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Tutorial 2
Lecture NotesDr. Rakhmad Arief SiregarUniversiti Malaysia Perlis
Applied Numerical Method for Engineers
2
Quiz (60 Minutes)
What do you know about mathematical model in solving engineering problem? (10 marks)
Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks)
Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)
3
Quiz (60 Minutes)
What do you know about mathematical model in solving engineering problem? (10 marks)
Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks)
Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)
6
Solution 1
The process seems to be diverging suggesting that a smaller step would be required for convergence
7
Quiz (60 Minutes)
What do you know about mathematical model in solving engineering problem? (10 marks)
Use zero through third order Taylor series expansions to predict f(2.5) for f(x) = ln x using a base point at x = 1. Compute the true percent relative error for each approximation. (15 marks)
Determine the real root of f(x)= 5x3-5x2+6x-2 using bisection method. Employ initial guesses of xl = 0 and xu = 1. iterate until the estimated error a falls below a level of s = 15% (20 marks)
10
Solution 3
First iteration The process can be repeated until the approximate error falls
below 10%. As summarized below, this occurs after 5 iterations yielding a root estimate of 0.40625.
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Problems 5.1
Solution A plot indicates that a single real root occurs at
about x = 0.58
-8
-4
0
4
8
-5 0 5 10
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Solution 5.1
Using quadratic formula
First iteration:
40512.6
40512.1
)5.0(2
)5.4)(5.0(4)5.2(5.2 2
x