Linear Spaces And Differentiation Theory
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Linear Spaces And Differentiation Theory
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Author : Alfred Frölicher
language : en
Publisher:
Release Date : 1988-08-18
Linear Spaces And Differentiation Theory written by Alfred Frölicher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08-18 with Mathematics categories.
This book presents a new basis for differential calculus. Classical differentiation in linear spaces of arbitrary dimension uses Banach spaces--but most function spaces are not Banach spaces. Any attempts to develop a theory of differentiation covering non-normable linear spaces have always involved arbitrary conditions. This book bases the theory of differentiability of linear spaces on the fundamental idea of reducing the differentiability of general maps to that of functions on the real numbers. And the property ``continuously differentiable'' is replaced by that of ``Lipschitz differentiable.'' The result is a more natural theory, of conceptual simplicity that leads to the the same categories of linear spaces, but in a more general setting.
Topological Vector Spaces And Their Applications
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Author : V.I. Bogachev
language : en
Publisher: Springer
Release Date : 2017-05-16
Topological Vector Spaces And Their Applications written by V.I. Bogachev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Differential Geometrical Methods In Theoretical Physics
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Author : K. Bleuler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Differential Geometrical Methods In Theoretical Physics written by K. Bleuler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987
Handbook Of The History Of General Topology
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Author : C.E. Aull
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Handbook Of The History Of General Topology written by C.E. Aull and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
Introduction To Topology And Geometry
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Author : Saul Stahl
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-21
Introduction To Topology And Geometry written by Saul Stahl and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-21 with Mathematics categories.
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
Optimization By Vector Space Methods
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Author : David G. Luenberger
language : en
Publisher: John Wiley & Sons
Release Date : 1997-01-23
Optimization By Vector Space Methods written by David G. Luenberger and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-23 with Technology & Engineering categories.
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
Solutions Manual To Accompany Beginning Partial Differential Equations
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Author : Peter V. O'Neil
language : en
Publisher: John Wiley & Sons
Release Date : 2014-10-13
Solutions Manual To Accompany Beginning Partial Differential Equations written by Peter V. O'Neil and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy.
Extremes And Recurrence In Dynamical Systems
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Author : Valerio Lucarini
language : en
Publisher: John Wiley & Sons
Release Date : 2016-04-04
Extremes And Recurrence In Dynamical Systems written by Valerio Lucarini and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-04 with Mathematics categories.
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Synthetic Differential Geometry
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Synthetic Differential Geometry written by Anders Kock and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-22 with Mathematics categories.
This book, first published in 2006, details how limit processes can be represented algebraically.
Beyond Topology
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Author : Frdric Mynard
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-05-15
Beyond Topology written by Frdric Mynard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-15 with Mathematics categories.
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.