Foundations Of Differential Calculus
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Foundations Of Differential Calculus
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Author : Euler
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-23
Foundations Of Differential Calculus written by Euler 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 2000-05-23 with Mathematics categories.
What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.
Foundations Of Differential Calculus
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Author : Euler
language : en
Publisher: Springer
Release Date : 2013-10-03
Foundations Of Differential Calculus written by Euler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.
The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.
Foundations Of Differential Geodesy
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Author : Joseph Zund
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Differential Geodesy written by Joseph Zund 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 2012-12-06 with Science categories.
Differential geodesy is concerned with the geometry of the gravity field of the Earth, which is of fundamental importance to both theoretical geodesy and geophysics. This monograph presents a unified treatment of the foundations of differential geodesy as proposed originally by Antonio Marussi and Martin Hotine in their work. The principal features of the Marussi-Hotine approach to theoretical aspects are given in the first five chapters (based on leg calculus), while the last five chapters are devoted to the fundamental ideas of the Marussi and Hotine theory. The text includes practical problems and is intended for use by research geodesists, graduate students in geodesy, and theoretical geophysicists.
Foundations Of Differential Geometry Volume 1
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Author : Shoshichi Kobayashi
language : en
Publisher: John Wiley & Sons
Release Date : 1996-02-22
Foundations Of Differential Geometry Volume 1 written by Shoshichi Kobayashi 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 1996-02-22 with Mathematics categories.
This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
Fundamentals Of Differential Geometry
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamentals Of Differential Geometry written by Serge Lang 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 2012-12-06 with Mathematics categories.
The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ). One may also use differentiable structures on topological manifolds to deter mine the topological structure of the manifold (for example, it la Smale [Sm 67]). In differential geometry, one puts an additional structure on the differentiable manifold (a vector field, a spray, a 2-form, a Riemannian metric, ad lib. ) and studies properties connected especially with these objects. Formally, one may say that one studies properties invariant under the group of differentiable automorphisms which preserve the additional structure. In differential equations, one studies vector fields and their in tegral curves, singular points, stable and unstable manifolds, etc. A certain number of concepts are essential for all three, and are so basic and elementary that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginnings.
Foundations Of Differentiable Manifolds And Lie Groups
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Author : Frank W. Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Foundations Of Differentiable Manifolds And Lie Groups written by Frank W. Warner 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 2013-11-11 with Mathematics categories.
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this beginning graduate-level text extremely useful.
Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Foundations Of Optimization
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Author : Osman Güler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-03
Foundations Of Optimization written by Osman Güler 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 2010-08-03 with Business & Economics categories.
This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.
Foundations Of Infinitesimal Calculus
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Author : H. Jerome Keisler
language : en
Publisher: Prindle Weber & Schmidt
Release Date : 1976-01-01
Foundations Of Infinitesimal Calculus written by H. Jerome Keisler and has been published by Prindle Weber & Schmidt this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-01-01 with Mathematics categories.
Handbook Of Analysis And Its Foundations
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Author : Eric Schechter
language : en
Publisher: Academic Press
Release Date : 1996-10-24
Handbook Of Analysis And Its Foundations written by Eric Schechter and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-24 with Mathematics categories.
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/