Fundamentals Of Differential Geometry
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Fundamentals Of Differential Geometry
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-09-21
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 2001-09-21 with Mathematics categories.
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Introduction To Differentiable Manifolds
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Introduction To Differentiable Manifolds 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 2006-03-30 with Mathematics categories.
Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics
Differential Geometric Foundations Of Non Equilibrium Thermodynamics
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Author : Marcus Hildebrandt
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-02-19
Differential Geometric Foundations Of Non Equilibrium Thermodynamics written by Marcus Hildebrandt and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-19 with Science categories.
While all field theories are nowadays available in a modern, differential geometric, coordinate free formulation on manifolds this has been so far only rudimentary accomplished in general non-equilibrium thermodynamics. In this work it is shown how a fitting geometric structure can be derived for arbitrary compact (discrete Schottky Systems) thermodynamic systems, such as stars and black holes, using only a few thermodynamic principles. This leads to deep geometric insights. Some central results are the following: while in the theory of relativity the energy-momentum tensor determines the geometry of the space, in non-equilibrium thermodynamics, the 1-form of the entropy production rate is responsible for the emergence of a well-known geometric structure: the contact geometry. Relaxation processes remain in the fibers in which they start and end on an attractor manifold, that can be identified with the classical equilibrium subspace of thermostatics. One then proves, that outside this attractor manifold there are no reversible process directions. As a consequence of this, the 2nd Law of thermodynamics lives mainly on the fibers of the state manifold, the so called vertical geometric structure, while the 1st Law of thermodynamics is formulated on the horizontal components of the state manifold. The internal energy provides a physical gauge for each fiber. The 1st and 2nd Law of thermodynamics are coupled via the representation of the entropy flux 1-form that can be represented in the dual basis of exchange 1-forms such as the heat 1-form. This fact can be used to provide a "coordinate free" ("invariant") definition of non-equilibrium temperature. Finally, it is shown that probably the most general geometric structure to model non-equilibrium thermodynamics of compact (discrete Schottky systems) systems is given by a composite fibred cocontact phase manifold that includes time as an explicit dimension.
Foundations Of Differential Geometry Volume 2
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Author : Shoshichi Kobayashi
language : en
Publisher: John Wiley & Sons
Release Date : 1996-02-22
Foundations Of Differential Geometry Volume 2 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.
Visualization Handbook
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Author : Charles D. Hansen
language : en
Publisher: Elsevier
Release Date : 2011-08-30
Visualization Handbook written by Charles D. Hansen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Technology & Engineering categories.
The Visualization Handbook provides an overview of the field of visualization by presenting the basic concepts, providing a snapshot of current visualization software systems, and examining research topics that are advancing the field. This text is intended for a broad audience, including not only the visualization expert seeking advanced methods to solve a particular problem, but also the novice looking for general background information on visualization topics. The largest collection of state-of-the-art visualization research yet gathered in a single volume, this book includes articles by a "who's who of international scientific visualization researchers covering every aspect of the discipline, including:·Virtual environments for visualization·Basic visualization algorithms·Large-scale data visualization·Scalar data isosurface methods·Visualization software and frameworks·Scalar data volume rendering·Perceptual issues in visualization·Various application topics, including information visualization.* Edited by two of the best known people in the world on the subject; chapter authors are authoritative experts in their own fields;* Covers a wide range of topics, in 47 chapters, representing the state-of-the-art of scientific visualization.
Handbook Of Mathematics For Engineers And Scientists
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2006-11-27
Handbook Of Mathematics For Engineers And Scientists written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-27 with Mathematics categories.
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
Fundamentals Of Matrix Computations
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Author : David S. Watkins
language : en
Publisher: John Wiley & Sons
Release Date : 2004-08-13
Fundamentals Of Matrix Computations written by David S. Watkins 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 2004-08-13 with Mathematics categories.
A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights. This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: * Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations * Early introduction of the singular value decomposition * A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems * An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.
Foundations Of Differential Geometry
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Author : Shoshichi Kobayashi
language : en
Publisher:
Release Date : 1996
Foundations Of Differential Geometry written by Shoshichi Kobayashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Geometry, Differential categories.
Quantum Field Theory I Basics In Mathematics And Physics
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-18
Quantum Field Theory I Basics In Mathematics And Physics written by Eberhard Zeidler 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 2007-04-18 with Science categories.
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
Introduction To Differential Geometry
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Author : Joel W. Robbin
language : en
Publisher: Springer Nature
Release Date : 2022-01-12
Introduction To Differential Geometry written by Joel W. Robbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-12 with Mathematics categories.
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.