28 Aug 2007

KKKQ 3013KKKQ 3013PENGIRAAN BERANGKAPENGIRAAN BERANGKA

Week 8 – Numerical Derivatives & Integrals28 August 2007

8.00 am – 9.00 am

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Topics

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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

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Tutorial Example 1

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Tutorial Example 1

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Tutorial Example 1