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10 Mar 2004: Most algorithms have some kind of “overheads”. For instance, suppose we wish tocalculate (. b 3. nc)! where b. c denotes the integer part. We would need to calculate m = b 3. ... g(n). )iff g(n) = O. (f (n). ); i.e., is (in some sense) the.

2 Mar 2004: Given that the particle’s trajectoryis r = a sin θ for some constant a, deduce that (up to an arbitrary additive constant)V r4. ... 7 If µ(r) = |f(r)| for some function f, show that B.

2 Mar 2004: Show that for any vector x,Ax may be written as! x for some suitable! ... σij = 2µ(eij 13 δij ekk) pδijfor some scalar µ known as the coefficient of viscosity.

8 Mar 2004: Let y(x) be a function of x in some interval a < x < b, and consider the definite integral. ... What shape must. the wire have for the bead to reach some lower point B in the shortest time?

8 Mar 2004: annulus a < |z z0| < b for some a, b (regardless of whether f isanalytic at z0 itself) then f has a unique Laurent expansion. ... some non-zero an’s – then f is said to have an essentialisolated singularity.

19 Jan 2004: cz2), where A, a, b, c are some constants that needed to be estimatednumerically. ... Rev. B 65 174518[2] Berloff N G and Roberts P H 2000 J.

30 Sep 2004: Take for instance thecase in which rigid boundaries are introduced at y = b a for some positive constant a; it is easyto show that this always replaces the 12 |k|. ... B sinh(2kb).ek(yb) (y < b). (10). for some pair of constant coefficients A and B.