Methods of Nonlinear Analysis

The contents of this volume comprise the proceedings of the International Symposia in Economic Theory and Econometrics conference held in 1987 at the IC^T2 (Innovation, Creativity, and Capital) Institute at the University of Texas at Austin. The essays present fundamental new research on the analysis of complicated outcomes in relatively simple macroeconomic models. The book covers econometric modelling and time series analysis techniques in five parts. Part I focuses on sunspot equilibria, the study of uncertainty generated by nonstochastic economic models. Part II examines the more traditional examples of deterministic chaos: bubbles, instability, and hyperinflation. Part III contains the most current literature dealing with empirical tests for chaos and strange attractors. Part IV deals with chaos and informational complexity. Part V, Nonlinear Econometric Modelling, includes tests for and applications of nonlinearity.

This is the third edition of a successful textbook, now with material added to illustrate the potential of computers for biologists. It is a lucid introduction to the principles and more elementary techniques of statistical reasoning, particularly as they are relevant to the biologist. Special attention is paid to the validity and use of statistical procedures, the interpretation of results, and the meanings of the conclusions which can then be drawn. The understanding of statistical methods is aided by full explanations of how calculations are built up. A particular feature of this edition is the inclusion, of new material to demonstrate the potential usefulness of computers in biological statistical analysis and to this end computer analyses of a selection of the examples are presented, using several different statistical languages. The examples are designed to guide and encourage the biologist to pursue the use of these languages further. The book assumes no mathematical training an

Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models tha

In the past few decades, methods of linear algebra have become central to economic analysis, replacing older tools such as the calculus. David Gale has provided the first complete and lucid treatment

Volume I of a two-volume set, this text for a course in numerical analysis offers a broad overview of computer-oriented numerical algorithms. Topics include solution of a single nonlinear equation wit

How do I decide I am ill; how do I decide that my children are ill? How do I learn effective ways of conveying to others that I am ill? This book discusses the languages of illness which we use to present our discomforts to others through an exploration of the child's world of illness. It looks at how illness concepts are introduced to children, how the causes of illness and 'germ' rationales are incorporated into the socialisation of children, and how a particular morality about health and illness is expressed. Besides the analysis of the social context within which the children's views are developing, the book presents the children's own views from three years old up to thirteen. How we talk about illness can have as important consequences as the methods we use to cure it. This book persuades the reader to look more closely at the language of illness, allowing a reappraisal to medical practice, school health programmes and class teaching, health education and even the differences in

In this book, Professor David Starrett organizes within a single framework the major theoretical foundations of modern public sector economics. He presents a unified treatment of market failure that encompasses externalities, pure public goods, local public goods and natural monopolies. Professor Starrett then develops and assesses the efficacy of the various planning procedures - including representative voting, benefit cost analysis, incentive compatible design mechanisms and the free market. He devotes attention to both national and local issues, with the aim of identifying those methods that are best suited to each arena separately. Special attention is paid to financial arrangements, techniques for eliciting necessary information that is not readily available, and identification of biases that will result from incorrect procedures. This study will be useful to graduate students and economists who are interested in public finance or welfare economics.

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Canada and Immigration is a portrait of Canadian immigration since the end of the Second World War. It is an important record and analysis of immigration policies, laws, and methods of management duri

This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.

This book is a rigorous introduction to the abstract theory of partial differential equations. The main prerequisite is familiarity with basic functional analysis: more advanced topics such as Fredholm operators, the Schauder fixed point theorem and Bochner integrals are introduced when needed, and the book begins by introducing the necessary material from the theory of distributions and Sobolev spaces. Using such techniques, the author presents different methods available for solving elliptic, parabolic and hyperbolic equations. He also considers the difference process for the practical solution of a partial differential equation, emphasising that it is possible to solve them numerically by simple methods. Many examples and exercises are provided throughout, and care is taken to explain difficult points. Advanced undergraduates and graduate students will appreciate this self-contained and practical introduction.

