# Multivariable calc “second course” that does differential forms

I've worked through a computation-heavy, "standard" but quite nonrigorous treatment of multivariable calculus in the past. What book would do well as a rigorous (but not overly) "second course"? In particular, I'm looking for a book that

• treats differential forms

• treats the inverse and implicit function theorems

and leads well into an intro manifolds book like Tu's one. (Bonus points if it actually talks a bit about manifolds itself or works with differential forms defined on manifolds instead of only $\Bbb R^n$!)

• Zorich's Mathematical Analys (vol. I & II) perhaps? – Hans Lundmark Nov 12 '15 at 5:47
• I do not think I want an analysis book. I'd like something with plenty of pictures and one that does not spend a lot of time with epsilon-delta arguments. (My idea of analysis books is that they don't do that kind of thing; I may be wrong.) – Soham Chowdhury Nov 12 '15 at 5:51
• Fine, it was just a suggestion. But what do you mean by "treating" the inverse and implicit function theorems then? I got the impression that you already know how to use them, and were looking for a more advanced book where you could see how they actually are proved. – Hans Lundmark Nov 12 '15 at 7:06
• No, I do not know those two theorems. I only know that they are something that I should know before studying manifolds. – Soham Chowdhury Nov 12 '15 at 10:52
• I see. Yes, in that case, some other book is probably more suitable. – Hans Lundmark Nov 12 '15 at 11:05