Vector Analysis and the Theory of Relativity, Vol. 1.

A rigorous, problem‑driven guide to four‑dimensional space–time and gravitation, built around concrete methods and Einstein’s ideas.

This edition presents a careful treatment of the metric space around a gravitating center, the paths of material particles and light, and how different observers relate their natural coordinate systems. It emphasizes a tensor form for the laws of physics and includes detailed problem work that guides readers through the core calculations of relativity.

Readers will encounter:

• How to define natural coordinate systems and relate them across observers.
• Derivation of the Einstein tensor for orthogonal coordinate systems in a gravitating field.
• Geodesic paths for particles and light, with methods for solving the associated equations.
• Conceptual tools for resolving covariant and contravariant tensors in practical settings.

Ideal for students and professionals who want a clear, quantitative approach to relativity and gravitation, using concrete problems to build understanding.