Øyvind Grøn, Oslo University College, Oslo, Norway, oyvind.gron@fys.uio.no

Arne Næss, Oslo University College, Oslo, Norway (deceased)

This introduction to the mathematics used in relativity covers both special and general theories and includes numerous features that aid those with less mathematical training, such as 'in-between' calculations and a gradual, rigorous explanation of the theory.

Covers both special and general theory of relativity and applications to cosmology in a logical and self-contained way

Vectors.- Differential calculus.- Tangent vectors.- Curvilinear coordinate systems.- The metric tensor.- The Christoffel symbols.- Covariant differentiation.- Geodesics.- Curvature.- Conservation laws of classical mechanics.- Einstein's field equations.- Einstein's theory of spacetime and gravitation.- Some applications.- Relativistic universe models.

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity.

First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.

The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.