Calculus Multivariable Calculus, Hubbard and Hubbard and Lang's

[unintuit]

I do not know multivariable calculus. I have studied out of Apostol Vol.1.

I do not want to learn the material from Apostol Vol. II.

Therefore I want to know If it would be worthwhile to go through Hubbard and Hubbard's 'Vector Calculus, Linear Algebra, and Differential Forms' after going through Serge Lang's 'Linear Algebra' or would it be better to go through Serge Lang's 'Calculus of Several Variables' and then Baby Rudin followed by Spivak's 'Calculus on Manifolds'?

Regardless, I am going to go through Baby Rudin and Spivak's 'Calculus on Manifolds' book, I really just want to know if it is worth the time to go through Hubbard and Hubbard or Lang's 'Calculus of Several Variables' or can I skip these and do Rudin and Spivak's book?

Thank you for your helpful responses.

 

[unintuit]

I want to apply the knowledge of Spivak's 'Calculus on Manifolds' to physics. However, I am still a math major. Physics is just an interesting aside.

 

[slider142]

That depends on your emphasis. I always recommend Hubbard/Hubbard as a companion to Spivak's Calculus on Manifolds due to the latter's extreme emphasis on purely theoretical applications. Hubbard/Hubbard includes practical considerations, such as finite precision techniques for computers, and applied examples of the theory of calculus on manifolds to physical and mechanical scenarios. Spivak, on the other hand, presents calculus on manifolds in an extremely elegant and concise way, so that every part of the general theory is well motivated and internally connected using very simple notation and definitions. So exposure to both can keep your ability to work with the abstract machinery in both theoretical and practical situations well rounded.