MAT 127A: Advanced Calculus (Winter 2004)

MTWF 15:10 - 16:00 pm, HART 1128


Course: MAT-127A-2
Title: Advanced Calculus
Quarter: Winter 2004
CRN: 51909
Instructor: Roman Vershynin (vershynin@math.ucdavis.edu)
TA: Huang, Yuan-Kai (akai@math.ucdavis.edu)
Location: HART 1128
Times: MTWF 15:10 - 16:00 pm
Office hours:
    Roman Vershynin: 671 Kerr Hall, MWF 13:20-14:20 or by appointment
    Yuan-Kai Huang: 460 Kerr Hall, Thursday 14:00-15:00

TEXTS:

1. K.A.Ross, Elementary Analysis: The Theory of Calculus, 1980, Springer-Verlag.
This is a required textbook for the course. All course study material will be from this text and class notes.
We will cover sections: 1-5, 7-12, 17-20, 28-29 and, if time permits, also 6, 13, and 31.

2. W.Rudin, Principles of mathematical analysis, Third edition, 1976, McGraw-Hill Book Co., NewYork - Auckland - Duesseldorf.
This is an optional textbookfor the course. This book has become a classical text in Mathematical Analysis. It is comprehensive, profound and sometimes challenging. Familiarizing oneself with this book is definitely recommended to our Mathematics majors, for whom MAT127 is a key course.

PREREQUISITES: 21D, 22A, 108

ASSESSMENT:

Homeworks   20%  Homework posted (see below)

Midterm  30% (February 13)
 Problems     Solutions
Final   50% (March 23 at 8:00 am)   Closed book, closed notes, no calculators

Homework assignments will be posted on this webpage each Wednesday. Homeworks will be due the following Wednesday 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 80% and the midterm will not count.

WEB: http://www.math.ucdavis.edu/~vershynin/teaching/127/course.html

Homework 1
due 01/20/04
15:00
Ross 1.2, 1.4, 1.8, 3.2, 3.4, 3.6, 4.2 (e), (h), (i), (j), (k), (n), (r), (u), (v)
For 3.4, when you are proving that 0<1, assume that our field does not consist entirely of one element {0}.
Keys/Solutions
Homework 2 due 01/27/04
15:00
Ross 4.4 all parts, 4.6, 4.8, 4.10, 4.12, 4.14, 4.16
Keys/Solutions
Homework 3 due 02/03/04
15:00
Ross 5.2, 7.2, 7.4, 8.2, 8.6 (a), 8.8 (b), 8.10, 9.2, 9.4, 9.8
Keys/Solutions
Homework 4 due 02/11/04
15:00
Ross 9.10, 9.16, 9.18, 10.2, 10.8, 10.10. Do all parts in all problems
Keys/Solutions
Homework 5
due 02/25/04
15:00
Ross 11.2, 11.4, 11.8, 11.10, 17.4, 17.10 (a), (b), (c), 17.12
Bonus problem (additional 10%): Ross 17.14
Keys/Solutions
Homework 6
due 03/03/04
15:00
Ross 17.2, 17.6, 17.8, 17.10 (d) using only the epsilon-delta definition, 18.2, 18.4
Keys/Solutions
Homework 7
due 03/10/04
15:00
Ross 18.5 (a), 18.6 (hint: use 18.5(a)), 18.8, 19.1 (b), (c), (d), (e), 19.2, 19.6, 19.10 (no proof required for part (c))
Keys/Solutions
Homework 8
due at the review session
03/17 or can be handed in
to the TA at the discussion session 03/16
Ross 20.2, 20.4, 20.6, 20.8, 20.12, 20.14, 20.18, 28.2, 28.14(a)
Bonus problem (additional 10%): 28.8

Keys/Solutions