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11 Nov 2006: 2.6.2 Three dimensional space. 23. 2.6.3 Higher dimensional spaces. 24. 2.7 Components. ... 24. 2.7.1 The Cartesian or standard basis in 3D. 24. 2.7.2 Direction cosines.

28 Oct 2006: 1.7.13 Aide Memoire. 24. 2 Partial Differential Equations 25. 2.0 Why Study This? ... You should be able to do example sheets 1/2/3/4 after lectures 6/12/18/24 respectively.

28 Oct 2006: 1.7.13 Aide Memoire. 24. 2 Partial Differential Equations 25. 2.0 Why Study This? ... You should be able to do example sheets 1/2/3/4 after lectures 6/12/18/24 respectively.

23 May 2006: 24. ). 1/2. Can also use for β 1 once βT 1. ... HKM shocks – p.24/25. Conclusions. Transients decay. γ2 α, γ 1: exponentially.

20 Jun 2006: 24. Intriguingly, Filon-type methods (3.11) lend themselves to an alternative interpretation.Comparing (3.11) with (3.1), we observe that. ... Num. Anal.24, 365–391. Iserles, A. & Nørsett, S. P. (2004), ‘On quadrature methods for highly oscillatory

2 Sep 2006: the literature (see [11, 16, 23, 24, 27]and references therein) which have been specifically designed for different familiesof problems. ... x/xj )2 1). (2.24). This completes the proof. 2. 9. 2.4 Accuracy.

22 May 2006: 22. 3.2.2 properties of limits. 24. 3.2.3 l’Hôpital’s rule. 24. 3.2.4 more examples. ... that. |un l| < ǫ for all n > N. 3 ELEMENTARY ANALYSIS 24.

22 May 2006: 1.4 Inverse of a matrix. 24. 1.4.1 Uniqueness of inverse. 24. ... . (. 1 4 2). =. . . 6 24 124 16 81 4 2.

20 Oct 2006: From Eq. 22 we have. U1 =E1/y0p1/y0. =1. 2y0, 24. as expected.For large y0 an accurate approximation to the solution.

23 Nov 2006: 16. 13. 13. 16. Part III: Numerical Solution of Differential Equations 24.