# 2009 paper - School of Engineering and Design SED06...

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School of Engineering and Design SED06: Examinations Cover Sheet SUBJECT AREA: Mechanical Engineering Module Code: ME1302 Module Title: Analytical Skills and Quantitative Methods Date-Month: MAY Year: 2009 Time allowed – Hours: 2 Answer-questions: Answer THREE questions - All questions carry equal marks Examiner(s): Professor L C Wrobel and Dr J Chen Special Stationery Requirements: None Only School approved calculators are allowed. Use a separate answer book for each section. If you submit answers to more questions than specified, final marks for the examination will be determined using the best marks which satisfy the rubric.

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___________________________________________________________________________ - 1 - 1. (a) Given the complex numbers z 1 = 1 i , z 2 = 1 + 2 i and z 3 = 2 + 5 i , calculate: (i) 5 3 1 2 3 2 1 z z z [10%] where 1 z is the complex conjugate of 1 z . (ii) 5 2 3 3 2 1 z z z [10%] (b) Find a and b given that: i bi a i a 2 ) 2 )( 3 ( 2 [15%] (c) Find the modulus and argument, and then the real and imaginary parts, of the complex number: i e 2 3 2 [15%] (d) Apply the method of separation of variables to find the solution of the equation: 3 ) 4 cos( 2 1 y dx dy x with initial conditions 4 y when 8 / x .
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2009 paper - School of Engineering and Design SED06...

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