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CE 5143 Homework 8 Due 11/8/07 — David Wagner 2007/11/08 17:49

Problem 1: #13.2

  • (a) B=(D+1)f = (40-11+1)*3=90
  • (b) B=(D+1)f = (5+1)*3=18
1 -  6 - 11 - 16 - 21 - 26 - 31 - 36
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2 -  7 - 12 - 17 - 22 - 27 - 32 - 37
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3 -  8 - 13 - 18 - 23 - 28 - 33 - 38
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4 -  9 - 14 - 19 - 24 - 29 - 34 - 39
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5 - 10 - 15 - 20 - 25 - 30 - 35 - 40

Problem 2: #13.3

  1. a_2=m={Delta A}/{Delta x}={100-50}/{20-80}=-0.8333
  2. A=mx+b=100=-0.8333*20+b right a_1=b=100+16.6667=116.6667
  3. A=116.6667-0.8333x

phi(x) = a_1 +a_2x = delim{lbrace}{ matrix{1}{2}{1 x} }{rbrace} delim{lbrace}{ matrix{2}{1}{a_1 a_2} }{rbrace}= delim{lbrace}{ matrix{1}{2}{1 x} }{rbrace} delim{lbrace}{ matrix{2}{1}{116.667 {-0.8333}} }{rbrace}

This is a one-dimensional simplex element.

Problem 3: #13.4

  1. a_2=m={Delta T}/{Delta x}={150-50}/{10-20}=-10
  2. T=mx+b=150=-10*10+b right a_1=b=150+100=250
  3. T=250-10x

phi(x) = a_1 +a_2x = delim{lbrace}{ matrix{1}{2}{1 x} }{rbrace} delim{lbrace}{ matrix{2}{1}{a_1 a_2} }{rbrace}= delim{lbrace}{ matrix{1}{2}{1 x} }{rbrace} delim{lbrace}{ matrix{2}{1}{250 {-10}} }{rbrace}

The gradient is m=-10ºF/in

Problem 4: #13.5

Problem 5

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