Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Tutorial 2 Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Applied Numerical Method for Engineers

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)

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)

Solution 2 True value:f(2.5) = ln(2.5) = 0.916291...

Solution 1 True value:f(2.5) = ln(2.5) = 0.916291...

Solution 1 The process seems to be diverging suggesting that a smaller step would be required for convergence

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)

Solution 3 Graphically

Solution 3 First iteration 563-583

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.

Problems 5.1 Solution A plot indicates that a single real root occurs at about x = 0.58

Solution 5.1 Using quadratic formula First iteration:

Solution 5.1 Second iteration:

Solution 5.1 Third iteration:

Solution 5.4 Solve for the reactions:

Solution 5.4 A plot of these equations can be generated