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16 Feb 2005: Mathematical Tripos: Part II. Lecture notes for the course. Numerical Analysis. Herewith lecture notes for the Part II Numerical Analysis course, as. pdf. files. In each case, the latest version is displayed. This might be this year's for current

31 Jan 2005: Proof In the notation of Lemma 2.20, the first column ofAk1 is Q̄>k AQ̄ke1. ... Then,ask , the bottom row ofAk1 tends toλre>n. Proof It follows from Lemma 2.20, Remark 2.23, the eigenvalue equation v>r A = λrv>.

1 Mar 2005: ρ. D Dt. 20 = ρ Φcg p T,where Φcg = Φ 12 20r2 is the centrifugal–gravitational potential. ... Thus. t 2A0x y ( 2A0x y ) 20 ( 2A0x y ) = Φcg 1ρ p+ 1ρ T.

9 Jan 2005: su=2pi/150; sv=2pi/20; [u,v]=meshgrid(0:su:(2pi),0:sv:(2pi)); r1=2; % Main radius r2=0.4; % Radius of torus r3=0.3; % Radius of tube

20 Jan 2005: significant fraction (about 20%) of the rest-massenergy of the particle, and accretion is an even more efficient source of energy than nuclear. ... cm. Jupiter data: mass MJ = 1.90 1030 g 0.001 M, radius RJ = 7.14 109 cm 0.1 R,orbital semi-major axis

28 Feb 2005: PDE. Thus, the above example is within adifferent framework to both the direct stability analysis of Lecture 19 and to the eigenvalue analysis ofLecture 20.

4 Mar 2005: Method 5.20(The leapfrog method) We semidiscretize in equation (5.8) with the finite-difference approx-imation u(mx, t)/x 12 (x).

3 Feb 2005: GIO 2005 20. Green function of the linear diffusion equation, in units such that s = 1 and ν̄ = 1.

21 Feb 2005: Applications 4.20 The FFT has numerous further applications: spectral and pseudospectral discretizationmethods for PDEs, computation of Fourier harmonics, image processing, filtering and reconstruction, com-puter vision, solution of integral

7 Feb 2005: Mathematical Tripos Part IILent 2005. Professor A. Iserles. Numerical Analysis – Lecture 101. Definition 3.10 (Multistep methods)It is often useful to use past solution values in computing a new value.Thus, assuming thatyn, yn1,. , yns1 are