Principles of Tensor Calculus: Tensor Calculus

by Taha Sochi

This book is based on my previous Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.

Genres: Mathematics

188 pages, Paperback

Published August 8, 2017

Reviews

[Andrew Davis · Rating 3 out of 5]

Tacha Sochi’s Principles of Tensor Calculus (2014) is a more detailed and formal companion to his later, shorter work Tensor Calculus Made Simple.
Where Made Simple focuses on intuition and accessibility, Principles of Tensor Calculus is more comprehensive, mathematical, and rigorous, often used as a bridge between undergraduate calculus and graduate-level differential geometry or relativity.

It covers:
- The Nature and Definition of Tensors,
- Tensor Algebra and Operations,
- Coordinate Systems and Transformation Laws
- The Metric Tensor and the Geometry of Space
- Tensor Differentiation
- Curvature and the Riemann Tensor

Sochi closes the book with practical uses:
- Classical mechanics: stress and strain tensors, moment of inertia tensor,
- Electromagnetism: expressing Maxwell’s equations compactly.
- Fluid dynamics: velocity-gradient tensor and deformation,
- General Relativity: Einstein field equations