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Math 240C-Real Analysis, General Information
Spring 2022



Course Description

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.


Instructors

Name Office E-mail Phone Office Hours
Ni, Lei AP&M 7321 leni@ucsd.edu 534-2704 M 11-11:50, W 10-11:50 am, via canvas Zoom link


Course Time and Location

Section Instructor Time Place
A00 Ni TuTh 3:30-4:50 pm APM 7321


Texts

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;

References: Lectures on Geometric Measure Theory, by Leon Simon, Centre for Mathematical Analysis, Australian National University, 1984

Important Resources
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


Exams

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


Homework

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)


Schedule

The course schedule will be updated weekly.


Grades

Grades will be based on the following percentages.
Homework 40%
Midterm Exam 30%
Final Exam/Presentations 30%

Last modified: Wed March 22, 12:49:08 PST 2022