Vector Analysis and Cartesian Tensors by Bourne and Kendall

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Whitehole
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I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good intro for undergrads. I just noticed that the topics of the book seems to be lacking, i.e. Lagrange multipliers, etc.

Can anyone also recommend other good books on vector analysis with some tensors included, i.e. vector calculus in tensor notations, etc.
 

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While certainly not a modern book one of the coauthors was a student of Dirk Struik:

Vectors by P. Moon and D.E. Spencer D.Van Nostrand Company Inc (1965)

notation follows the contravariant/covariant convention