Sanders, J. W. (2018, June), Demystifying Tensors: a Friendly Approach for Students of All Disciplines  Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. 10.18260/1-2--30255

\bibitem{asee_peer_30255}
  Sanders, J. W. (2018, June), \emph{Demystifying Tensors: a Friendly Approach for Students of All Disciplines}
  Paper presented at 2018 ASEE Annual Conference \& Exposition , Salt Lake City, Utah.
  10.18260/1-2--30255

John W. Sanders.  "Demystifying Tensors: a Friendly Approach for Students of All Disciplines".  2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah, 2018, June.  ASEE Conferences, 2018.  https://peer.asee.org/30255 Internet.  27 Jul, 2024

\bibitem{asee_peer_30255}
  John W. Sanders.
  "Demystifying Tensors: a Friendly Approach for Students of All Disciplines".
  \emph{2018 ASEE Annual Conference \& Exposition , Salt Lake City, Utah, 2018, June}.
  ASEE Conferences, 2018.
  https://peer.asee.org/30255 Internet.  27 Jul, 2024

@INPROCEEDINGS{asee_peer_30255
author = "John W. Sanders"
title = "Demystifying Tensors: a Friendly Approach for Students of All Disciplines"
booktitle = "2018 ASEE Annual Conference \& Exposition "
year = "2018"
month = "June"
address = "Salt Lake City, Utah"
publisher = "ASEE Conferences"
note = {https://peer.asee.org/30255}
number = {10.18260/1-2--30255}
}

TY  - CPAPER
AB  - The concept of a "tensor" is an extremely important one in science and engineering.  And yet, it is notoriously one of the most difficult concepts for students to grasp. In fact, there is much confusion as to what tensors truly are and why they exist in the first place. In this paper, I pose the question: "How should tensors be introduced to science and engineering students for the first time, and at what point in their education?" I seek an answer to this question that is both formally and pedagogically correct.  I note that there are two primary approaches to tensors currently used in science and engineering courses.  The "component approach" (which appears to be favored by most instructors for higher-rank tensors) views tensors as sets of components that transform in a given way under certain coordinate transformations, and usually involves the added complexity of indicial notation.  The "geometric approach" (which appears to be favored by most instructors for vectors) views tensors as singular objects with certain geometric properties. While many regard these two approaches as equivalent, I argue that the geometric approach is the more pedagogically correct of the two, for tensors of all ranks. Indeed, it is possible to take the geometric approach without recourse to indicial notation or cumbersome component transformation rules, and I have done so in three different undergraduate-level engineering courses: a sophomore-level dynamics course, a junior-level strength of materials course, and a senior-level advanced engineering mathematics course. In this paper I discuss the methods I used to illustrate the geometric approach in these courses, and report the results of end-of-semester surveys designed to assess my students' cognitive and metacognitive understanding of tensors.  Based on my experience, I encourage other instructors to adopt the geometric approach in their own courses.  By doing so, I believe it is possible to remove some of the mystery surrounding tensors, making them more accessible, understandable, and perhaps even a little more interesting.
AU  - John W. Sanders
CY  - Salt Lake City, Utah
DA  - 2018/06/23
PB  - ASEE Conferences
TI  - Demystifying Tensors: a Friendly Approach for Students of All Disciplines
UR  - https://peer.asee.org/30255
DO  - 10.18260/1-2--30255
ER  -