## Overview

In January 2015, SIAM published my book titled*Model Emergent Dynamics in Complex Systems*on rational mathematical modelling of dynamics. Via this web page you may create a PDF book of supplementary material tailored to the interests you specify.

*Currently this is a draft version.*

## Errata of printed first edition

- p.8, Fig.1.1: \(x=1-\frac12\epsilon+\cdots\), not \(+\frac12\epsilon\).
- p.52, l.-6: \(\lim_{x\to0}\frac{\cos x}2\) not the negative.
- p.60, Ex. 2.11: the ODE \(x^2y''+xy'+xy^2=0\), not \(x^2y''+x^2y'+xy^3=0\).
- p.75, l.7: \(\vartheta\) denotes the phase of the left-travelling wave (not the right-travelling).
- p.158, Ex. 4.6 (a slow subspace): use \(\dot x=-ay\), not \(\dot x=-ax\).
- p.160, Ex. 4.12 (instability at higher order): construct the slow manifold to higher order, such as \(O(x^3+y^3)\), and find that the conclusion is not quite correct!
- p.206, Ex 5.4 and 5.5: in the answers there is no need for the error component ``\(,\alpha^2\)'', omit.
- p.246, Eqn (7.5): omit the \(\theta\) derivatives (in the last term).
- p.253: last line of the first displayed maths should read \(=(uU-U^2)w\frac{\partial^2C}{\partial x^2}\).
- p.300: "decay rate \(\pi/4\)" should be "decay rate \(\pi^2/4\)".
- p.304, lateral momentum equation: the RHS of the update PDE needs a factor of \(1/Re\); the residual of the tangential stress equation needs to be negated; and "change to the pressure field is due to viscous stresses at the free surface and the need to accelerate the flow vertically" should read "change to the horizontal velocity field is due to viscous drag at the bed, flagged by factor~\(\gamma\), and the acceleration due to spatial variations".
- p.305, last line before ``Iterative construction'': boundary condition "\(\hat u=0\)" should read "\(\partial\hat u/\partial Z=0\)".
- p.708--712, Algorithm 21.4--8 does not work when there is large noise in the slow variables. It does appear to be OK when the slow variable noise is small or zero.

## Among the chapters that follow, choose the interesting ones

The chapters labelled BOOK are in the published book. At the end click Submit to process, typeset and produce a PDF supplement tailored just for you. The processing automatically detects all prerequisite chapters and includes them as well. Only select what interests you.

## Print the book 2up

The book is typeset onto A5 pages (in colour) so please save forests and print two pages per sheet of paper. Also, A5 is by far the best standard size for reading electronically on your computer screen.If you like this web page, please link to it so others can find it more easily.