Parker L., Christensen S.M. MathTensor. A system for doing tensor analysis by computer

Addison-Wesley Publishing Company, 1994. — 396 p.This book should be of interest to practitioners, researchers, and students in the sciences, engineering, and mathematics who wish to make efficient and accurate use of tensors and differential forms in solving problems. Math Tensor is a computer program that works with Mathematica by extending its capabilities to include tensor analysis and differential forms. These pages are intended to serve, first of all, as a comprehensive introduction to all aspects of Math Tensor. In addition, they contain pedagogical introductions to tensors and differential forms. The mathematical techniques for dealing with tensors have been developed by mathematicians and scientists over many years. Tensors are applied, among other things, to describe electromagnetic fields, energy and momentum, elementary particles, gravitational fields and spacetime, elastic stresses and strains in deformed bodies, fluid dynamics, the geometry of curved surfaces and spaces, and the curvature of the cornea of the eye. These applications range from physics, elasticity, and differential geometry to aerodynamics, meteorology, and medicine. Whether you are doing extensive tensor analysis or are only starting to learn about tensors and differential forms, you will find this book worth reading. Pedagogical introductions to tensors and differential forms make this book an excellent learning tool, suitable for self-study or as a textbook in a computer-based college or introductory graduate level course.