Vector Analysis: Bridging Math and Physics with Rigor and Visuals

[ice109]

something for a mathematician that likes physics or a physicist that likes math. rigorous but with pictures and examples and the such?

 

[robphy]

Marsden
https://www.amazon.com/dp/0716724324/?tag=pfamazon01-20

Bamberg & Sternberg (but probably more than you want)
https://www.amazon.com/dp/0521406498/?tag=pfamazon01-20

 

[ice109]

Marsden
https://www.amazon.com/dp/0716724324/?tag=pfamazon01-20

Bamberg & Sternberg (but probably more than you want)
https://www.amazon.com/dp/0521406498/?tag=pfamazon01-20

the first one is a calc book apparently and has terrible reviews and the second one is a math methods book with terrible reviews but thanks anyway

 

[robphy]

I like them both...especially the Bamberg&Sternberg one.

 

[las3rjock]

the first one is a calc book apparently and has terrible reviews and the second one is a math methods book with terrible reviews but thanks anyway

I would take terrible reviews on Amazon.com with a grain of salt. Many of those reviews are by lazy, underprepared, or unprepared students who are looking to vent their frustrations with a book that they were not willing, ready or able to tackle. If none of those suggestions appeal to you, some standard textbooks for a second course in vector calculus / calculus on manifolds include Spivak, Calculus on Manifolds; Munkres, Analysis on Manifolds; C. H. Edwards, Advanced Calculus of Several Variables; and H. M. Edwards, Advanced Calculus: A Differential Forms Approach. Of those, the last book by H. M. Edwards is probably the closest to what you're looking for. But I would warn you that, since you cannot identify that vector analysis is the same as vector calculus or that it would likely be covered fairly extensively in a math methods book, you may not be adequately prepared to tackle any of these books.

 

[robphy]

You might like
http://www1.mengr.tamu.edu/rbowen/

 

[eGuevara]

Bowen's book posted by robphy is really good, if you're willing to deal with ugly typesetting and some typos. Edwards' book on advanced calculus with differential forms is a current project of mine, so I'll let you know how it goes. A more typical book on vector analysis though,is Marsden & Tromba's Vector Calculus. EDIT: which I just realized has already been posted. Sorry.

YET ANOTHER EDIT: If you'd like to learn about differential forms, here's a paper on the arXiv which was turned into a book: A Geometric Approach to Differential Forms