Kees Dullemond & Kasper Peeters

Introduction to Tensor CalculusKees Dullemond & Kasper Peetersc 1991-2010 This booklet contains an explanation about tensor calculusfor students of physicsand engineering with a basic knowledge of linear algebra. The focus lies mainly onacquiring an understanding of the principles and ideas underlying the concept of tensor . We have not pursued mathematical strictness and pureness, but insteademphasise practical use (for a more mathematically pure resum e, please see the bib-liography). Although tensors are applied in a very broad range of physics and math-ematics, this booklet focuses on the application in specialand general are indebted to all people who read earlier versions of this manuscript and gaveuseful comments, in particular G. B auerle (University of Amsterdam) and C.

2.1 Intuitive approach e e v=(0.4 0.8) 1 2 v=(0.4) e’ 2 e’ 1 1.6 Figure2.1: Thebehaviourofthetransformationofthecomponentsofavectorunder the transformation of a basis vector~e 1′ = 1

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