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Author: Curtis Tuckey
Publisher: CRC Press
Published: 1993-11-22
Total Pages: 116
ISBN-13: 9780582231801
DOWNLOAD EBOOKThis monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.
Author: A.G. Kusraev
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 447
ISBN-13: 9401111367
DOWNLOAD EBOOKNonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last twenty-five years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work.
Author: Nigel J. Cutland
Publisher: Cambridge University Press
Published: 2017-03-30
Total Pages: 260
ISBN-13: 1108621295
DOWNLOAD EBOOKSince their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12–16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education.
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
Published: 2004-06-30
Total Pages: 692
ISBN-13: 9783540579618
DOWNLOAD EBOOKThis book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins of the theory. Both individually and collectively these volumes have already become standard references.
Author: Ricardo Almeida
Publisher: World Scientific Publishing Company
Published: 2015-03-19
Total Pages: 279
ISBN-13: 1783266422
DOWNLOAD EBOOKThis book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.
Author: Nigel J Cutland
Publisher: CRC Press
Published: 2020-01-30
Total Pages: 278
ISBN-13: 1000724646
DOWNLOAD EBOOKThis book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.
Author: I. M. Gelfand
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 260
ISBN-13: 0486135012
DOWNLOAD EBOOKFresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Author: Mariano Giaquinta
Publisher: Springer Science & Business Media
Published: 2004-06-23
Total Pages: 512
ISBN-13: 9783540506256
DOWNLOAD EBOOKThis two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.
Author: Achintya Kumar Pramanick
Publisher: Springer
Published: 2014-08-23
Total Pages: 171
ISBN-13: 3642544711
DOWNLOAD EBOOKIn this monograph Prof. Pramanick explicates the law of motive force, a fundamental law of nature that can be observed and appreciated as an addition to the existing laws of thermodynamics. This unmistakable and remarkable tendency of nature is equally applicable to all other branches of studies. He first conceptualized the law of motive force in 1989, when he was an undergraduate student. Here he reports various applications of the law in the area of thermodynamics, heat transfer, fluid mechanics and solid mechanics, and shows how it is possible to solve analytically century-old unsolved problems through its application. This book offers a comprehensive account of the law and its relation to other laws and principles, such as the generalized conservation principle, variational formulation, Fermat’s principle, Bejan’s constructal law, entropy generation minimization, Bejan’s method of intersecting asymptotes and equipartition principle. Furthermore, the author addresses some interrelated fundamental problems of contemporary interest, especially to thermodynamicists, by combining analytical methods, physical reasoning and the proposed law of motive force. This foundational work is a valuable reading for both students and researchers in exact as well as non-exact sciences and, at the same time, a pleasant learning experience for the novice.
Author: Edward Barbeau
Publisher: MAA
Published: 2000-06-15
Total Pages: 188
ISBN-13: 9780883855294
DOWNLOAD EBOOKThrough hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition can often be misleading. This book collects and analyses a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves.
