A Geometric Approach To Differential Forms
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A Geometric Approach To Differential Forms
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Author : David Bachman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
A Geometric Approach To Differential Forms written by David Bachman 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 2012-02-02 with Mathematics categories.
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
A Geometric Approach To Differential Forms
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Author : David Bachman
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-03
A Geometric Approach To Differential Forms written by David Bachman 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 2007-07-03 with Mathematics categories.
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
A Geometric Approach To Differential Forms
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Author : David Bachman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-30
A Geometric Approach To Differential Forms written by David Bachman 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 2006-08-30 with Mathematics categories.
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
Geometric Approaches To Differential Equations
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Author : Peter J. Vassiliou
language : en
Publisher: Cambridge University Press
Release Date : 2000-03-13
Geometric Approaches To Differential Equations written by Peter J. Vassiliou 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 2000-03-13 with Mathematics categories.
A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.
A Visual Introduction To Differential Forms And Calculus On Manifolds
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Author : Jon Pierre Fortney
language : en
Publisher: Springer
Release Date : 2018-11-03
A Visual Introduction To Differential Forms And Calculus On Manifolds written by Jon Pierre Fortney and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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Author : John Snygg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-08
A New Approach To Differential Geometry Using Clifford S Geometric Algebra written by John Snygg 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 2011-12-08 with Mathematics categories.
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
Differential Forms And The Geometry Of General Relativity
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Author : Tevian Dray
language : en
Publisher: CRC Press
Release Date : 2014-10-20
Differential Forms And The Geometry Of General Relativity written by Tevian Dray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-20 with Mathematics categories.
Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
Differential Forms And Applications
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Author : Manfredo P. Do Carmo
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-20
Differential Forms And Applications written by Manfredo P. Do Carmo 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 1998-05-20 with Mathematics categories.
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Visual Differential Geometry And Forms
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Author : Tristan Needham
language : en
Publisher: Princeton University Press
Release Date : 2021-07-13
Visual Differential Geometry And Forms written by Tristan Needham and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-13 with Mathematics categories.
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Advanced Calculus
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Author : Harold M. Edwards
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advanced Calculus written by Harold M. Edwards 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 2013-12-01 with Mathematics categories.
This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.