Advanced calculus like Sternberg's but less abstract

[whyevengothere]

I've read Spivak 's calculus so I tried Sternberg 's book,IT IS kind of hard,because the abstraction is put upfront,I know of his other book with Bamberg, but a review on amazon deterred me from buying it,was I right in doing so?
Any adv.Calculus book that have some physics in it like Sternberg's?

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[whyevengothere]

When I'd like to know if there any advanced calculus book that doesn't adhere to axiomatic methods,is rigorous but with strong appeal to ‘geometric intuition'.

 

[verty]

When I'd like to know if there any advanced calculus book that doesn't adhere to axiomatic methods,is rigorous but with strong appeal to ‘geometric intuition'.

You could try this one, it has a ton of exercises and looks at each topic from every angle. It is very mathematical, there is not a lot of explanation, but if you do the exercises, you should get a lot of intuition. Not a lot will be left uncovered.

That said, it is a pretty unfriendly book. Be prepared to put in the effort of doing the problems even if they seem unmotivated. You won't find the perfect book, but this one will satisfy your need for intuition because the problems will give you that encompassing knowledge.

https://www.amazon.com/dp/0716749920/?tag=pfamazon01-20

PS. It doesn't have any physics in it. I can't imagine there is such a book. I mean that it is thorough and doing the exercises in order will be rather exhaustive.

 

[verty]

Hmm, there are some very odd reviews of that book I mentioned. Here is one excerpt:

On almost all the topics, I found that the textbook just did not confer any meaningful understanding. It spends a lot of time on proofs yet at the end of the day it came down to a cookbook-style attack on some standard, uninspiring problems. I had such a bad experience with the material that I concluded that math probably just wasn't for me.
...
Despite not getting 2nd year calculus at all, I took 3rd year honors real analysis and scored very close to 100%.

This reviewer complains that the book comes down to a cookbook-style attack on problems, and that he struggled to understand things. But clearly the book worked because he aced real analysis afterwards, probably because he had the intuition already from this book. He gives it 1 star out of 5, why I don't know because it clearly helped him.

 

[mathwonk]

have you looked at courant's calculus volume 2?

https://archive.org/details/DifferentialIntegralCalculusVol2

 

[whyevengothere]

have you looked at courant's calculus volume 2?

https://archive.org/details/DifferentialIntegralCalculusVol2

I've read his ''what is math?'' and a bit of the first volume of that ,I liked the content,but the writing style was bit weird to me.

 

[alan2]

Are you looking for a mathematics text or for a methods book suitable for physicists? There is wide variety in things called "advanced calculus".

 

[mathwonk]

have you tried apostol vol 2?or maybe the version of courant rewritten by fritz john would suit your tastes better as to style. i.e. courant and john vol. 2 is a rewrite of courant's vol. 2 but in a more modern and standard style.