Math 240C-Real Analysis, General Information
This course is the part III of 240 series. We will mainly cover the Fourier transform and the distributions. But also will fill some holes left in Math 240AB, particularly more discussions on the distribution functions and interpolations (in 6.4, 6.5 of Folland) and Randon measures and representation theorem (7.2, 7.3 of Folland).
We shall continue use Folland as the main text. But use Lieb and Loss, Evans-Gariepy as the supplements when the presentation fits better. One can find much more comprehensive coverage of the Fourier transform and distribution theory in the Hormander's Analysis of Linear Partial Differential Operators and Gelfand's Generalized Functions.
There will be a midterm and a final exam.
The complete course schedule will be available and updated weekly.
||M 11-11:50, W 10-11:50 am, via canvas Zoom link
Course Time and Location
||TuTh 3:30-4:50 pm
Required Text: Real Analysis, 2nd edition, by Folland. Johns Wiley & Sons, Inc. 1999
Recommend Alternate Text: (1) Measure theory and fine properties of functions, by Evans and Gariepy, CRC press 1992;
(2) Analysis, by Lieb and Loss, AMS, 2001;
Lectures on Geometric Measure Theory, by Leon Simon, Centre for Mathematical Analysis, Australian National University, 1984
Errata for Folland's text: [html]
Errata for Evans/Gariepy's text: [html]
Problem Solving Techniques in Analysis by Terence Tao: [html]
LaTeX homework template: [tex]
Everything you need to know to typeset your homework in LaTeX: [pdf]
(i) Handout1 on L^p spaces;
(ii) Handout of lecture notes
(iii) Handout2 on L^p spaces;
(iv) Handout on Sobolev spaces
(v) Handout1 on BV functions; (vi) Handout1 on Fourier Transforms
(vii) Handout1 on Distributions
(viii) Handout on general Riesz representation theorem
(ix) Handout on BV-functuions II
There will be one midterm and one final exam.
Solution to final in Fall 2014
Solution to midterm in Winter 2015
Example 240B final1
Example 240B final2 Solutions
Solution to the final of 240B
Solution to the midterm of 240C
Content covered by the Qualifying Exam
There will be weekly homework
assignments. Please check weekly for the updates. Many problems will be assigned every week. The one with (*) have to be turned in by the next week's Friday 11:00pm PST. The rest problems are recommended (which means that you should think about them and know how to solve them too). The exams will be based on lectures and homework problems. The course TA is Nandagopal Ramachandran . For the Spring 2022, his in person office hours are Friday 1-3pm. His office is AP&M 5748.
Solutions to the HWs of 240A
Solutions to the HWs of 240B
Solutions to the HWs of 240C (including the all previous solutions)
The course schedule will be updated weekly.
Grades will be based on the following percentages.
Last modified: Wed March 22, 12:49:08 PST 2022