Intro to Real Analysis — §102, Fall, '13 (134)

Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.

— Thomas Jefferson (1743-1826) in his First Inaugural Address.

Homework List

✈ Jump down to '♞ This Week.'

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Week 1

• Tuesday, Aug 20 — First day of classes
  
  
• Wednesday, Aug 21
  ◊ Read the Course Information pages.
  §1.1, pg 7.  No. 1bc, 4a, 5bc.
  §1.2, pg 17.  No. 3, 4, 8abdfgj, 13, 18ab, 23; LA (“look at”) 22.
  
  
• Friday, Aug 23
  ◊ The Functions Homework (Hmwk 1) is due Monday, 8-26.
  §1.4, pg 35.  No. 1, 4a.
  §1.5, pg 38.  No. 1b, 2b, 4, 13.
  
  

Week 2

• Monday, Aug 26 — Last day to drop/add classes
  §1.7, pg 47.  No. 2, 8, 16.
  ◊ Query: Can an irrational number raised to an irrational power be rational?
  
  
• Wednesday, Aug 28
  §1.8, pg 52.  No. 2, 4e, 5a, 15f, 19, LA 21 (important inequalities in analysis!)
  
  
• Friday, Aug 30
  §2.1, pg 72.  No. 1, 2acgj, 3b, LA 8.
  ¤ Short quiz next Friday!
  
  

Week 3

• Monday, Sept 2 — Labor Day holiday; no classes
  
  
• Wednesday, Sept 4
  §2.1, pg 72.  No. 10 (Look up Cesàro convergence.), 11, 14, 18.
  
  
• Friday, Sept 6
  ¤ Quiz today!
  §2.2, pg 79.  No. 1, 2, 9, 11 (Hint: If you can't tell, graph it!).
  
  

Week 4

• Monday, Sept 9
  §2.3, pg 86.  No. 2a, 3b, 4, 5.
  
  
• Wednesday, Sept 11
  §2.4, pg 93.  No. 1, 2, 3 (cf. Maple Sequence graphing worksheet), 4d, 6dfg, 11b, LA 12, 18.
  
  
• Friday, Sept 13
  ¤ The Sequence worksheet is due by 5:00 pm Monday, 9/16.
  
  

Week 5

• Monday, Sept 16
  §2.5, pg. 103.  No. 1, 3, 6.
  ◊ It's time to start thinking about our first test...
  
  
• Wednesday, Sept 18
  §2.5, pg. 103.  No. 7, 8.
  
  
• Friday, Sept 20
  §2.5, pg. 103.  No. 14, 19.
  
  

Week 6

• Monday, Sept 23
  ◊ Start making your note sheet (8.5"×11") for Test 1.
  §2.6, pg. 110.  No. 1, 2ad, 7, LA 4, 5.
  
  
• Wednesday, Sept 25
  §1.9, pg. 55.  No. 1→ 61.
  §2.7, pg. 111.  No. 1→ 50.
  ¤ See the Test 1 Topics List.
  
  
• Friday, Sept 27
  ◊ Test 1
  
  

Week 7

• Monday, Sept 30
  §3.1, pg. 123.  No. 1, 3, 5, 8.
  
  
• Wednesday, Oct 2
  §3.1, pg. 123.  No. 9, 10, 11.
  
  
• Friday, Oct 4
  §3.2, pg. 131.  No. 1cdf, 5, 7d, 8c, 14.
  
  

Week 8

• Monday, Oct 7
  §3.3, pg. 138.  No. 1, 4aceh, 5c, 9h.
  
  
• Wednesday, Oct 9
  §3.4, pg. 142.  No. 1→44.
  
  
• Friday, Oct 11
  ◊ Quiz today!
  ¤ A clean copy of Test 1 (for the proofs due Monday).
  
  

Week 9

• Monday, Oct 14
  ◊ Rewrites of proofs from Test 1 are due today!
  §4.1, pg. 153.  No. 1, 3, 6abcgn, 14.
  
  
• Wednesday, Oct 16
  ◊ Finish the Discontinuity Worksheet.
  
  
• Thursday & Friday, Oct 17-18
  ◊ No classes — Fall Break! So go explore Explore.org.
  
  

Week 10

• Monday, Oct 21
  §4.3, pg. 166.  No. 1, 2a, 3.
  
  
• Wednesday, Oct 23
  §4.3, pg. 166.  No. 4, 5, 6 (apply 5), 7.
  
  
• Thursday, Oct 24 — Last day to drop any course.
  
