MATH3320 Analysis
 Spring 2017  Gasson 203

Dan Chambers   543 Maloney Hall

chambers@bc.edu    617-552-3769 (email is more reliable)


Office Hours: Mondays 10-11, Wednesday 2-3, Fridays 12-1, or by appointment.

Analysis is concerned with the theoretical underpinnings of calculus. We'll start with properties of the real numbers, then consider sequences and limits, functions and their derivatives and integrals.

The text we'll use is An Introduction to Analysis, 2nd edition, by G.G. Bilodeau, P.R. Thie, and G.E. Keough. We'll cover selected portions of the first five chapters and, time permitting, some of the sixth.

Here is a link to the syllabus.

This is a work in progress; check back for updates.



Date
topic/section
HW assigned
HW due/solutions
January



18
1.1 Sets


20
1.2 Functions


23
1.2 concluded

25
1.3 Properties of real numbers

27
1.3 ct'd


25
1.3 concluded
HW #1

28
1.5 Least upper bound axiom

30
1.5 ct'd


February



1
1.5 concluded
HW #1, solns
3
2.1 Sequences and limits HW#2

6
2.1/2.2 Limit theorems

8
2.2 ct'd


10
2.2/2.3 Monotonic sequences
HW#3
HW #2, solns
13
2.3/2.4 Sequences defined inductively


15
2.4/2.5 Subsequences


17
2.5 Nested interval and Bolzano-Weierstrass Thms
HW#4
HW#3, solns
20
2.6 Cauchy sequences


22
2.7 Infinite limits
HW#4, solns
24
midterm 1 (through 2.4) solutions


27
3.1 Limit of a function


March



1
3.1 ct'd


3
3.2 Limit theorems
HW#5

6
spring break


8
spring break


10
spring break

13
3.2 ct'd


15
3.3 Other limits

HW#5, solns
17
3.4 Continuity
HW#6

20
3.4 ct'd


22
3.4 ct'd


24
3.4/3.5 begun

HW#6
27
3.5 IVT


29
3.5 EVT
HW#7

31
4.1 Derivatives


April


3
4.1 ct'd

HW#7, solns
5
midterm 2 solutions


7
4.2 Differentiation rules


10
4.3 MVT begun


12
4.3 ct'd


14
Easter break

17
Patriot's Day


19
class canceled


21
4.3/5.1 Integration
HW#8

24
5.1 ct'd


26
5.2 Properties of the integral

28
5.3 Existence theory

HW#8, solns
May



1
5.3/5.4 Fundamental theorem of calculus
HW#9

3
5.4 ct'd

HW#9, solns