This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.

Sugar cane plantations had operated across almost every island in the West Indies since the seventeenth century. Run by British planters, they relied on slavery as their main source of labour. A surgeon and Anglican minister, James Ramsay (1733 89) witnessed at first hand the exploitation of African slaves in Britain's West Indian colonies. Working there for over twenty years, as both a Christian missionary and a practising surgeon, he became keenly involved in the campaign to improve the welfare of slaves. This extended essay, first published in 1784, was an early and highly influential contribution to the anti-slavery movement, generating both enlightened acclaim and deep opposition. Analysing the relationships between slaves and their masters, discussing the role of slaves in society, and proposing various measures to improve their lives, this work remains a relevant text in Caribbean and colonial history.

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997.

Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition.

Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author.

This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002).

This user's manual also provides the documentation for the S+FDA library for S-Plus.

The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems

Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book

The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems