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A friend of mine gifted me his copy of Spivak's Calculus on Manifolds. I was looking out for a good book to relearn MV Calculus to the extent of :

Multivariable Limits, Continuity and Differentiation Differential Calculus of Vector and Scalar Fields Multiple/Surface Integrals

My intention was to go through a nice rigorous text to prepare me for my research in Numerical Optimization.

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    Caro @Siminore, my comment was not to be taken too seriously. Yet, I have the optimistic vision that a book can be profound, beautiful, instructive...and easy:-)2012-07-09

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For a textbook which presents multivariable calculus with an attention to rigor and geometric ideas, but which is not as abstract and terse as Spivak's book, I recommend my colleague Ted Shifrin's text Multivariable Mathematics.

(My only caveat is that it is extremely expensive...as it seems that many undergraduate level math textbooks from mainstream publishing houses now are.)