Oct 18 Mon Dec 06 6.1.2, 6.2.4, 6.2.6, 6.4.1, 6.4.4, 7.1.3, 7.1.6.
PS07 7.2, 7.3, 7.4, 7.5. Wed Oct 27 Mon Nov 01 Mon Dec 06 7.2.4, 7.2.5, 7.3.1, 7.3.4, 7.3.6, 7.4.3, 7.5.4.
PS08 7.6, 8.1, 8.2. Wed Nov 03 Mon Nov 08 Mon Dec 06 7.5.10, 7.6.2, 7.6.4, 7.6.7, 8.2.2, 8.2.6, 8.2.7.
PS09 8.3, 8.4, 8.5.3. Wed Nov 10 Mon Nov 15 Mon Dec 13 8.3.1, 8.3.2, 8.3.3, 8.4.1, 8.4.3, 8.4.6, 8.5.5.
PS10 4.7, 4.8, 12.1, 12.2. n/a Tue Nov 30 TBA 4.7.3, 4.8.3, 12.1.1, 12.2.3, 12.2.5, 12.2.8, 12.2.10.
PS11 12.3, 12.4. Wed Dec 01 Mon Dec 06 TBA 12.3.1, 12.3.3, 12.3.5, 12.3.7, 12.4.2.

Reading assigned in course so far:

From textbook: 1.1-1.2, 2.1-2.5, 3.1-3.5, 4.1-4.6, 5.1-5.3, 6.1-6.2, 6.4, 7.1-7.6, 8.1-8.4, 8.5.3, 4.7, 12.1, 12.2, 12.3.

Proof notes: Sec 23 (epsilonics)

Further topics:

Here are some possibilities for further study after this class, grouped into three categories, along with links or suggested reading that should give you an idea of what the topic is like. (For master's students: Most of these topics would make good master's theses projects.)
  1. More theory

  2. Practical applications

  3. Less practical applications

Other useful links: