- Principles of Tensor Calculus | Physics / Math / Brain Teasers | Calculus, Math notes, Mathematics
- You may also be interested in...
- Theory of relativity
- Tensor Calculus for Engineers and Physicists pdf

Have you studied linear algebra now?

The intuition behind tensor calculus is that we can construct tensor fields smoothly varying from point to point. At every point of a manifold or Euclidean space, if you prefer we can conceptualize the vector space of velocities through that point. Once we have a vector space, we have its dual, and from the space and its dual, we construct all sorts of tensor spaces. A tensor field is just one such tensor at every point that varies in a differentiable fashion across the manifold. Let's make a concrete example.

You're an EE student, hopefully you'll forgive me if I use a concept from mechanical engineering. Consider a voluminous body with internal stresses. Fix a point.

## Principles of Tensor Calculus | Physics / Math / Brain Teasers | Calculus, Math notes, Mathematics

It is a tensor because it does so in a linear fashion, at each point mapping a vector to another vector. If you're interested in general relativity and differential geometry, consider also picking up some differential geometry textbooks. As a plus, if by then your linear algebra is rusty, the first chapter is devoted to the basics of multilinear algebra and tensor mechanics.

First all, study multivariable differential calculus from Rudin's PMA. Then learn Smooth manifolds through Sinha's book, and Lee's book. Only then O'Neill's Semi-Reimannian geometry could be intelligible. This book will teach you the true SR and GR.

### You may also be interested in...

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Tensor Calculus Ask Question.

- Geography Basics (2 Volumes Set)?
- Continuum and solid mechanics : concepts and applications!
- Tensor Analysis for Physicists.

Asked 3 years ago. Active 1 year, 7 months ago. Viewed 3k times. Salim Salim 41 1 1 silver badge 3 3 bronze badges. Neal Neal 25k 2 2 gold badges 44 44 silver badges 90 90 bronze badges. Rajniant Sinha Rajniant Sinha 1. A Student's Guide to Entropy. Don S. A Student's Guide to Lagrangians and Hamiltonians.

- English Language Arts Units for Grades 9-12.
- International Mobility and Educational Desire: Chinese Foreign Talent Students in Singapore.
- The Oyster Vol. 1: The Victorian Underground Magazine of Erotica!

Patrick Hamill. Statistical Mechanics in a Nutshell. Luca Peliti.

## Theory of relativity

Statistical and Thermal Physics. Harvey Gould. An Introduction to Statistical Mechanics and Thermodynamics. Robert H. Quantum Mechanics. Roy McWeeny. Cartesian Tensors. Hagen Kleinert. Understanding Geometric Algebra for Electromagnetic Theory. John W. Tensor Analysis and Its Applications.

Quddus Khan.

Quantum Gravity. Carlo Rovelli. Statistical Mechanics.

Avijith Lahiri. Quantum Field Theory. Claude Itzykson. Classical Dynamics. Donald T. Techniques and Applications of Path Integration. Symmetries in Fundamental Physics. Kurt Sundermeyer. Path Integrals for Pedestrians. Ennio Gozzi.

alexacmobil.com/components/wogujim/kaxew-come-rintracciare.php Lectures on Quantum Mechanics. Berthold-Georg Englert. Lie Groups, Physics, and Geometry. Robert Gilmore. Elements of Statistical Thermodynamics. Leonard K. Jurgen M. Condensed Matter Field Theory. Alexander Altland. Finite Quantum Electrodynamics. Gunter Scharf. Foundations of Statistical Mechanics. Oliver Penrose. Nonlinear Dynamics.

### Tensor Calculus for Engineers and Physicists pdf

Peter B. Claus Kiefer. Scattering Theory. John R. Superstring Theory: Volume 1, Introduction. Michael B. From Spinors to Quantum Mechanics. Gerrit Coddens. Applied Group Theory. George H.