I have background in calculus, linear algebra, single variable analysis, topology, ode and some abstract algebra.
So I've decided to study multivariable analysis before/alongside Lee's smooth manifolds. But since I have had trouble with Rudin and Spivak, I have done some research to find different textbook.
After some researching, I have narrowed down to 3 books: Zorich, Hubbard, and Callahan's book. However, I have some question regarding Callahan's book.
Is the book rigorous enough to be used in a multivariable analysis course or should it be used as a supplement instead of main textbook?
Thanks in advance.