A Primer in Tensor Analysis and Relativity

  • Ilya L. Shapiro

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Tensor Algebra and Analysis

  3. Elements of Electrodynamics and Special Relativity

    1. Front Matter
      Pages 129-129
    2. Ilya L. Shapiro
      Pages 131-142
    3. Ilya L. Shapiro
      Pages 143-158
    4. Ilya L. Shapiro
      Pages 159-187
  4. Applications to General Relativity

    1. Front Matter
      Pages 189-190
    2. Ilya L. Shapiro
      Pages 271-292
    3. Ilya L. Shapiro
      Pages 293-319
  5. Back Matter
    Pages 321-324

About this book


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.


vector calculus Special Relativity textbook general relativity equations covariant methods linear spaces grad, div, rot Lorentz force relativistic dynamics general relativity textbook tensors for physics

Authors and affiliations

  • Ilya L. Shapiro
    • 1
  1. 1.Departamento de FísicaUniversidade Federal de Juiz de ForaJuiz de ForaBrazil

Bibliographic information

Industry Sectors
Energy, Utilities & Environment