Math 401 Introduction to Real Analysis

Fall 2013, Ed Bueler


Ed Bueler
elbueler@alaska.edu    x7693
Office: Chapman 301C (hours here)
Class time: 9:15--10:15 MWF
Classroom: Brooks 104A

Text: Ken Ross, Elementary Analysis: The Theory of Calculus, 2nd ed. Springer 2013

Grader:

   Kris Kilpatrick
   in MathLab (= Chapman 305)
      Sat and Sun 8am - 10:30am

Syllabus

LaTeX:  In this class, we'll use LaTeX to typeset solutions. I recommend David Maxwell's installation guides:
(See me if you use Linux; it is easier.) Then download this file into a good location:
When you successfully PDFLaTeX you get
When you successfully LaTeX it you get
David also wrote nice LaTeX notes:
LINKS:

 Schedule:  (version 8 December)

Day

Sections
(in text)
Topic
Assigned or Due
(links are PDF)
Fri 9/6
1
review: natural numbers and induction
Assignment #1 (PDF)
Mon 9/9

cont.

Wed 9/11
3
axioms for ordered fields (both rationals and reals are that)

Fri 9/13
2
rational zeros A#1 DUE
Mon 9/16
4
real numbers are complete (unlike rationals)
note on finite sets and maxima
A#1 DUE
Assignment #2 (PDF)
Wed 9/18

cont.

Fri 9/20

cont.

Mon 9/23
5
6
use of the symbols "∞" and "-∞"
construction of R
A#2 DUE
Assignment #3 (PDF)
Wed 9/25
7
sequences and convergence
Fri 9/27
8
cont.

Mon 9/30
9
limit rules
A#3 DUE
Assignment #4 (PDF)
Wed 10/2

cont.

Fri 10/4

cont.

Mon 10/7
10
monotone sequences
MIDTERM I in class
A#4 DUE
Wed 10/9

MIDTERM I in class
  covers sections 1--9

Fri 10/11

lim sup & lim inf Assignment #5 (PDF)
Mon 10/14

Cauchy sequences
Wed 10/16
11
subsequences
Fri 10/18
12
cont.  (read section 12; section 13 is skipped)

Mon 10/21
14
series
A#5 DUE
Assignment #6 (PDF)
Wed 10/23

cont.

Fri 10/25

cont.

Mon 10/28

cont.
A#6 DUE
Wed 10/30
15, 16 alternating series and decimals A#6 DUE
Assignment #7 (PDF)
Fri 11/1
17
continuity

Mon 11/4

cont.
Assignment #8 (PDF)
Wed 11/6
18
properties of continuous functions

Fri 11/8

cont.

Mon 11/11

MIDTERM II in class
cont.
A#7 DUE (firm)
(I'll hand out solns in class)
Wed 11/13

MIDTERM II
in class; covers sections 10-17
Midterm 2 (PDF)
solns to Midterm 2 (PDF)
Fri 11/15
19
uniform continuity
Mon 11/18
20
limits of functions
A#8 DUE
Assignment #9 (PDF)
Wed 11/20
23
power series

Fri 11/22

[cont]

Mon 11/25
24
uniform convergence

Wed 11/27
25
more
A#9 DUE
Assignment #10 (PDF)
Fri 11/29

Thanksgiving Break: no class

Mon 12/2

[cont]

Wed 12/4
28
derivatives

Fri 12/6

[cont]
A#10 DUE
Mon 12/9
29
mean value theorem
(take-home final here)

Wed 12/11
32
Riemann integral

Fri 12/13
33
[cont]
(last day of lecture)

Thurs 12/19

TAKE-HOME FINAL EXAM
   due in my office box (Chapman 101)
   at 5pm


Download Adobe's Acrobat Reader for free to view PDF files.