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Theories of Generalised Functions
Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins. - Explains and compares the various standard types of generalised functions that have been developed during the 20th Century - Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions
The Strength of Nonstandard Analysis
This book reflects the progress made in the forty years since the appearance of Abraham Robinson’s revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
Infinitesimal Methods of Mathematical Analysis
This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. - Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers - Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis
Lectures on the Hyperreals
An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
The Elements of Materia Medica and Therapeutics
This encyclopaedic work, a pioneering text in pharmacology, is reissued here in its revised and expanded fourth edition (1854-7).
Geometry, Analysis & Applications, Procs Of The Intl Conf
Geometrical concepts play a significant role in the analysis of physical systems. Apart from the intrinsic interest, the knowledge of differentiable manifolds has become useful — even mandatory — in an ever-increasing number of areas of mathematics and its applications. Many results/concepts in analysis find their most natural (generalized) setting in manifold theory. An interrelation of geometry and analysis can be found in this volume.The book presents original research, besides a few survey articles by eminent experts from all over the world on current trends of research in differential and algebraic geometry, classical and modern analysis including the theory of distributions (linear and nonlinear), partial differential equations and wavelets.
Histórias da Luz e das Cores, volume 2
Perante o extraordinário esforço que os cientistas de oitocentos realizaram no estudo da ciência da luz e das cores, pareceu adequado consagrar este volume exclusivamente ao séc. XIX. Foi neste século que o caráter sobrenatural dos fenómenos luminosos sucumbiu totalmente perante a razão; que a magia ótica se transformou em conhecimento tangível; que se estabeleceram as bases sólidas da ótica clássica. Este volume das Histórias da Luz e das Cores ocupa-se destes homens, da ciência e tecnologia óticas que criaram, e das mudanças sociais que estas atividades provocaram. A forte componente cultural destes cientistas coloca-os num lugar privilegiado entre os filósofos escolásticos ou naturais ─ que sabiam quase nada de quase tudo ─ e os cientistas contemporâneos ─ que sabem quase tudo de quase nada. A leitura deste volume revela ainda que o Homem oitocentista continuou a revelar as mais profundas inclinações humanas, através de crenças infantis, especulações fantasiosas e antropomorfismos absurdos.
