Synthetic Differential Topology
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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.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-29
Synthetic Differential Topology written by Marta Bunge 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 2018-03-29 with Mathematics categories.
Represents the state of the art in the new field of synthetic differential topology.
Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds 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 2010 with Mathematics categories.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher:
Release Date : 2018
Synthetic Differential Topology written by Marta Bunge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
Represents the state of the art in the new field of synthetic differential topology.
Topological Derivatives In Shape Optimization
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Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2012-12-14
Topological Derivatives In Shape Optimization written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.
A Comprehensive Course In Analysis
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Author : Barry Simon
language : en
Publisher:
Release Date : 2015
A Comprehensive Course In Analysis written by Barry Simon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematical analysis categories.
A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis
Algebraic Topology A Structural Introduction
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2021-12-24
Algebraic Topology A Structural Introduction written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-24 with Mathematics categories.
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.
New Foundations For Physical Geometry
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Author : Tim Maudlin
language : en
Publisher:
Release Date : 2014-02
New Foundations For Physical Geometry written by Tim Maudlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02 with Mathematics categories.
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
From Calculus To Cohomology
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Author : Ib H. Madsen
language : en
Publisher: Cambridge University Press
Release Date : 1997-03-13
From Calculus To Cohomology written by Ib H. Madsen 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 1997-03-13 with Mathematics categories.
An introductory textbook on cohomology and curvature with emphasis on applications.
Equivariant Topology And Derived Algebra
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Author : Scott Balchin
language : en
Publisher: Cambridge University Press
Release Date : 2022
Equivariant Topology And Derived Algebra written by Scott Balchin 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 2022 with Mathematics categories.
A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.