ENGR391_FinalSummer2007

# ENGR391_FinalSummer2007 - ENGR 391 FINAL EXAM FACULTY OF...

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ENGR 391 FINAL EXAM ENGR-391 NUMERICAL METHODS FOR ENGINEERS Student’s Name: I.D.: Duration 3 hours PROBLEM 1 [Solving Nonlinear Equations] [5 marks] Solve the following nonlinear equation using the secant method with x 0 =2.0 and x 1 =1.0: 1 3 2 ) ( 2 3 - - + = x x x x f Give the answer with 4 significant digits. Check your result and discuss. PROBLEM 2 [Solving Systems of Linear Equations] [5 marks] a) Find the LU decomposition of following matrix: - - = 1 0 4 3 4 0 0 1 2 A Check your results b) Compute the determinant of A 1 FACULTY OF ENGINEERING AND COMPUTER SCIENCE DEPARTMENT OF MECHANICAL ENGINEERING

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ENGR 391 FINAL EXAM PROBLEM 3 [Numerical Integration] [5 marks] Compute the following integral: dx e x I x = 3 0 ) sin( Using multi-segment Trapezoidal rule with two segments (n=2) and with four segments (n=4). Estimate your global truncation error and give your answer with an appropriate number of significant digits. Hint: The order in the global truncation error of the trapezoidal rule in its multiple
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ENGR391_FinalSummer2007 - ENGR 391 FINAL EXAM FACULTY OF...

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