Alwyn Scott - Böcker

Much mathematical modelling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which, although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems, however, lead to the emergence of new structures that reflect reality much more closely. This second edition of Nonlinear Science, covers several important areas of nonlinear science, and places a strong emphasis on applications to realistic problems. It includes numerous new topics such as empirical results in molecular dynamics, solid-state physics, neuroscience, fluid dynamics, and biophysics; numerous new exercises and solutions; updated sections on nerve impulse dynamics, quantum-theory of pump-probe measures, and local modes on lattices. With over 350 problems, including hints and solutions, this is an invaluable resource for graduate students and researchers in the applied sciences, mathematics, biology, physics and engineering.This is the latest title in the Oxford Texts in Applied and Engineering Mathematics, which includes a range of texts from the undergraduate through to the graduate level. Most titles should be based on taught courses which explain the mathematical or computational techniques required for the resolution of fundamental applied problems. Other books in the series include: D. W. Jordan and P. Smith: Nonlinear ordinary differential equations: an introduction to dynamical systems 3rd Edition; I. J. Sobey: Introduction to interactive boundary layer theory; A. B. Tayler: Mathematical Models in Applied Mechanics (reissue); Ramdas Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Lapeyre et al: Introduction to Monte-Carlo Methods for Transport and Diffusion Equations; Isaac Elishakoff & Yong Jin Ren: Finite Element Methods for Structures with Large Stochastic Variations

Stairway to the Mind explores one of the most exciting and controversial areas of modern science: consciousness and the nature of the mind. The book proposes that consciousness emerges from hierarchical layers of mental reality, in the same way that life emerges from layers of biological reality. The book is aimed at general readers with an interest in the mind and neuroscience, as well as a wide range of scientists whose work is related to the rapidly-growing field of neuroscience and consciousness research.

This is an introductory text of mathematical neuroscience intended for anyone who wants to appreciate the role that mathematics and mathematical modeling and analysis can do to aid an understanding of how the brain works and the nature of the mind. In particular, the book will be of interest to established neuroscientists and neuroscience students who wish to know what roles mathematical formulations can play in attempting to comprehend the dynamics of a human brain. For this purpose, the book is designed as a text with problems at the end of each chapter. It is expected that this text will be interesting for mathematics faculty teaching in neuroscience programs. It also aims to serve as a general introduction to neuromathematics in neuroscience programs at both undergraduate and graduate levels. Physical scientists and bioengineers who plan to extend their research activities into the realms of cognitive science will find this an ideal guide, as will philosophers and social scientists who wish to understand the degree to which dynamics of a brain can be reduced to mathematical formulations.Mathematical formulations in neuroscience are of five sorts: (i) Exact descriptions of well understood dynamic processes, like the Hodgkin-Huxley theory of the nerve impulse. (ii) Metaphorical descriptions of more complex phenomena, like the stationary states of a Hopfield model. (iii) Information theory for dealing with the storage and transmission of data. (iv) Logical calculus (Boolean algebra) for the analysis of information processing systems. (v) Number theory for counting large numbers of possibilities. (vi) Statistical tools for organizing and evaluating data.

This is an introductory text of mathematical neuroscience intended for anyone who wants to appreciate the role that mathematics and mathematical modeling and analysis can do to aid an understanding of how the brain works and the nature of the mind. In particular, the book will be of interest to established neuroscientists and neuroscience students who wish to know what roles mathematical formulations can play in attempting to comprehend the dynamics of a human brain. For this purpose, the book is designed as a text with problems at the end of each chapter. It is expected that this text will be interesting for mathematics faculty teaching in neuroscience programs. It also aims to serve as a general introduction to neuromathematics in neuroscience programs at both undergraduate and graduate levels. Physical scientists and bioengineers who plan to extend their research activities into the realms of cognitive science will find this an ideal guide, as will philosophers and social scientists who wish to understand the degree to which dynamics of a brain can be reduced to mathematical formulations.Mathematical formulations in neuroscience are of five sorts: (i) Exact descriptions of well understood dynamic processes, like the Hodgkin-Huxley theory of the nerve impulse. (ii) Metaphorical descriptions of more complex phenomena, like the stationary states of a Hopfield model. (iii) Information theory for dealing with the storage and transmission of data. (iv) Logical calculus (Boolean algebra) for the analysis of information processing systems. (v) Number theory for counting large numbers of possibilities. (vi) Statistical tools for organizing and evaluating data.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Starting to Read ECGs

​​​The ECG is one of the most widely available diagnostic tests used in clinical practice today. This book is intended to build upon the topics covered in Starting to Read ECGs: The Basics thus allowing the reader to enhance their previous knowledge. Additional topics covered include a detailed look at calculating cardiac axis, an area often considered difficult to grasp, and alternative methods such as the various ways the heart rate can be calculated, the different criteria for determining LVH. Technical details about specific cardiac conditions, how to interpret pediatric ECGs, and the effect of medical devices on the ECG will also be discussed. Plentiful diagrams, tables and colour images used throughout to illustrate complex points in a simple and easy to understand way. The key facts section at the end of each chapter highlights the most important information and summary tables are provided to allow the book to be used as a quick reference guide. Each chapter will contain a mind map for revision and to aid dyslexic learners, practice questions and a few practice ECGs to consolidate the readers knowledge.The book tells the practitioner what they need to know clinically and doesn't assume any prior knowledge. It is ideal for junior doctors and clinicians, nurses, paramedics, students and health care professionals involved in the recording of 12-lead ECGs.

Stairway to the Mind explores one of the most exciting and controversial areas of modern science: consciousness and the nature of the mind. The book proposes that consciousness emerges from hierarchical layers of mental reality, in the same way that life emerges from layers of biological reality. The book is aimed at general readers with an interest in the mind and neuroscience, as well as a wide range of scientists whose work is related to the rapidly-growing field of neuroscience and consciousness research.