# COMPREHENSIVE EXAMINATION : Engenering Mathematics

May 19th, 2015
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Directions: Encircle the correct answer. Show your solutions. Cheating in any form will be penalized according to the student’s norm of conduct. 1. Evaluate (2x – 5y)3 a. a. 2x3 + 30x2y + 75xy2 + 50y3 b. b. 2x3 – 30x2y + 75xy2 – 50y3

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COURSE INSTRUCTOR:Pourbashash, Hosseine mail:pourbashash@gmail.comEngineering Mathematics is the art of applying mathematics to complex real-world problems. It combines mathematical theory, practical engineering and scientific computing to address todays technological challenges.Partial differential equations are the basis of all physical theorems. In the theory of sound in gases, liquid and solids, in the investigations of elasticity, in optics, everywhere partial differential equations formulate basic laws of nature which can be checked against experiments.Bernhard RiemannSynopsisThis course covers topics including Fourier Analysis and Partial Differential Equations. Complex Numbers and Functions are also studied. Complex Differentiation, Complex Integration and Complex Analysis and Potential Theory are discussed. Learning Outcomes:By the end of the course, students should be able to:No.Course Learning OutcomesAssessment MethodsCO1Find the Fourier series of periodic functions Find the Fourier sine and cosine series for functions defined on an interval Apply the Fourier convergence theorem Find the Fourier sine and cosine integral for functionsFind the Fourier translators for functions Q1,T1, FCO2Explain the fundamental concepts of partial differential equations and their role in modern mathematics and applied contexts Solve linear second order PDEs using canonical variables for initial-value problems, Separation of Variables a

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