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2006_p1

2006_p1 - (3(3 L(3 b(3(l(3 MCGI L V FACULTY OF ENGINEERING...

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Unformatted text preview: (3) (3) ( ) L_.) (3) ( ) b) (3) (l) (3) MCGI L V FACULTY OF ENGINEERING APPLIED MATHEMATICS MECH60Â§ FINAL EXAMINATION EXAMINER: G.G.BACH aÃ©ï¬‚zÃ©/â€™ DATE: Tues, Dec 12, 2006 TIME: 18:00 NOTES: ALL BOOKS, NOTES, ETC PERMITTED.â€™MARK.INâ€˜%â€™BESIDE EACH PROBLEM WHICH ADD UP TO MORE THAN 100% 1. Put the following into VectornCeloulus form. BE CLEAR! (8) AijkiJBk (b) Aiij3Â§kÂ¥ (c) EijkA3BÂ§nCn 25 Put the following VeÃ©Ã©fâ€”Caloulus forms into Tensor notation. I) <,,) image] (b) (ANEA.(ENE) *-" u' -â€™ (c) (AXB)X(CXD) 3. The rectilinear set uvw is related to the Cartesigns xyz by x = Zu â€” V, y = 2V - w, z = â€”u + 2w - o o . .D (8) Find the covariant and contrgvariant b851S vectors e; â€™5'? . . . _._ and eâ€˜ as well as the covariant and contrsvarient metric tensors iâ€˜ n. . T gij and g 3. Also 11nd the Jacobian u. (b) What is the angle between the X and v axes? . I . - . 2 . (0) Find the detailed expression for Q7qÃ©l,where 1s a scalar function in the uvw system. 7 (Problem 4 on the next page) ...
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