Kirjahaku

This book is designed for a first course in numerical analysis. It differs considerably from other such texts in its choice of topics.

This book is designed for a first course in numerical analysis. It differs considerably from other such texts in its choice of topics.

A reference for the field of particle modelling - the study of dynamical behaviour of solids and fluids in response to external forces, with the solids and fluids modelled as systems of atoms and molecules.

This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises.

The study and application of N-body problems has had an important role in the history of mathematics. In recent years, the availability of modern computer technology has added to their significance, since computers can now be used to model material bodies as atomic and molecular configurations, i.e. as N-body configurations.This book can serve either as a handbook or as a text. Methodology, intuition, and applications are interwoven throughout. Nonlinearity and determinism are emphasized. The book can be used on any level provided that the reader has at least some ability with numerical methodology, computer programming, and basic physics. It will be of interest to mathematicians, engineers, computer scientists, physicists, chemists, and biologists.Some unique features of the book include: (1) development of turbulent flow which is consistent with experimentation, unlike any continuum model; (2) applicability to rotating tops with nonuniform density; (3) conservative methodology which conserves the same energy and momentum as continuous systems.

Turbulence is the most fundamental and, simultaneously, the most complex form of fluid flow. However, because an understanding of turbulence requires an understanding of laminar flow, both are explored in this book.Groundwork is laid by careful delineation of the necessary physical, mathematical, and numerical requirements for the studies which follow, and include discussions of N-body problems, classical molecular mechanics, dynamical equations, and the leap frog formulas for very large systems of second order ordinary differential equations.Molecular systems are studied first in both two and three dimensions. Extension into the large is also of great interest, and it is for this purpose that we develop particle mechanics, which uses lump massing of molecules. All calculations are limited to a personal scientific computer, so that the methods can be utilized readily by others.

In this book the author has tried to apply “a little imagination and thinking” to modelling dynamical phenomena from a classical atomic and molecular point of view. Nonlinearity is emphasized, as are phenomena which are elusive from the continuum mechanics point of view. FORTRAN programs are provided in the Appendices.