Which Calculus Book Will Give Me the True Understanding I'm Looking For?

[thrill3rnit3]

You know, computers nowadays are often connected with a printer, so you can convert digital text into paper with ink

yeah I'm going to print 600 pages of text off of my home printer

no way man

 

[Landau]

Long live free printing at our university!

 

[thrill3rnit3]

Long live free printing at our university!

Well I'm not a college student

 

[thrill3rnit3]

Anyways, will Spivak's Calculus be an enough preparation for his Calculus on Manifolds?

 

[qspeechc]

In the preface, Spivak says linear algebra and "a respectable first-year calculus course. So linear algebra + Spivak's Calculus would suffice, I presume.

 

[Sankaku]

Here is a great quote (not me!) about Spivak's Calculus on Manifolds:

"...Spivak's Calculus on Manifolds, the terrifying little white book. When I took the course and was in the bookstore picking up the text, I felt a sense of trepidation as I looked at this tiny white paperback, only about 120 pages long, for a two semester course (26 weeks). That's less than a page a day, on average. And even putting aside the pages with problems on them, just the text pages can sometimes take a day each, if you're serious about understanding every (often omitted) detail. I don't actually mean it would take you the whole day to understand, but sufficient effort that you would feel like that was enough for one day. There are also sometimes errors in the book because the author was not being careful - easy to correct if you are at his level and pause for a moment to think about it, but sometimes daunting for a beginning student really trying to understand all the details...

When I took that course I breathed, slept and ate the Little White Book. I still remember approximately the pages and range of problem numbers in which to find particular results and particular problems, ten years later. I made sure to understand every detail of every proof, and to fill in everything that had been omitted, and to correct every error that I noticed. In this way I was able to do very well, and to really feel like I had achieved something."

 

[n!kofeyn]

Anyways, will Spivak's Calculus be an enough preparation for his Calculus on Manifolds?

It will definitely be enough for the calculus, but I'm not for sure how much linear algebra he covers in the calculus book. So you might want to pick up some linear algebra before tackling his manifolds book. It is not an easy book as the exercises drive the book's worth, and there isn't much material to go off of.

When I took the course and was in the bookstore picking up the text, I felt a sense of trepidation as I looked at this tiny white paperback, only about 120 pages long, for a two semester course (26 weeks).

I somehow find this hard to believe. I wonder if it was a graduate or undergraduate level course or if it was an independent study type course. My graduate course in calculus on manifolds covered chapters 1-14 (minus 9 & 10) of Lee's Introduction to Smooth Manifolds, which amounts to around 300 pages of very dense material in a one-semester course. I also don't think it is normal with one page taking you an entire day to fill in the details.

 

[Sankaku]

I somehow find this hard to believe.

I am only quoting...
http://linguan.blogspot.com/search/label/spivak