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Author : Jean Dieudonne
Publisher : Academic Press
Page : 407 pages
File Size : 49,8 Mb
Release : 1960-08-28
Category : Science
ISBN : 9780080873183
Treatise on Analysis
Author : J. Dieudonne
Publisher : Hesperides Press
Page : 412 pages
File Size : 52,8 Mb
Release : 2008-11
Category : Mathematics
ISBN : 9781443724265
FOUNDATIONS OFMODERN ANALYSISEnlarged and Corrected PrintingJ. DIEUDONNEThis book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentiallywithout changes, of my Foundations of Modern Analysis, published in1960. Many readers, colleagues, and friends have urged me to write a sequelto that book, and in the end I became convinced that there was a place fora survey of modern analysis, somewhere between the minimum tool kitof an elementary nature which I had intended to write, and specialistmonographs leading to the frontiers of research. My experience of teachinghas also persuaded me that the mathematical apprentice, after taking the firststep of Foundations, needs further guidance and a kind of general birdseyeview of his subject before he is launched onto the ocean of mathematicalliterature or set on the narrow path of his own topic of research.Thus I have finally been led to attempt to write an equivalent, for themathematicians of 1970, of what the Cours dAnalyse of Jordan, Picard, and Goursat were for mathematical students between 1880 and 1920.It is manifestly out of the question to attempt encyclopedic coverage, andcertainly superfluous to rewrite the works of N. Bourbaki. I have thereforebeen obliged to cut ruthlessly in order to keep within limits comparable tothose of the classical treatises. I have opted for breadth rather than depth, inthe opinion that it is better to show the reader rudiments of many branchesof modern analysis rather than to provide him with a complete and detailedexposition of a small number of topics.Experience seems to show that the student usually finds a new theorydifficult tograsp at a first reading. He needs to return to it several times beforehe becomes really familiar with it and can distinguish for himself whichare the essential ideas and which results are of minor importance, and onlythen will he be able to apply it intelligently. The chapters of this treatise arevi PREFACE TO THE ENLARGED AND CORRECTED PRINTINGtherefore samples rather than complete theories: indeed, I have systematically tried not to be exhaustive. The works quoted in the bibliography willalways enable the reader to go deeper into any particular theory.However, I have refused to distort the main ideas of analysis by presentingthem in too specialized a form, and thereby obscuring their power andgenerality. It gives a false impression, for example, if differential geometryis restricted to two or three dimensions, or if integration is restricted to Lebesgue measure, on the pretext of making these subjects more accessible orintuitive.On the other hand I do not believe that the essential content of the ideasinvolved is lost, in a first study, by restricting attention to separable metrizabletopological spaces. The mathematicians of my own generation were certainlyright to banish, hypotheses of countability wherever they were not needed: thiswas the only way to get a clear understanding.
Author : E. Bishop,Douglas Bridges
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642616679
This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.
Author : Jean Alexandre Dieudonné
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 1960
Category : Mathematical analysis
ISBN : OCLC:6549202
Author : Mei-Mei Berssenbrugge
Publisher : New Directions Publishing
Page : 152 pages
File Size : 41,8 Mb
Release : 2020-02-25
Category : Poetry
ISBN : 9780811229395
An ethereal new collection that is “visceral with intellection” (David Lau) Winner of the Bollingen Prize Finalist for the National Book Award Finalist for the Pulitzer Prize for Poetry Finalist for the PEN Open Book Award Finalist for the Kingsley Tufts Prize A Treatise on Stars extends Mei-mei Berssenbrugge’s intensely phenomenological poetics to the fiery bodies in a “field of heaven…outside spacetime.” Long, lyrical lines map a geography of interconnected, interdimensional intelligence that exists in all places and sentient beings. These are poems of deep listening and patient waiting, open to the cosmic loom, the channeling of daily experience and conversation, gestalt and angels, dolphins and a star-visitor beneath a tree. Family, too, becomes a type of constellation, a thought “a form of organized light.” All of our sense are activated by Berssenbrugge’s radiant lines, giving us a poetry of keen perception grounded in the physical world, where “days fill with splendor, and earth offers its pristine beauty to an expanding present.”
Author : Colin Maclaurin
Publisher : Unknown
Page : 482 pages
File Size : 42,8 Mb
Release : 1742
Category : Calculus
ISBN : GENT:900000066734
Author : J. Dieudonné
Publisher : Elsevier
Page : 374 pages
File Size : 49,5 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483266831
Treatise on Analysis, Volume 10–VIII provides information pertinent to the study of the most common boundary problems for partial differential equations. This book presents the study of Cauchy's problem in its most elementary form. Comprised of one chapter, this volume begins with an overview of Hilbert-von Neumann spectral theory and explores all possible boundary conditions related to spectral theory. This text then examines the link of Cauchy's problem with the behavior of the equation's characteristics. This book discusses as well the case of linear elliptic operators. The reader is also introduced to Sobolev spaces and some of their generalizations that provide an essential tool in the study of these elliptic problems, and their manipulation requires delicate upper bounds to obtain the best possible results. This book is a valuable resource for mathematicians.
Author : Augustus Edward Hough Love
Publisher : Courier Corporation
Page : 674 pages
File Size : 48,9 Mb
Release : 1944-01-01
Category : Technology & Engineering
ISBN : 9780486601748
The most complete single-volume treatment of classical elasticity, this text features extensive editorial apparatus, including a historical introduction. Topics include stress, strain, bending, torsion, gravitational effects, and much more. 1927 edition.
Author : Jean Alexandre Dieudonné
Publisher : Unknown
Page : 128 pages
File Size : 55,8 Mb
Release : 1993
Category : Electronic
ISBN : 0122155084
Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 46,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642593154
This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
Author : George Boole
Publisher : Unknown
Page : 534 pages
File Size : 52,8 Mb
Release : 1859
Category : Electronic
ISBN : RMS:RMS45DOP000000589$$$T
Author : Erwin Kreyszig
Publisher : John Wiley & Sons
Page : 706 pages
File Size : 49,7 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 9780471504597
KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry
Author : G. N. Watson
Publisher : Cambridge University Press
Page : 816 pages
File Size : 53,8 Mb
Release : 1995-08-25
Category : Mathematics
ISBN : 0521483913
This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.
Author : H. S. Bear
Publisher : Academic Press
Page : 184 pages
File Size : 49,8 Mb
Release : 2002
Category : Mathematics
ISBN : 0120839717
The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.
Author : G. Berkeley
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789401125925
Berkeley's philosophy has been much studied and discussed over the years, and a growing number of scholars have come to the realization that scientific and mathematical writings are an essential part of his philosophical enterprise. The aim of this volume is to present Berkeley's two most important scientific texts in a form which meets contemporary standards of scholarship while rendering them accessible to the modern reader. Although editions of both are contained in the fourth volume of the Works, these lack adequate introductions and do not provide com plete and corrected texts. The present edition contains a complete and critically established text of both De Motu and The Analyst, in addi tion to a new translation of De Motu. The introductions and notes are designed to provide the background necessary for a full understanding of Berkeley's account of science and mathematics. Although these two texts are very different, they are united by a shared a concern with the work of Newton and Leibniz. Berkeley's De Motu deals extensively with Newton's Principia and Leibniz's Specimen Dynamicum, while The Analyst critiques both Leibnizian and Newto nian mathematics. Berkeley is commonly thought of as a successor to Locke or Malebranche, but as these works show he is also a successor to Newton and Leibniz.