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Author: Yu Aminov
Publisher:
ISBN: 9780415706865
Category : Geometry
Languages : en
Pages : 0
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Book Description
This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in mechanics. Topics covered include Pfaffian forms, systems in n-dimensional space, and foliations and their Godbillion-Vey invariant. There is much interest in the study of geometrical objects in n-dimensional Euclidean space and this volume provides a useful and comprehensive presentation.
Author: Yu Aminov
Publisher:
ISBN: 9780415706865
Category : Geometry
Languages : en
Pages : 0
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Book Description
This volume, first published in 2000, presents a classical approach to the foundations and development of the geometry of vector fields, describing vector fields in three-dimensional Euclidean space, triply-orthogonal systems and applications in mechanics. Topics covered include Pfaffian forms, systems in n-dimensional space, and foliations and their Godbillion-Vey invariant. There is much interest in the study of geometrical objects in n-dimensional Euclidean space and this volume provides a useful and comprehensive presentation.
Author: Stefano Biagi
Publisher: World Scientific
ISBN: 9813276630
Category : Mathematics
Languages : en
Pages : 450
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Book Description
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Author: Andreas Görlitz
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Kathleen M. Urwin
Publisher: Elsevier
ISBN: 1483195333
Category : Mathematics
Languages : en
Pages : 279
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Book Description
THIS book falls naturally into two parts. In Chapters 1-5 the basic ideas and techniques of partial differentiation, and of line, multiple and surface integrals are discussed. Chapters 6 and 7 give the elements of vector field theory, taking the integral definitions of the divergence and curl of a vector field as their starting points; the last chapter surveys very briefly some of the immediate applications of vector field theory to five branches of applied mathematics. Throughout I have given numerous worked examples. In these I have paid particular attention to those points which in my own experience I have found to give most difficulty to students. In the text I have denoted spherical polar coordinates by (/-, 0, ?)9 and cylindrical polar coordinates by (p, ?, ?), so that ? measures the same angle in both systems. Since there is no one standard notation for these systems, the reader will meet different notations in the course of his reading, and in quoting examination questions in the exercises I have kept to the notation of the originals. The Exercises at the end of each section are intended to give practice in the basic techniques just discussed. The Miscellaneous Exercises are more varied, and contain many examination questions.
Author: Richmond Beckett MacQuistan
Publisher:
ISBN: 9780471587200
Category :
Languages : en
Pages : 0
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Book Description
Author: J. A. Shercliff
Publisher: Cambridge University Press
ISBN: 9780521213066
Category : Mathematics
Languages : en
Pages : 350
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Book Description
A field is a distribution in space of physical quantities of obvious significance, such as pressure, velocity, or electromagnetic influence. This 1977 book was written for any reader who would not be content with a purely mathematical approach to the handling of fields. In letting the mathematical concepts invent themselves out of the need to describe the physical world quantitatively, Professor Shercliff shows how the same mathematical ideas may be used in a wide range of apparently different contexts including electromagnetism, fluid dynamics, nuclear reactor criticality, plasma oscillations and rotational flow. Mathematical methods are explored only far enough to give the interested reader a glimpse of activities that lie beyond, yet the unifying approach to increasingly powerful, generalised ideas at a level not reached in many books on vector analysis at the time. Special features of the book are a wealth of examples of physical interest, and a thorough appendix.
Author: Stefano Biagi
Publisher:
ISBN: 9789813276628
Category : MATHEMATICS
Languages : en
Pages : 423
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Book Description
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Author: Anthony O'Hear
Publisher: Routledge
ISBN: 1317917367
Category : Philosophy
Languages : en
Pages : 192
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Book Description
First published in 1988, the aim of this book can be stated in Nietzsche’s words: ‘To look at science from the perspective of the artist, but at art from that of life’. The title contests the notions that science alone can provide us with the most objective truth about the world, and that artistic endeavour can produce nothing more valuable than entertainment. O’Hear argues that art and the study of art are not indispensable aspects of human life, and that this is equally as important as the investigation of the natural world.
Author: D. E. Bourne
Publisher: Academic Press
ISBN: 1483260704
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.
Author: Peter Zvengrowski
Publisher:
ISBN:
Category : Vector analysis
Languages : en
Pages : 182
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Book Description
