Softcover ISBN:  9781470456283 
Product Code:  STML/93 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470463137 
Product Code:  STML/93.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470456283 
eBook: ISBN:  9781470463137 
Product Code:  STML/93.B 
List Price:  $118.00 $88.50 
Softcover ISBN:  9781470456283 
Product Code:  STML/93 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470463137 
Product Code:  STML/93.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470456283 
eBook ISBN:  9781470463137 
Product Code:  STML/93.B 
List Price:  $118.00 $88.50 

Book DetailsStudent Mathematical LibraryIAS/Park City Mathematics SubseriesVolume: 93; 2020; 243 ppMSC: Primary 83; 53
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, stressenergy tensor, Schwarzschild spacetime, 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 selfcontained 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.ReadershipUndergraduate and graduate students interested in differential geometry and relativity.

Table of Contents

Chapters

Introduction to Riemannian geometry

Differential calculus with tensors

Curvature

General relativity

Introduction to geometry analysis


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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, stressenergy tensor, Schwarzschild spacetime, 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 selfcontained 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.
Undergraduate and graduate students interested in differential geometry and relativity.

Chapters

Introduction to Riemannian geometry

Differential calculus with tensors

Curvature

General relativity

Introduction to geometry analysis