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Unformatted text preview: EECS‘l45 Electrical Engineering Analysis
Fall 2009 Second Midterm Examination
Chin C. Lee 1:001:50pm, Nov. 6, Friday Each problem has 20 points. 1. Present the three most important secondorder partial differential ‘equations in
engineering. For each equation, you need to write down the name (title) of the equation, the equation itself, and the type of problems that it can solve.
2. The electric field component of an electromagnetic plane wave is given by:
E(x, y, z, t) = (3, 4, DEC exp [j(kz —— (Um, where (3, 4, 0) = 3i+4j+0k, a vector. Using one of Maxwell's equations, derive the magnetic field component of this piane
wave H(x, y, z, t). You are required to present your derivation procedure step by step. Guessing alone will not give your any credit. 3. f(z) = z2 + 11(22). Find the points on zplane at which f(z) is not a conformal mapping function. 4. w(z) = u(x,y) + j v(x,y) = sinh(z). Find u(x,y) and v(x,y), and prove that
grad u(x,y)grad v(x,y) = O 5. w(z) = e'z. A domain on the z—plane is chosen as a rectangle defined by: 0 s x s 1
and 1 s y s 1. Find and sketch the range (image) on the w—plane. You must label your range clearly with equations. JM Jud Heth 1%.sz (WOW? eqthah) Won/e Ylfo‘vjem WC—FMSRM . (a), I’llQr/‘f (OmeC'hcA Ea _ ) DPPLSFM FEM?!”
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 Fall '10
 ChinC.Lee
 electric field component, electrical engineering analysis, Chin C. Lee, partial differential ‘equations, magnetic field component

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