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Author: Manfredo P. Do Carmo
Publisher: Springer Science & Business Media
ISBN: 3642579515
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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.
Author: Manfredo P. Do Carmo
Publisher: Springer Science & Business Media
ISBN: 3642579515
Category : Mathematics
Languages : en
Pages : 124
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Book Description
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.
Author: Jon Pierre Fortney
Publisher: Springer
ISBN: 3319969927
Category : Mathematics
Languages : en
Pages : 470
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Book Description
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.
Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780817637071
Category : Education
Languages : en
Pages : 532
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Book Description
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.
Author: Ernst Kunz
Publisher: American Mathematical Soc.
ISBN: 0821850857
Category : Mathematics
Languages : en
Pages : 166
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Book Description
Suitable for students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines, this book introduces various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms.
Author: Chris J. Isham
Publisher: Allied Publishers
ISBN: 9788177643169
Category : Geometry, Differential
Languages : en
Pages : 308
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Book Description
Author: Tevian Dray
Publisher: CRC Press
ISBN: 1466510005
Category : Mathematics
Languages : en
Pages : 324
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Book Description
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.
Author: Raoul Bott
Publisher: Springer Science & Business Media
ISBN: 1475739516
Category : Mathematics
Languages : en
Pages : 319
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Book Description
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Author: John Hamal Hubbard
Publisher:
ISBN: 9780971576674
Category : Algebras, Linear
Languages : en
Pages : 284
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Book Description
Author: David Bachman
Publisher: Springer Science & Business Media
ISBN: 0817683046
Category : Mathematics
Languages : en
Pages : 167
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Book Description
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.
