Tensor Calculus

TL;DR

This paper extends tensor calculus by focusing on curvilinear coordinate systems, developing advanced concepts and techniques beyond Cartesian approaches.

Contribution

It introduces a comprehensive treatment of tensor calculus in curvilinear coordinates, expanding on previous Cartesian-based methods with new concepts and techniques.

Findings

Developed tensor calculus techniques for curvilinear coordinates

Expanded on tensor transformation rules in non-Cartesian systems

Provided advanced examples and applications in tensor analysis

Abstract

These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques. Unlike the previous notes which are largely based on a Cartesian approach, the present notes are essentially based on assuming an underlying general curvilinear coordinate system.