- Linear Algebra Reformed for 21st Application This textbook provides an innovative introduction and development of the power of linear algebra in modern science, engineering and computing. I make draft versions and source available on github for others to collaborate in this venture.
- The best LaTeX introduction shows how to transform plain text into a beautifully typeset document in LaTeX. It introduces what many consider are the most important fundamentals of LaTeX2e.
- Modelling emergence Sick of fat textbooks that are 80% wasted? Compile your own tailored version here to learn modern methods of modelling complex dynamical systems.
- Holistic discretisation of dynamical Partial Differential Equations obtain the spatial discretisation of one or three coupled dynamical PDEs using dynamical systems theory.
- SDE normal form provides you with a normal form of any supplied stochastic differential equation (SDE), or deterministic non-autonomous ODE or Delay ODEs, when the DEs have slow modes and fast stable/unstable modes. The normal form decouples the slow modes from the fast and so supplies you with a faithful large time model of the stochastic dynamics.
- SDE slow manifold provides you more quickly with just the slow manifold of any supplied stochastic differential equation (SDE), or deterministic non-autonomous ODE or Delay ODEs, when the DEs have slow modes and fast stable/unstable modes. The slow manifold model supplies you with a faithful large time model of the stochastic dynamics.
- Find a centre manifold provides a centre manifold and evolution thereon of your specified system of ordinary differential equations. It applies to pitchfork or Hopf bifurcations or higher order degeneracies. It even transforms one or coupled oscillators into modulation equations to replace averaging and homogenisation. 2014: added code to compute a basis of normal vectors to the isochrons in order to model initial conditions, forcing, and uncertainty quantification.
- Multifractal analyser estimation of fractal dimensions, let alone multifractal dimensions, are fraught with subtle difficulties. Use this state of the art service to estimate fractal dimensions for your 1D, 2D or 3D datasets.
- Construct lego fractals to stun your friends.
- List of research and teaching publications with links to many electronic versions.
Erdos number 3The Erdos Number is the distance from Paul Erdos (1913--1996) on a graph whose edges denote the relationship of coauthorship in scientific articles [ http://www.oakland.edu/enp]:
- Pollett, P. K.; Roberts, A. J. A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold. Adv. in Appl. Probab. 22 (1990), 111--128.
- Brown, T. C.; Pollett, P. K. Some distributional approximations in Markovian queueing networks. Adv. in Appl. Probab. 14 (1982), 654--671.
- Brown, T. C.; Erdos, P.; Chung, F. R. K.; Graham, R. L. Quantitative forms of a theorem of Hilbert. J. Combin. Theory Ser. A 38 (1985), 210--216.
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