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Curvature of Space and Time, with an Introduction to Geometric Analysis (Paperback)
Loot Price: R1,891
Discovery Miles 18 910
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Curvature of Space and Time, with an Introduction to Geometric Analysis (Paperback)
Series: Student Mathematical Library
Expected to ship within 9 - 15 working days
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Total price: R1,911
Discovery Miles: 19 110
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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. This book is
published in cooperation with IAS/Park City Mathematics Institute.
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