Curvature of Space and Time, with an Introduction to Geometric Analysis

Curvature of Space and Time, with an Introduction to Geometric Analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 259
Release :
ISBN-10 : 9781470456283
ISBN-13 : 1470456281
Rating : 4/5 (281 Downloads)

Book Synopsis Curvature of Space and Time, with an Introduction to Geometric Analysis by : Iva Stavrov

Download or read book Curvature of Space and Time, with an Introduction to Geometric Analysis written by Iva Stavrov and published by American Mathematical Soc.. This book was released on 2020-11-12 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations. After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-energy tensor, Schwarzschild space-time, ADM mass and geodesic incompleteness. The concluding chapters of the book introduce the reader to geometric analysis: original results of the author and her undergraduate student collaborators illustrate how methods of analysis and differential equations are used in addressing questions from geometry and relativity. The book is mostly self-contained and the reader is only expected to have a solid foundation in multivariable and vector calculus and linear algebra. The material in this book was first developed for the 2013 summer program in geometric analysis at the Park City Math Institute, and was recently modified and expanded to reflect the author's experience of teaching mathematical general relativity to advanced undergraduates at Lewis & Clark College.


Curvature of Space and Time, with an Introduction to Geometric Analysis Related Books

Curvature of Space and Time, with an Introduction to Geometric Analysis
Language: en
Pages: 259
Authors: Iva Stavrov
Categories: Education
Type: BOOK - Published: 2020-11-12 - Publisher: American Mathematical Soc.

GET EBOOK

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the conc
Curvature of Space and Time, with an Introduction to Geometric Analysis
Language: en
Pages: 259
Authors: Iva Stavrov
Categories: Education
Type: BOOK - Published: 2020-11-12 - Publisher: American Mathematical Soc.

GET EBOOK

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the conc
Gravitational Curvature
Language: en
Pages: 194
Authors: Theodore Frankel
Categories: Science
Type: BOOK - Published: 2013-04-10 - Publisher: Courier Corporation

GET EBOOK

This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvatu
Spacetime and Geometry
Language: en
Pages: 529
Authors: Sean M. Carroll
Categories: Science
Type: BOOK - Published: 2019-08-08 - Publisher: Cambridge University Press

GET EBOOK

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
The Geometry of Spacetime
Language: en
Pages: 474
Authors: James J. Callahan
Categories: Science
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

GET EBOOK

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski,