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In keeping with the theme of this book, this chapter is presented for the undergraduate-level student and those who teach undergraduates. The author has found that the average electrical engineering junior can begin his or her excursion into tensors if the concepts are presented at the level given here. (It is assumed that a EE junior will have successfully completed 16 to 18 units of math from Calculus I through differential equations and linear algebra.) There is no reason why students of this caliber should not be shown the power of tensors, especially in light of the inevitable shift into photonics for the design of ultrahigh-speed devices and transmission systems. Students of civil and mechanical engineering can also utilize these concepts in their investigation of composite materials, as can their instructors. In fact, one could take the position that there is an even greater need for tensors in these disciplines because stress, strain, and elastic modulus are tensors even for linear isotropic materials. Many introductory electromagnetics texts, especially those published more recently, make some mention of tensors when discussing anisotropic media. for example, some authors use the term “dyadic,” the more precise expression for the particular tensor that provides the needed parameters for linear anisotropic media. The mention of tensors is also included in discussions of linear bianisotropic media, especially composite materials, covered in more advanced treatises. In addition, the scattering of electromagnetic waves from objects is skillfully treated in texts by the use of the scattering dyadic. Others use the less precise term “tensor,” and define it with the nine components of a dyadic. Yet others, especially in earlier works, discuss the nine-component expansion of the anisotropic media without mentioning either tensors or dyadics. The more advanced a text in electromagnetics is, the more probable it is that dyadic tensors are used to formulate the mathematical description of the physics, regardless of the whether the text is a classic or written more recently.
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