Math 411 (Advanced Calculus II)
  Spring 2016
The syllabus for Math 411 is linked.  Much of that information is repeated bellow (but not all of it, so read the syllabus!) 


Instructor
Rebecca E. Field
fieldre@math.jmu.edu
(540) 568-4962
Office: Roop 114
Preliminary Office Hours: MWF 12:00-1:00pm, Tu 12:00-2:00pm
Also by appointment



Textbooks

An Introduction to Analysis by James R. Kirkwood (second edition, 1995, Waveland Press Inc.) ISBN-13: 978-1-57766-232-7

Understanding Analysis by Stephen Abbott (2000, Springer) ISBN-13: 978-0387-95060-0

Principals of Mathematical Analysis by Walter Rudin (3rd edition, 1976, McGraw-Hill, Inc.) ISBN: 0-07-054235-X



Course summary:
The goal of Math 411 is to complete the rigorous introduction to analysis that we started last semester.  We are going to use all of the machinery that we so laberously built last semester (the real number line, topology, limits, continuity) to actually prove the Fundamental Theorem of Calculus!! (Really do it this time, we will come to find that the super quick outline we did the last day of 410 included lots of cheating.)  The other fundamental topic in analysis we will cover is convergence in the space of functions.  Further topics will be covered as time permits.  This will/may include measure theory, Lebesgue integrating, Taylor series/PDEs. 

Here is my most important piece of advise about this course:     We are going to be going FASTER than we did in Math 410, so DO NOT FALL BEHIND!!  This includes things like DO NOT MISS CLASS!!  (If you must miss a class, get notes from one of your classmates and read them before the next class.)  It also includes things like DO YOUR HOMEWORK!!  It is not possible to actually learn this material without doing problems.  You might be able to convince yourself you understand, but if you can't do problems, you aren't at the level of understanding required to pass the class.  In fact, if the class seems too easy at any point, do extra problems!

Exams:
Big Quiz: Friday, February 5, during class time
Midterm: Wednesday, March 16, evening
Big Quiz 2: Friday, April 22, self scheduled


Homework:

Homework 1 (Connectedness and Uniform Continuity)
Homework 2 (Derivatives and MVT)
Homework 3 (Applications of MVT and Riemann-Stiltjes Integration)
Homework 4 (Measure Theory and the Riemann Lebesgue Theorem)
Homework 5 (FTC and Convergence on Function Spaces)
Homework 6 (Stone-Weierstrass Theorem, Series, and Series of Functions)
Extra Help:
Please come by my office hours or make an appointment if you need extra help!  You can also obtain a list of math tutors available for hire through the math office on the third floor of Roop Hall.

Topics we will cover are roughly as follows:

Functional Limits and Continuity/Continuous Functions/Continuity
The Derivative/Differentiation/Differentiation
The Riemann Integral/Integration/The Riemann-Stieltjes Integral
Measure Theory (sigma algebras, Lebesgue measure)
Sequences and Series of Functions/Sequences and Series of Functions/Sequences and Series of Functions
Series of Real Numbers (we skipped this in 410, this chapter title is from Kirkwood)
Series of Functions
Taylor Series and PDEs