MV Calc Book for E&M: Best Options for Rigor & Theory

[conquerer7]

I want a MV Calc book that has a good covering of vector field operations, mostly for studying Maxwell's equations and stuff later on. Rigor would be nice; I would prefer a book that proves most theorems, but not one as crazy as Spivak (I have only a few months!). Interesting theoretical problems and good intro to linear algebra would be a plus.

Any recommendations?

 

[clope023]

I want a MV Calc book that has a good covering of vector field operations, mostly for studying Maxwell's equations and stuff later on. Rigor would be nice; I would prefer a book that proves most theorems, but not one as crazy as Spivak (I have only a few months!). Interesting theoretical problems and good intro to linear algebra would be a plus.

Any recommendations?

https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20

Informal text on vector calc from the context of e&m, not that proofy though.

 

[qspeechc]

In addition to the book named above, I recommend Marsden and Tromba:
https://www.amazon.com/dp/0716749920/?tag=pfamazon01-20
The first review is probably the most sensible. I don't think it covers much linear algebra however (going by my memory, I may be wrong), so you'll have to get that elsewhere.

For a quick and simple intro to linear algebra you can try Lang's book:
https://www.amazon.com/dp/3540780602/?tag=pfamazon01-20
but I must warn you it is not very advanced or abstract, so if you are a maths student will sooner or later need a more substantial book, but it is more than enough for Marsden and Tromba.