Math 2583H, Spring '03

Last changed: May 10, 2003.

Old news:



News April 11: Practice Test 3 is now available.

News April 8: A link to an important note on Taylor's Theorem w/Remainder
has been added


News April 7: A link to a note on Complex Numbers has been added


News April 6: An addition to Miscellany: limsup (so we can
use the definition of "radius of convergence") and a Theorem about
convergence of power series. It's done in lots of detail...
Let me know if you need a shorter version.


News April 2: The sections-covered list below has been updated.


News April 1: An addition to Miscellany: the stuff done in
class March 31 about the uniform convergence of a certain
series on [-1, 0], done in excessive detail!


News March 27:


Here are the two choices for your Project:


Project A: Make an easy-to-understand presentation of some
Cauchy-product proofs, of the two following statements:


* If at least one of the series \sum a_n and \sum b_n
convergeres absolutely, and both converge, then their
Cauchy-product series converges to the product of the
sums of the original series.


* If the Cauchy-product series of two convergent series
converges, then its sum is the product of the sums of
the original series.


Project B: Prove or disprove that the decimal formed by
sequential juxtaposition of the decimal representations of
all the integers is a rational number. If it is, find
the numerator and denominator of it in lowest terms.


Your number to work with is


x=.123456789101112131415161718192021222324252627282930...





News Mar 24: We're done with 6.1 thru 6.7. We skip 6.8 & 6.9.
Today we began 6.10, working on a special case: when all the terms
in the a_n nbsp; and nbsp; b_n nbsp; series are non-negative.


News Mar 13: Test 2 is in Nicholson Hall 211! Best wishes!


News Mar 8: A link to a document, "Miscellany" is below.
It contains (right now) a proof that log x/x \to 0 as x \to \infty.


News Mar 7: A link to a practice Test for test 2, 3/14, is below.


News Mar 6: The examples are now in "no-sup no-inf Cauchy Criterion."


News Mar 5: A link to the no-sup no-inf Cauchy Criterion is below.
The two examples are not in there yet.


The list of sections covered is updated below.


A question for you: should the Test 2 and Test 3

dates be changed to: March 28 and May 2 ?

News Mar 2: A list of sections we have covered:

A list of sections we have covered:
6.15: BARELY BEGUN

6.13, 6.14, plus the example (2) in "Miscellany."

6.11, 6.12

6.10

6.8, 6.9: SKIPPED

6.6, completed; 6.7 (as examples).

6.6 thru Theorem 16.
The previous list; additions will be in push-down format:
5.1 - 5.6; you read 5.7, 5.8;
5.9 - 5.12; you read 5.13
6.1, 6.2; 6.3, you read, know how to find
limsup and liminf; 6.4 (Cauchy criterion) -- an alternate
version of this section will be put on the Web soon;
6.5 we did ahead of time...


Unofficial: suggested review: 4.1, 4.3, 4.5 and 4.6;
Definitions and some explanations: 4.7;
Suggested for info: 4.10, 4.11.

News Feb. 15: Test 1 will take place in rm 143
at 1701 University. Bring warm clothes!

News Feb. 9: Test 1 has been moved to February 17.
A list of problems to work, to prepare for Test 1, is below.

Suggested problems before Test 1:

4.7 # 4
5.3 # 2b, 4a
5.7 # 2a, 4, 10b
5.10 # 1a, 5a, 8a
5.11 # 2a


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