MAT 201C: Analysis
(Spring 2005)

MWF 1100-1150A, WELLMN 7

**Course:**
MAT-201C, Analysis

**Quarter:** Spring 2005

**CRN:** 60214

**Instructor:** Roman
Vershynin
(671 Kerr, vershynin@math.ucdavis.edu)

**TA:** Zeke Kwan Vogler (474 Kerr, zekius@math.ucdavis.edu)

**When/Where:**

Lectures MWF 1100-1150A in Wellman 7

Discussion R 0210-0300P in HICKEY
GYM 290

**Office hours:**

Roman Vershynin: F 1:30-3

Zeke Kwan Vogler:
Tu 2-3

**TEXT**

Applied Analysis,
by John Hunter and Bruno
Nachtergaele, World Scientific
2001 ISBN 9810241917.

You can view the text chapter by chapter from Prof. Hunter's webpage in
postscript
and
pdf formats.

**ASSESSMENT**

Grade distribution: Homework 25%, Midterm 25%, Final 50%.

The Midterm Exam will be in class on Friday
05/13. Solutions to the Midterm

The Final Exam (comprehensive, Chapters
10-11), is on Saturday, June
11,
10:30am-12:30pm, Wellman 7. Solutions to
the Final

Most homework assignments will be from the
Hunter-Nachtengaele's textbook. They will be posted on this webpage.
The
assignments will be due at the start of class. No late homeworks will
be
accepted. If you miss a homework for a medical reason, that homework
will not
count towards the final grade and you will not be required to submit
that
homework later. Keys or solutions to the homeworks will also be posted
on this
webpage.

There will be no makeup midterms given. If you
miss the midterm for a medical reason, the final exam will count for
75% and
the midterm will not count.

**OLD MATERIALS** can be found in the webpages of Prof. Nachtengaele.

**WEB**:
http://www.math.ucdavis.edu/~vershynin/teaching/201C-2005/course.html

Homework 1, due
04/11 |
10.1, 10.2, 10.3, 10.4, 10.5, 10.6 |

Homework
2, due 04/18 |
10.7, 10.8,
10.10, 10.11 (Exercise 10.9 is not assigned
anymore) |

Homework
3, due 04/25 |
1. Prove that
the operator A3 in Example 10.1 is closed. |

Homework
4, due 05/02 |
1. Prove that
a function u from L2 on the real line belongs to H2 and has a second
weak derivative v = u'' if and only if the identity |

Homework 5,
due 05/09 |
1. Prove that (11.3) defines a seminorm for
each alpha and beta. |

Homework 6, due 05/23 | Note: Solutions to the midterm are posted. 11.5, 11.6, 11.7, 11.8, 11.9, 11.10 |

Homework 7, due 06/01 | 11.11, 11.12 (see Definition
11.38). Find the orthonormal set of eigenvectors (and eigenvalues) of the Fourier transform L2 -> L2. (see p.312). Prove your claims. Example 11.40 (only the first part, on the differential operator -Delta + I). 11.13, 11.14, 11.15, 11.16 |

Homework 8, due 06/08 | 11.17, 11.18, 11.19, 11.20,
11.21, 11.27, 11.28 (Use Example 11.33). NOTE: Please
check errata |