Analysis I, Spring '11 (111)

"They that can give up essential liberty to obtain a little temporary safety
deserve neither liberty nor safety"   — Benjamin Franklin. (1706-1790)

Homework List

✈ Jump down to 'This Week.'
✈ Jump to the Class Notes directory.

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Week 1

• Monday, Jan 10 — First day of class
  ¤ Determine why Borzellino's example is continuous at a = 0.
  §4.5; pg. 176, No. 4, 5, 7, 8, 12, 18, 26, 49. (pdf)
  
  
• Wednesday, Jan 12
  ➀ No classes – ASU is closed today due to weather.
  ¤ Determine whether \(f(x)=\sqrt{\,x\,\sin(1/x)}\)
  1. has a limit as \(x\to 0\)
  2. is continuous at \(x = 0\)
  
  
• Friday, Jan 14
  §4.6, Part 1; pg. 180. Prove:
  • Theorem 4.6.7. A finite union of compact sets is compact.
  • Theorem 4.6.10. Let \(f:K\to\mathbb{R}\) be continuous and \(K\) be compact. Then \(f\) attains maximum and minimum values on \(K\).
  
  

Week 2

• Monday, Jan 17 — No classes
  ◊ Dr. Martin Luther King, Jr Day.
  
  
• Wednesday, Jan 19
  §5.1, No. 1, 3a→e, 4.
  ¤ Determine the following limits:
  1. \( \displaystyle \lim_{h\to\ 0} \frac{f(x+h)-f(x)}{h} = \)
  2. \( \displaystyle \lim_{h\to\ 0} \frac{f(x+h) - f(x-h)}{2h} = \)
  3. \( \displaystyle \lim_{h\to\ 0} \frac{f(x+2h)-3f(x+h)+3f(x-h)-f(x-2h)}{-2h} = \)
  What would the next fraction in the sequence be?
  
  
• Friday, Jan 21
  §5.2, No. 1bdfh, 5, 12.
  
  

Week 3

• Monday, Jan 24
  §5.3, No. 4, 7, 15abg, 16, LA 29.
  ◊ Rudin: Pg. 115, No. 13a→d. (See class notes.)
  ¤ Derivative Questions (due Fri, Jan 28). [LaTeX source]
  
  
• Wednesday, Jan 26
  §5.4, No. 2, 8, 10, LA 11
  ◊ Look at Grabiner on Taylor's Thm
  
  
• Friday, Jan 28
  §5.4, No. 13, 20ad; LA 27, 30.
  ◊ Read the section "The Taylor Series Process" in Fraser on Lagrange
  
  

Week 4

• Monday, Jan 31
  §5.3, No. 4. [Hint: \(f(t)=0 \Rightarrow 1=e^t \sin(t) \Rightarrow e^{-t}-\sin(t)=0\). Consider \(h(x)=e^{-x} - \sin(x)\).]
  §5.4, No. 9, 14, 25, LA 23.
  ¤ Explore the Maclaurin polynomials of \(\Psi(x)=\tan(\sin(x))\).
  
  
• Wednesday, Feb 2
  §5.5, No. 1aciknr, 6, 11, 15abcd.
  
  
• Friday, Feb 4
  ◊ No 11→17 from today's notes.
  
  

Week 5

• Monday, Feb 7
  ¤ Explore the problems in the class notes.
  
  
• Wednesday, Feb 9
  §6.1, No. 1, 3, LA 4.
  
  
• Friday, Feb 11
  ¤ Explore the problems in the class notes.
  §6.1: Give an example showing 4 is 'false'.
  §6.1, No 9, 11, 13.
  
  

Week 6

• Monday, Feb 14 — "Is it Valentine's Day or is it Lupercalia?"
  §6.2, No 2, 3, 7 (often appears on 'comps'), 14.
  
  
• Wednesday, Feb 16
  §6.3, No 1, 4, 5, LA 13.
  
  
• Friday, Feb 18
  §6.3, No 13, 14, 15, 17.
  
  

Week 7  ☺ (This Week)

• Monday, Feb 21 — «Midterm time»
  §6.4, No 3, 5
  
  
• Wednesday, Feb 23
  ◊ Exercises 1 and 2 from the end of today's notes.
  
  
• Friday, Feb 25
  ¤ Test 1 (LaTeX source)
  

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

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