1. 28 Aug 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 8 – Numerical Derivatives & Integrals 28 August 2007 8.00 am – 9.00 am

2. 28 Aug 2007 Week 8 Page 2 Topics

3. 28 Aug 2007 Week 8 Page 3 Tutorial Example 1 (adapted courtesy of ref. [1]) [1] KQ3013 lecture notes For the following function f(x) = sin x a)Apply the first, second and third order Taylor series to predict f(x) at x =  /6 with x = 0 as base point. Use step sizes  /6,  /12 and  /18. For each case, determine the true relative error. b)Evaluate the forward, backward and centred finite divided difference of the function at x =  /6 with step sizes  /6,  /12 and  /18. Similarly, for each case, determine the true relative error. c)Numerically evaluate the integration of the function between x = 0 and  using i.Trapezoidal rule with 4 segments ii.1/3-Simpson rule with 4 segments

4. 28 Aug 2007 Week 8 Page 4 Tutorial Example 1

5. 28 Aug 2007 Week 8 Page 5 Tutorial Example 1

6. 28 Aug 2007 Week 8 Page 6 Tutorial Example 1

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8. 28 Aug 2007 Week 8 Page 8 Tutorial Example 1

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10. 28 Aug 2007 Week 8 Page 10 Tutorial Example 1