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Differentiable Manifolds

A Theoretical Physics Approach (Sprache: Englisch)
Autor: Gerardo F. Torres del Castillo
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The theory of differentiable manifolds extends the application of Rn spaces calculus to sets that do not possess the structure of a normed vector space. This textbook explores the theory of differentiable manifolds while detailing various physics applications.
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The theory of differentiable manifolds extends the application of Rn spaces calculus to sets that do not possess the structure of a normed vector space. This textbook explores the theory of differentiable manifolds while detailing various physics applications.
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Produktdetails
Produktinformationen zu „Differentiable Manifolds “
The theory of differentiable manifolds extends the application of Rn spaces calculus to sets that do not possess the structure of a normed vector space. This textbook explores the theory of differentiable manifolds while detailing various physics applications.
Klappentext zu „Differentiable Manifolds “
This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. The basic objective of the theory of differentiable manifolds is to extend the application of the calculus of Rn spaces to sets that do not possess the structure of a normed vector space. The differentiability of a function from Rn to Rm means that around each interior point of its domain, the function can be approximated by a linear transformation.
Basic concepts, such as differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential forms, are briefly introduced in the first three chapters. Chapter 4 gives a concise introduction to differential geometry needed in subsequent chapters. Chapters 5 and 6 provide interesting applications to differential geometry and general relativity. Lie groups and Hamiltonian mechanics are closely examined in the last two chapters. Included throughout the book are a collection of exercises of varying degrees of difficulty.
Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.
This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.
Inhaltsverzeichnis zu „Differentiable Manifolds “
- Preface

1. Manifolds

2. Lie Derivatives

3. Differential Forms

4. Integral Manifolds

5. Connections

6. Riemannian Manifolds

7. Lie Groups

8. Hamiltonian Classical Mechanics

- References

- Index
Autoren-Porträt von Gerardo F. Torres del Castillo
Gerardo Torres del Castillo has published two books previously, both in Birkhauser's Progress in Mathematical Physics series: "3-D Spinors, Spin-Weighted Functions and their Applications," and "Spinors in Four-Dimensional Spaces."
Bibliographische Angaben

  • Autor: Gerardo F. Torres del Castillo
  • 2011, 2012., VIII, 275 Seiten, 21 Schwarz-Weiß-Abbildungen, Maße: 16,7 x 24,8 cm, Gebunden, Englisch
  • Verlag: Springer
  • ISBN-10: 0817682708
  • ISBN-13: 9780817682705
  • Erscheinungsdatum: 19.10.2011

Sprache:
Englisch
Rezension zu „Differentiable Manifolds “
From the reviews:"The purpose of this book is to present some fundamental notions of differentiable geometry of manifolds and some applications in physics. The topics developed in the book are of interest of advanced undergraduate and graduate students in mathematics and physics. The author succeeded to connect differential geometry with mechanics. The computations are clearly explained and the theory is supported by several examples. Throughout the book there is a large collection of exercises ... which help the reader to fix the obtained knowledge." (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1237, 2012)
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