Tensor calculus: unlearning vector calculus

Wha-Suck Lee; Johann Engelbrecht; Rita Moller

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Tensor calculus: unlearning vector calculus

机译：张量微积分：学习向量微积分

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Tensor calculus; vector calculus%Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

机译：张量微积分;向量演算％Tensor演算在研究身体表面的向量演算中至关重要。实际上，张量微积分是矢量微积分的自然提升。本文介绍了矢量演算中传统课程向张量演算过渡的一些陷阱。我们展示了如何更深入地关注传统主题（例如Jacobian）可以充当向量微积分到张量微积分的桥梁。

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《International Journal of Mathematical Education in Science and Technology》 |2018年第2期|293-304|共12页
作者
Wha-Suck Lee; Johann Engelbrecht; Rita Moller;
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Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa;

Department of Science, Mathematics and Technology Education, University of Pretoria, Pretoria, South Africa;

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa;

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5. Physics experiences and calculus: How students use physics to construct meaningful conceptualizations of calculus concepts in an interdisciplinary calculus /physics course. [D] . Marrongelle, Karen Ann. 2001

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6. Analysis of Non-Commuting Vectors with Application to Quantum Mechanics and Vector Calculus [O] . G. H. Shortley, G. E. Kimball 1934

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7. Calculus and Linear Algebra. Vol. 1: Vectors in the Plane and One-Variable Calculus [O] . Wilfred Kaplan, Donald J. Lewis 2007

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Tensor calculus: unlearning vector calculus

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