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I am doing my 4th Analysis course. Now we are doing functions from $\mathbb{R}^{n}$ to $\mathbb{R}^{m}$ And we are talking about differentiabiity . I have a lot of problems understanding the course because geometrically it is not very intuitive. I mean obviously for higher dimensions it's normal that it's not really intuitive, because we can't actually imagine it. But the idea is the same with three dimensions. So can anyone suggest a book that explains the subject and gives geometric intuition to what is going on? Maybe a book that you have studies during your analysis course that helped you with geometric intuition. Looking forward for replies. Thanks!

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  • $\begingroup$ The best thing in mathematics (in my sens) is to work first maybe without intuition, and wait for have it with the exercises, the main theorems etc ... For your request, faculty.ksu.edu.sa/fawaz/482/Books/… is a nice book and after doing basic in $R^n$ gives some geometric applications. And they are lof of exercises inside ! $\endgroup$ – user171326 Mar 29 '15 at 17:40
  • $\begingroup$ Upvoted. Many popular analysis books like Royden/Apostol/Baby Rudin do not cover Multivariable Analysis in enough detail. $\endgroup$ – yoyostein Aug 9 '16 at 1:37

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