The American Novel series provides students of American literature with introductory critical guides to the great works of American fiction by giving details of the novel's composition, publication history and contemporary reception. The group of essays, each specially commissioned from a leading scholar in the field, examines the interpretative methods and prominent ideas on the text. There are also helpful guides to further reading. Specifically designed for undergraduates, the series will be a powerful resource for anyone engaged in the critical analysis of major American novels. This collection of essays on Moby-Dick reconnects Melville's great work with concerns that are central to readers in critical studies. Richard Brodhead introduces the volume with a discussion of the book's unique place in the canon of American literature. He then recounts the novel's history from its mixed reception in the mid-nineteenth century to its prevalent status as a classic. The five essays that fol

This book gives a new interpretation of the reception of the new world by the old. It is the first in-depth study of the pre-Enlightenment methods by which Europeans attempted to describe and classify the American Indian and his society. Between 1512 and 1724 a simple determinist view of human society was replaced by a more sophisticated relativist approach. Anthony Pagden uses new methods of technical analysis, already developed in philosophy and anthropology, to examine four groups of writers who analysed Indian culture: the sixteenth-century theologian, Francisco de Vitoria, and his followers; the 'champion of the Indians' Bartolomé de Las Casas; and the Jesuit historians José de Acosta and Joseph François Lafitau. Dr Pagden explains the sources for their theories and how these conditioned their observations. He also examines for the first time the key terms in each writer's vocabulary - words such as 'barbarian' and 'civil' - and the assumptions that lay beneath them.

Multiple Comparisons demonstrates the most important methods of investigating differences between levels of an independent variable within an experimental design. The authors review the analysis of va

This study examines the history of the sugar economy and the peculiar development of plantation society over a three hundred year period in Bahia, a major sugar plantation zone and an important terminus of the Atlantic slave trade. Drawing on little-used archival sources, plantations accounts, and notarial records, Professor Schwartz has examined through both quantitative and qualitative methods the various groups that made up plantation society. While he devotes much attention to masters and slaves, he views slavery ultimately as part of a larger structure of social and economic relations. The peculiarities of sugar-making and the nature of plantation labour are used throughout the book as keys to an understanding of roles and relationships in plantation society. A comparative perspective is also employed, so that studies of slavery elsewhere in the Americas inform the analysis, while at many points direct comparisons of the Bahian case with other plantation societies are also made.

Offers a systematic analysis of Freud's theories, examines the effectiveness of the retrospective clinical methods used in psychoanalysis, and discusses free association, dreams, and personality

The essays in this volume represent a wide range of approaches to one of the most popular of all American novels. Michael Bell re-examines the crucial issue of romanticism versus realism in the book. Janet McKay discusses the linguistic subtleties of the novel, showing the social implications inherent in Twain's brilliant use of the vernacular. Lee Mitchell draws on post-structuralist theories to question Huck's own assumption that words themselves can represent the social world. Steven Mailloux combines sociopolitical perspectives and the methods of contemporary 'reader-response' analysis to identify how humour is generated in Huckleberry Finn and to enrich our understanding of the novel's topical impact.

This book addresses one of the major theoretical issues that underlies, implicitly or explicitly, some recurrent controversies in macroeconomics - namely, whether a competitive monetary economy has built-in mechanisms that are strong enough to remove excess demands and supplies on all markets, through an automatic adjustment of the price system. Jean-Michel Grandmont sheds light on this complex subject by using the analytical techniques of general equilibrium theory alongside the methods of monetary analysis. The book warns against the indiscriminate use of the rational expectations hypothesis when approaching this topic, and conversely stresses the common-sense observation that short-run learning processes are among the most important characteristics of economic agents. Grandmont argues that such processes are deserving of careful theoretical study, and the result is a clear and rigorous analysis of all the issues involved.

Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.

Directed primarily at college and university undergraduates, this book covers at basic level the essential applications of mathematics to the physical sciences. It contains all the usual topics covered in a first-year course such as vectors, matrices, differential equations, basic mathematical functions and their analysis, and power series. There is a strong emphasis on qualitative understanding (such as curve sketching) and practical methods of solution. The latter take due account of the impact of computers on the subject. The principles of mathematical expression are illustrated by copious examples taken from a wide range of topics in physics and chemistry. Each of the short chapters concludes with a summary and a large number of problems.

As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional an

This book presents a theory motivated by the spaces LP, 0 ≤ p

There has been a surge of interest in methods of analysing data that typically arise from surveys of various kinds of experiments in which the number of people, animals, places or objects occupying various categories are counted. Such observations are known variously as category counts, contingency tables, or cross-tabulated or cross-classified categorical data. In this textbook, first published in 1984, Dr Fingleton describes some techniques centred on the log-linear model from the perspective of the social, behavioural and environmental scientist. His aim is to provide a route from conceptual appreciation to the practicalities of fitting models to data, and he therefore gives some consideration to appropriate computer software. The emphasis throughout is on data analysis and interpretation. Recently developed methods are clearly explained and mathematics has been kept to a minimum.

