Shapiro, Ilya L.

Primer in tensor analysis and relativity - Cham : Springer, 2019 - xviii, 324 p.; ill. 23 cm - Undergraduate lecture notes in physics .

Includes bibliographical references and index.

This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject


Tensor algebra
Calculus of tensors
Mathematical physics
Quantum field theory
String models
Conformal transformation
Covariant derivative
Einstein equations
Equivalence principle
Factorization theorem
Gauge invariance
Inverse matrix formula
Lorentz force
Maxwell equations
Metricity condition
Parity transformation
Stokes theorem

512.57 / SHA

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