Mathematically rigorous Calculus 2 book

[Rodrigo Schmidt]

So, i am currently studying physics in a brazilian university. I am going to have a Calculus 2 course which, in Brazil, covers Ordinary Differential Equations and multi-variable differential calculus. So which challenging and rigourous books would you guys recommend for that? Thanks for the attention!

 

[FactChecker]

If you know which textbook they will be using, it would be good to look at that first. Other than that, for self study, I have always been a fan of the Schaum's Outline series of books. They are fairly inexpensive and have a lot of worked examples and exercises.

 

[MidgetDwarf]

I would not call it rigorous by Mathematics standards, but Mardsen and Tromba: Vector Calculus fits the bill. It has a lot more substance than your typical intro Multi. Calculus book.

 

[Infrared]

Check out the second volume of Apostol's Calculus.

 

[Rodrigo Schmidt]

Thanks for all the suggestions! I will check on all of them.

 

[cpsinkule]

Rigorous multi variable calc would be on the level of Spivak Calculus on Manifolds or Munkres Analysis on Manifolds. Are you sure you want rigour for a first course?

 

[mathwonk]

I liked this book by lang: published in 1968 as Analysis I, possibly the same book now called Undergraduate Analysis.

https://www.abebooks.com/servlet/Se...centlyadded=all&sortby=17&sts=t&tn=analysis+I