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بسم هللا الرحمن الرحيم Kingdom of Saudi Arabia Ministry of Higher Education Majmaah University College of Engineering Department: Basic Engineering Sciences Exam Information First Exam Course code: Math 254 Course Title: Numerical Methods Instructor: Dr. Mukhtar Salah Section number: 1 Exam date: Mon. 27/10/2014 Exam time: From: 4:00 pm To: 6:00 pm Exam hall: 3D40-41 Number of pages: 5 Total score: 20 points Student’s Information Name: ID: Exam Instructions: Read the questions carefully and several times. Writing clearly will make it possible to assess your answers correctly. Any form of cheating, intention to cheating, or disruption of the exam will subject you to a disciplinary action as specified by the university’s regulations. Carrying or using the mobile phone during the exam is not allowed. Using the phone during the exam will carry a disciplinary action. The calculator is only permitted by the exam supervisor. No student can leave the exam room during the first half hour of the exam. Any student coming after the first half hour of the exam will not be permitted to enter the exam. A student leaving the exam, even for legitimate reasons, may not be given a makeup exam. Points Earned: Question Score 1 2 3 4 Total score in the exam: Dear student, we encourage you to answer the exam the best you can and we wish you all success. 1 Question 1:( 5pts) You are working for a start-up computer assembly company and have been asked to determine the minimum number of computers that the shop will have to sell to make a profit. The equation that gives the minimum number of computers n to be sold after considering the total costs and the total sales is f (n) 40 n3 875n 35000 0 Use the bisection method of finding roots of equations to find the minimum number of computers that need to be sold to make a profit. Conduct three iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration. 2 Question 2:( 5pts) To find the inverse of a number a , one can use the equation f (c ) a 1 0 c where c is the inverse of a . Use the Newton-Raphson method of finding roots of equations to find the inverse of a 2.5 . Conduct three iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration. 3 Question3 : (5pts) Thermistors are used to measure the temperature of bodies. Thermistors are based on materials’ change in resistance with temperature. To measure temperature, manufacturers provide you with a temperature vs. resistance calibration curve. If you measure resistance, you can find the temperature. A manufacturer of thermistors makes several observations with a thermistor, which are given in the following Table 1. Table 1 Temperature as a function of resistance. R ohm T C 910 630 450 30 40 50 Determine the temperature corresponding to 754.8 ohms using Newton’s divided difference method of interpolation and a second order polynomial. 4 Question4 : (5pts) Solve the following set of equations with LU decomposition: 2x1 − x2 + x3 = 1 3x1 + 3x2 +9x3 = 2 3x1 + 3x2 + 5x3 = 1 ============================================================= End of the Exam Good Luck Dr. Mukhtar Salah 5