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