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EE443 Nümerik analiz dersinin sınav soruları. Bazılarıın çözümleri de var. Word ve Excell dosyalarından oluşuyor. Kolay gelsin:)

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Middle East Technical University
Electrical and Electronics Engineering Department
EE 443, Computational Methods in Electrical Engineering

Final Examination
Please attempt four out five questions - Equal Credits - 90 Minutes

03.01.2006
1. Cos x may be approximated by using Taylor Series as

Cos x  1 – x2/2 + x4/4! – x6/6!

By using the Bairstow Quadratic Division Technique, calculate cos (1 + j).

2. BY using Gauss-Jordan Complete Elimination Technique, derive (Derive, do not just substitute) that the inverse of a complex matrix A + jB may be written as C + jD, where,

C = - (AB-1A + B)-1
D = B-1 A (AB-1A + B)-1,
3. Determine the definiteness of the matrix;



4. Solve the differential equation;

d/dx y(x) = xy1/2, y(x0) = 1, x0 = 0,

at point; x = 0.1, by expanding the solution at point x = 0.1 by using Taylor Series with h = 0.1 as;

y(x+h)  y(x) + h y(1) (x) + h2/2 y(2)(x) + h3/6 y(3)(x),

5. Consider a simple linear circuit with a resistance R, a DC voltage source VDC and an AC voltage source V, all connected in series. Source voltage and current in the circuit are measured. Measurements have different accuracies as shown below. Calculate R and VDC in a WLS error sense.

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