Analysis
Here are the analysis pictures! Note reverse ordering this time!
Here is our class picture -- the smartest students at Lamar!
What, nobody has anything to present???? Oh yeah, you had a take-home exam!
Ted completes the uniqueness of the solution to the ODE.
Ted proves a couple more...
Jeremy concludes that every Cauchy sequence converges, 115, with much abuse from Megan and me.
Jillian knocks out 113.
Jeremy tackles that every Cauchy sequence converges, 115.
Be sure to answer this question.
Jillian shows example where 117.2 holds for "f" in place of "f inverse," then
Jeremy shows a counter-example and we conclude it holds if "f" is bijective.
Ted does house clealing (96,87) and then shows extension of current results on ODEs to systems (102)
Bekah puts up 120.
Jeremy puts up 100/99, but Ted's poor statement of problem confuses the issue.
PJ puts up 117.2 -- does this hold if we replace "f inverse" by "f?"
Bekah puts up 84.
Megan puts up part of 117.
Jillian puts up part of 118 .
Jeremy puts up 97.
Chis, Jeremy, and Jillian work out 114.
See you Monday! Email me what happens on Friday!
Chris puts up 79.
Class comes back after getting 2nd in Calculus Bowl and still has material to present! Go class!
Jeremy puts up 95.
Jill puts up 112.
Ted lectures for an entire class period on existence and uniqueness of solutions to differential equations.
Jillian tackles 112 and I swear I took a picture, but it's not visible on the camera.
Jeremy tackles 95 - question about application of T26.
Bekah completes 80.
Ted discusses our Friend e.
Bekah completes 86.
Jeremy completes 94.
Jeremy completes 91.
Jillian starts 112. Remember, she did 111 even though it doesn't appear on-line!
Approximately 13 days and 21 problems remaining!
Reminder that 112-115 will yield that every Cauchy sequence of real numbers converges.
Megan forces Ted to prove 83, which she almost has...
Jeremy tackles 91 -- questions about what variables are defined, which function is continuous,...
Two things did not make it into the camera! My proof that every Lipschitz function is uniformly continuous (88) and the two line proof of 83 which used 78 and the fact that every differentiable function is continuous.
Here is the discussion of the proof that an absolutely convergent sequence is convergent
and the discussion of the proof that the uniform limit of a sequence of continuous functions is continuous.
Have a productive spring break! Are y'all slacking? Where are my proofs?
Jillian does 110 and I explain the significance of "complete" spaces.
Guest speaker Curtis blows away 75!
Jeremy does 90 in a way that also completes 89.
Ted gives notation for infinite series and sketches an argument for a function that is continuous but not uniformly continuous -- one of you can wrap that up for credit.
Ted proves the Fundamental Theorem of Calculus -- High School and University versions.
Bekah tackles 80 -- possible infinite partition a propblem!
Jillian completes second half of equivalent Cauchy definition.
P.J. finishes 109 -- closed intervals are compact -- using open cover definition of compactnes. If we have a slow
day in the future, he can show us the equivalence of the two definitions of compactness.
P.J. tackles 109 -- closed intervals are compact -- using open cover definition of compactnes.
Jeremy tackles 109 -- closed intervals are compact -- class wants inductive step and proof that subsequence converges.
Jillian does 1/2 of 110 -- beginning of Cauchy.
63 and 72 replaced the older versions below...
Conjectures about how many discontinuities can occur and still have a function be integrable on [a,b].
Jeremy P73.
Ted: Mean value theorem for derivatives.
Jeremy P70.
Bekah P74.
Jillian handles P108.
P.J. jumps in with P77.
Chris works on P71 -- class wants the contradiction clarified!
Megan finsihes up P67 - Go Megan!
Ted finishes up lemma that completes Rolle's Theorem, Lemma 81.
Megan closes in on P67!
Ted proves Rolle's Theorem (Lemma 81) and owes the class one lemma.
Jillian handles P106.
Ted discusses subsequence notation and three associated results.
Jermey handles P69 -- thanks to Chris for honesty here -- I had given him credit here (but not in my gradebook).
Bekah handles P66.
Chris handles P68. For any pair of partitions, there is a partion refining both.
Ted handles P77. The summation rule for integration.
Ted handles P63 and P72. Continuous functions on an interval have a maximum and the range is a closed interval or a point.
Bekah handles P65.
Ted addresses need for induction on inequalities as lemma to Bekah's proof.
Ted handles P62.
Chris tackles P59!
Ted completes P61.
Megan completes P64.
Ted makes a few notes on Jeremy's 58 and the lack of uniqueness of decimal expansions.
Unfortunately, he forgets to take pictures of the second set of boards where he developed the naturals, rationals, and real.
Jeremy does 58. Wow! He independently discovers Cantor's Diagonalization Argument!
Megan does 57.
Ted discusses subsequences, and the range of continuous functions on an interval, P61.
Megan does 55.
Ted does 60.
First day of class.
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