Tutorial Release 10.4 The Sage Development Team https://doc.sagemath.org/pdf/en/tutorial/sage_tutorial.pdf
Sage is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas. Both the Sage development model and the technology in Sage itself are distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. The overall goal of Sage is to create a viable, free, open-source alternative to Maple, Mathematica, Magma, and MATLAB.
This tutorial is the best way to become familiar with Sage in only a few hours. You can read it in HTML or PDF versions, or from the Sage notebook (click Help, then click Tutorial to interactively work through the tutorial from within Sage).
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 License.
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See the Vector Calculus Tutorial.
Tutorial: Vector Calculus in Euclidean Spaces
Author: Eric Gourgoulhon
This document contains various tutorials introducing vector calculus with SageMath. The first one regards vector calculus in the 3-dimensional Euclidean space in Cartesian coordinates, focusing on the evaluation of the standard vector operators. The second tutorial deals with the same topic but based on curvilinear (spherical and cylindrical) coordinates. The third tutorial is devoted to changes between the various coordinate systems. The fourth tutorial presents some advanced aspects, namely the treatment of as a Riemannian manifold. Finally, the last tutorial is devoted to 2-dimensional vector calculus, using both Cartesian and polar coordinates in the Euclidean plane ; it combines various features of the other tutorials.