  
• Friday, Oct 25
  ¤ The Newton And The Binomial Theorem Project. Due Monday, Oct 28.
  (Note: There's a typo in the displayed equation in 3. It should start \((1+x)^{\fbox{1/3}}=\;...\). )
  
  

Week 11

• Monday, Oct 28
  §4.4, pg. 173.  No. 1, 2.
  
  
• Wednesday, Oct 30
  §4.4, pg. 173.  No. 3, 6, 7 (replace Lipschitz with uniformly continuous), 14.
  
  
• Thursday, Oct 31
  ¤ Happy Birthday Karl T W Weierstrass — the “father of modern analysis!” (My Great, great, great, grandfather mathematically)
  
  
• Friday, Nov 1
  ¤ Quiz next Monday! (11/4)
  §4.5, pg. 176.  No. 1→50.
  ¤ See the Algebra of Uniform Continuity page.
  
  

Week 12

• Monday, Nov 4
  ¤ Quiz Today! (on uniform continuity)
  ◊ Read pg 179-180 on compactness up through Thm 4.6.10.
  
  
• Tuesday, Nov 5
  ¤ Election day in Boone.
  
  
• Wednesday, Nov 6
  ◊ It's time to start thinking about our next test...
  ¤ Read §5.1
  ¤ Be ready to write a proof carefully for the group portfolio.
  ❉ The Intro to \(\mathrm{\LaTeX}\).
  
  
• Friday, Nov 8
  ¤ Be ready to write the two proofs (3 & 4) from Test 1 carefully for your group portfolio.
  
  

Week 13

• Monday, Nov 11
  ¤ The typeset proofs for your group portfolio are due on Wodnesdœg.
  ◊ Read §5.1.
  ❉ Notation for the Derivative:
  • \(\dot{y}\), \(\ddot{y}\), and \(\dot{y}/\dot{x}\) are from Newton (1643-1727) first in an unpublished manuscript “Fluxionary Calculus” (May, 1665).
  • \(dx\), \(dy\), and \(dx/dy\) are from Leibniz (1646-1716) first in a manuscript of Nov. 11, 1675
  • \(y^{\prime}\) and \(y^{\prime\prime}\) are from Lagrange (1736-1813) first in Théorie des fonctions analytiques (1797). (Lagrange developed calculus without using ‘limits;’ he objected to infinitesimals.)
  • \(D_xy\) and \(D_x^2y\) are from Arbogast (1759-1803) first in De Calcul des Dérivations (1800).
  
  
• Wednesday, Nov 13
  §5.1, pg. 190.  No. 1, 2, 3acvf, 5; LA 10f.
  
  
• Friday, Nov 15
  ¤ Test next Mōnandœg!
  ¤ Test 2 topics.
  ◊ You can bring:
  • Calculator (check the batteries)
  • Two sheets (8½"×11") of notes
  
  

Week 14

• Monday, Nov 18
  ¤ Test today!
  
  
• Wednesday, Nov 20
  ¤ The next two portfolio proofs first drafts are due Monday.
  §5.2, pg. 199.  No. 1abcd.
  ¤ Let \(f(x)=e^{3x}\) and \(g(x)=e^{3x/2}\). What is the value of
  1. \(f^\prime(x) \cdot g^\prime(x)\) ?
  2. \((f\cdot g)^\prime(x)\) ?
  3. What happened and why?
  
  
• Friday, Nov 22 — Remembrance of President John F. Kennedy.
  §5.2, pg. 199.  No. 5, 6.
  
  

Week 15

• Monday, Nov 25
  §5.3, pg. 205.  No. 1, 10, 15e, LA 6.
  
  
• Wednesday, Nov 27 — Thanksgiving break - no classes.
  
  
• Friday, Nov 29 — Thanksgiving break - no classes.
  
  

Week 16

• Monday, Dec 2
  §5.4, pg. 216.  No. 2, 6, 22.
  
  
• Wednesday, Dec 4
  ◊ The Last Quiz is today!
  ¤ Review Chapters 2 (pg. 111) & 3 (pg. 142)
  
  
• Friday, Dec 6 — Last day of class!
  ¤ Review Chapters 4 (pg. 176) & 5 (pg. 228)
  
  

Week 17 — Final Exam Week    ♞  (This Week)

• Tuesday, Dec 11
  ◊ Office Hours: 1:00 to 3:00 pm
  
  
• Thursday, Dec 12
  ¤ Final Exam: 3:00 - 5:30 pm
  ◊ Final Exam Topics List
  ☞ You can bring:
  • Calculator (check the batteries)
  • Any notes; no books, no people.
  
  

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“Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypotheses?”

— Paul Halmos

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Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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