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Author: Ernst Kunz
Publisher: American Mathematical Soc.
Published: 1988
Total Pages: 166
ISBN-13: 0821850857
DOWNLOAD EBOOKSuitable 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: Manfredo P. Do Carmo
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 124
ISBN-13: 3642579515
DOWNLOAD EBOOKAn 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: Chris J. Isham
Publisher: Allied Publishers
Published: 2002
Total Pages: 308
ISBN-13: 9788177643169
DOWNLOAD EBOOKAuthor: Gerhard Paul Hochschild
Publisher:
Published: 1961
Total Pages: 102
ISBN-13:
DOWNLOAD EBOOKA mathematical discussion of the algebras of differential forms is treated as a special combination of linear algebra and homological alegbra. There is specific identification of this particular exterior algebra as applied to canical graded algebra based on the Tor functor and obtained by the cohomology of differential forms from the ext functor to a universal algebra i. e. Lie algebra. Attention is directed chiefly to a regular affine algebra, K-algebra, which is Noetherian with a finite Krull dimension, i. e. the largest non-negative integer.
Author: Raoul Bott
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 319
ISBN-13: 1475739516
DOWNLOAD EBOOKDeveloped 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: Harold M. Edwards
Publisher: Springer Science & Business Media
Published: 1994-01-05
Total Pages: 532
ISBN-13: 9780817637071
DOWNLOAD EBOOKThis 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: Jon Pierre Fortney
Publisher: Springer
Published: 2018-11-03
Total Pages: 470
ISBN-13: 3319969927
DOWNLOAD EBOOKThis 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: Tevian Dray
Publisher: CRC Press
Published: 2014-10-20
Total Pages: 324
ISBN-13: 1466510005
DOWNLOAD EBOOKDifferential 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: David Lovelock
Publisher: Courier Corporation
Published: 2012-04-20
Total Pages: 402
ISBN-13: 048613198X
DOWNLOAD EBOOKIncisive, 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: Vincenzo Ancona
Publisher: CRC Press
Published: 2005-08-24
Total Pages: 312
ISBN-13: 1420026526
DOWNLOAD EBOOKDifferential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of hig