The dynamic development of various processes is a central problem of biology and indeed of all the sciences. The mathematics describing that development is, in general, complicated, because the models that are realistic are usually nonlinear. Consequently many biologists may not notice a possible application of theory. They may be unable to decide whether a particular model captures the essence of a system, or to appreciate that analysis of a model can reveal important aspects of biological problems and may even describe in detail how a system works. The aim of this textbook is to remedy the situation by adopting a general approach to model analysis and applying it several times to problems (drawn primarily from molecular and cellular biology) of gradually increasing biological and mathematical complexity. Although material of considerable sophistication is included, little mathematical background is required - only some exposure to elementary calculus; appendixes supply the necessary

This guide to playreading for students and practitioners of both theater and literature complements, rather then contradicts or repeats, traditional methods of literary analysis of scripts.Ball devel

The division of the world into rich and poor nations, and the division within poor nations between a minority of rich people and a majority of poor people living at a minimum subsistence level, has been obvious to careful observers for a long time. This book gives an overview of the problems of underdevelopment confronting third-world countries, making use of both Marxist and neo-Keynesian methods of analysis. It makes clear the historical origins of these contemporary problems, particularly with reference to the major countries of Asia and Latin America, and discusses the ways in which inequalities, both within and between countries, are propaged and perpetuated. Other problems analysed are the typical patterns of fluctuating growth faced by third-world countries; the social structures in both rural and urban areas and their influence on the behaviour of governments and private investors in these countries; and environmental control and population planning issues faced by these countr

When this volume was first published, in 1969, plastic theory was the most modern method of structural analysis, and it made possible the direct design of steel frames in a way not available with only elastic methods. It is now recognized that this theory is also fundamental to structural design in materials such as reinforced concrete and aluminium. This is the first volume of a two-volume work by Professors Baker and Heyman that expounds and illustrates the methods of plastic design. Volume 1 gives the elements of the theory and covers the needs of most undergraduates and designers. A special feature of this work is the large number of exercises (140 in all) with answers. Volume 2 deals with advanced topics of theoretical analysis and practical design. The examples and the methods presented herein are extremely valuable to the engineer. The quality of the writing makes Professors Baker and Heyman's book a pleasure to read.

Positions of authority in any society are limited in number, and therefore rules of selection must operate in their recruitment. There must also be limitations upon the range of authority exercised. These problems are particularly acute in the case of high office, where the questions of recruitment and succession are of central importance. This 1979 volume provides a general and theoretical analysis of succession in different traditional African societies. Jack Goody's introduction spells out the main ways in which systems of succession to office differ, and assesses the problem each system solves and the dilemmas it creates. He also analyses the tensions to which succession gives rise, and relates these to specific methods of transferring office from one generation to the next, The four case studies, all based on extensive fieldwork, consider succession among the Bausto, the Baganda, the Nyamwezi and the Gonja.

Demography is the study by statistical methods of human populants involving the measurement of their size, growth and diminution, the proportions living within some areas, being born, marrying, having children or dying and the related functions of fertility, nuptially and morality. This book begins by defining a number of concepts which are useful for demographic analysis, including the significant events in life and types of statistical data which are collected, published and used. It then describes the various kinds of change which can occur and the underlying causes - social, economic and political. The central section provides an account of the history of population growth and development, and of the situation on an international and national scale. Resources available for the support of mankind and their relationship with living standards are explored. The politics of population and the prospects for the future are also described.

In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a uni

This book deals with technological innovations of the nineteenth century. In a number of self-contained but related essays it treats the salient aspects of technological change that have interested modern economists and economic historians, as well as historians of technology: economically induced invention and innovation, learning by doing in industrial operations, the diffusion of new production techniques, and the bearing of these upon the growth of a society's productivity. The studies are detailed, in the sense that they focus not upon the economy as a whole, but rather upon the experiences of specific industries, branches of manufacturing, and individual productive units such as the mid-Victorial grain farm and the New England cotton textile mill. They attempt to integrate traditional historical methods and materials with a more explicit reliance on economic theorizing and applications of statistical analysis to test hypotheses.

Curtin combines modern research and statistical methods with his broad knowledge of the field to present the first book-length quantitative analysis of the Atlantic slave trade. Its basic evide

Offers students with an understanding of fundamental models in macroeconomics, and introduces them to the methods of formal macroeconomic analysis. This book focuses on macroeconomics for the long run

Suitable for a one or two semester course, this book takes a practical approach to methods of statistical modeling and data analysis that are most often used in scientific work.

Chemical Analysis is an essential introduction to a wide range of analytical techniques and instruments. Assuming little in the way of prior knowledge, this text carefully guides the reader through th

Classic introduction to objectives and methods of schools of empiricism and linguistic analysis, especially of the logical positivism derived from the Vienna Circle. Topics: elimination of metaphysic