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Manifolds, Vector Fields, and Differential Forms

2023-04-25 Mathematics
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Release : 2023-04-25
Genre : Mathematics
Kind : eBook
Book Rating : 090/5 ( reviews)

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Book Synopsis Manifolds, Vector Fields, and Differential Forms by : Gal Gross

Download or read book Manifolds, Vector Fields, and Differential Forms written by Gal Gross. This book was released on 2023-04-25. Available in PDF, EPUB and Kindle. Book excerpt: This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.

Differential Forms and Applications

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 515/5 ( reviews)

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Book Synopsis Differential Forms and Applications by : Manfredo P. Do Carmo

Download or read book Differential Forms and Applications written by Manfredo P. Do Carmo. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Vector Fields

2011-10-26 Computers
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Release : 2011-10-26
Genre : Computers
Kind : eBook
Book Rating : 269/5 ( reviews)

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Book Synopsis Harmonic Vector Fields by : Sorin Dragomir

Download or read book Harmonic Vector Fields written by Sorin Dragomir. This book was released on 2011-10-26. Available in PDF, EPUB and Kindle. Book excerpt: An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods

Differential Forms and Connections

1994-09-22 Mathematics
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Release : 1994-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 686/5 ( reviews)

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Book Synopsis Differential Forms and Connections by : R. W. R. Darling

Download or read book Differential Forms and Connections written by R. W. R. Darling. This book was released on 1994-09-22. Available in PDF, EPUB and Kindle. Book excerpt: This 1994 book introduces the tools of modern differential geometry, exterior calculus, manifolds, vector bundles and connections, to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. The book covers both classical surface theory and the modern theory of connections and curvature, and includes a chapter on applications to theoretical physics. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. The powerful and concise calculus of differential forms is used throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. There are nearly 200 exercises, making the book ideal for both classroom use and self-study.

Differential Forms and Connections

1994-09-22 Mathematics
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Release : 1994-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 008/5 ( reviews)

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Book Synopsis Differential Forms and Connections by : R. W. R. Darling

Download or read book Differential Forms and Connections written by R. W. R. Darling. This book was released on 1994-09-22. Available in PDF, EPUB and Kindle. Book excerpt: Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.

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