Math 240C Home Page (Driver, S2018)

 

Homework
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240 Lecture Notes
Test Data

Math 240C -- Real Analysis (Spring 2018) Course Information

http://www.math.ucsd.edu/~bdriver/240C-S2018/index.htm


You should also routinely login to your TED =Triton ED (https://tritoned.ucsd.edu) account for more course information. TED  is the web interface through which solutions and possibly other course materials will be communicated. Please check it frequently for announcements. The TED site will also contain a record of your grades for this course -- please make sure they are accurate.


240C New Announcements

  • Final Exam = Qual Exam. Math 240 Qual is scheduled for Friday, May 25nd from 1:00 -- 4:00 PM in AP&M B412.   APM 6402.
  • The midterm is on Monday, May 7.
  • [Please postpone Exercise 1.33 (Sampling Theorem) of Homework 4 to Homework 5.]
  • I added some missing notation into Homework #3.
  • Please note that Exercise 1.6 on homework #2 has been corrected, see the updated problem sheet.
  • Supplementary notes may be found in Supplements.pdf. This has been updated on May 16, 2018.
  • I set up an experimental Piazza site for this class to at
  • https://piazza.com/ucsd/spring2018/math240c/home
  • Final Exam = Qual Exam. Math 240 Qual is scheduled for Friday, May 25nd from 1:00 -- 4:00 PM in AP&M B412.   APM 6402.
  • The qualifying exam is cumulative over the whole years material!!
  • Here is the Spring 2012 Qualifying Exam for Practice:  240qual_s2012_test.pdf
    There will be no classes during the qual exam week of May 21 -- May 30, 2018.
  • Monday, May 28 is Memorial day, a UCSD holiday.

Instructor: Bruce Driver (bdriver@ucsd.edu  /  534-2648) in AP&M 5260.
Office Hours:  M. & W. 1-2 PM in my office (AP&M 5260). [These are subject to change.]

Grader:  Donlapark Pornnopparath  (dpornnop@ucsd.edu) AP&M 5748:
Office Hours: M. & W. 4-5 PM in APM 5748.

Course Meeting times: MWF 12:00 -- 12:50 PM in AP&M 5402.

Textbook:        We will use the course lecture notes and also the book; "Real Analysis, "Modern Techniques and Their Applications," 2nd edition by Gerald B. Folland,

Prerequisites: This is a continuation of Math 240A-B. Students are assumed to be familiar with the material already covered in the first two quarters. The previous quarter web-pages may be found at:

http://www.math.ucsd.edu/~aioana/Math240A.html     and
http://www.math.ucsd.edu/~aioana/Math240B.html

Homework:    Homework  is assigned, collected, and partially graded regularly. Each homework is due at the beginning of each Friday class unless otherwise instructed.

  • Please print your names and student ID numbers on your homework. Please staple together your homework pages.

  • No late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
     

Test times:  Note: neither rescheduled nor make-up exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.

  • There will be one in class midterm on Monday, May 7.

  • The final exam will be the same as the qualifying exam which is scheduled from 1:00 -- 4:00 PM on Friday, May 25 (in APM 6402). The qualifying exam is cumulative over the whole years material!!

Grading:         The course grade will be computed using the following formula:

Grade=.3(Home Work)+.3(Midterm)+.4(Final=Qual Exam).


Topics  to be covered

Math 240C (Spring 2018)

  • Integration in Polar Coordinates: Section 2.7.

  • Continue L^p spaces in sections 6.2-6.3 and partially 6.4 including convolution inequalities.

  • Chapter 8 on Elements of Fourier Analysis

  • Describe results on Radon measure in Chapter 7.

Possible further topics

  • Distribution theory and elliptic regularity, see Chapter 9 of Folland..

  • Some basic Sobolev space theory. 

  • Hilbert Schmidt operators, the spectral theorem for self-adjoint compact operators.

  • Differential Calculus on Banach spaces and the Inverse and implicit Function Theorems.

  • Basic non-linear ODE theory on Banach spaces

  • A little complex analysis.

  • The Spectral Theorem for bounded self-adjoint operators on a Hilbert space.

  • Unbounded operators and the Spectral Theorem for self-adjoint operators.

  • Properties of ordinary differential equations.

 

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Last modified on Monday, 30 April 2018 11:57 AM.