Spring-06. Math 104 - Section 2 (ccn 54879):
Introduction to Analysis
Instructor: Alexander Givental
Lectures:
TuTh 11-12:30, 71 Evans
Office hours: TuTh 4-6 p.m., in 701 Evans
Text: K. Ross, Elementary Analysis: The Theory of Calculus
, Springer. We hope to cover the whole book.
Grading: Final (50%)+Midterm (25%)+Homework (25%)
HW: Weekly homework assignments are posted
to this web-page, and your solutions are due on Tuesdays in the class.
GSI: Ari Nieh
ari@math.berkeley.edu will hold office hours (for all sections of
Math 104) at 891 Evans on Mo 10-12, 12:30-3:30 and Tu 10-12, 2-5.
HW1 (due by Tue, Jan. 24)
1.1, 1.9, 1.12bc, 2.5
HW2 (due by Tue, Jan. 31)
3.6b, 4.4, 4.12, 4.14b, 4.15
HW3 (due by Tue, Feb. 7)
8.7a, 8.8c, 9.5, 9.12a, 9.14
HW4 (due by Tue, Feb. 14)
(i) Solve 10.6ab, 10.7, 12.3
(ii) Let p_n denote the semiperimeter of a regular 3x2^n-gon
(i.e. 3-angle, 6-gon, 12-gon, 24-gon, etc.) inscribed into
a circle of radius 1. Prove that the sequence p_n
converges, and that the limit (commonly called "pi")
is greater than 3.
HW5 (due by Tue, Feb. 21)
(i) A set is called closed if it contains all its subsequential
limits (see p. 72). A set is called open if its complement is closed.
Prove that a set is open if and only if togeher with any point, it contains
some open interval containing this point.
(ii)
Solve 11.9b, 12.10, 14.4b, 14.10.
HW6 (due by Tue, Feb. 28)
MIDTERM EXAM, based on Chapters 1 and 2: Tue, Feb. 28.
HW7 (due by Tue, March 7)
17.7b, 17.8c, 17.12b, 17.13b, 17.14.
HW8 (due by Tue, March 14)
17.6, 18.2, 18.4, 18.6, 18.10
HW9 (due by Tue, March 21)
19.2b, 19.4a, 19.6a, 20.18, 19.10
HW10 (due by Tue, April 4)
28.15, 28.4c, 29.10, 29.15, 29.18
HW11 (due by Tue, April 11)
HW12 (due by Tue, April 18)
31.2, 23.2cd, 23.6b, 23.8
HW13 (due by Tue, April 25)
24.10a, 24.13, 25.10bc, 26.8b
HW14 (due by Tue, May 2)
32.8, 33.4, 33.5, 33.8, 33.10
HW15 (due by Tue, May 9)
34.2a, 34.6, 34.10, 34.12, 27.2
