Best book on advanced calculus?

K.I.L.E.R

Retarded moron
Veteran
I have lots of maths books and engineering books but I want something that is more advanced.

What's the best book on advanced calculus? Are there any two books and not just one?
 
By advanced calculus, you mean what would be found at say the 100-200 lvl math classes, say a reference text? Or do you want something more along the lines of an analysis book?

If its the former, Spivak 'calculus' is a fairly canonical text, albeit a little bit dated.

If you want something a little more specialized.. say sequences/series, or integration or multivariable calculus, again there are texts for each specific thing that are far more in depth than a broad overview text.
 
Analysis books.

Specialisations I'd like:
Multivariate calculus and series.

I'd like to be able to derive my own methods for numerical computation(more complex ones than I now know), this tends to involve series a lot as well as analysis of functions.
 
Im not sure if you are ready for this or not, but the standard text for say a 400 lvl analysis class (typically given to juniors in a math department) would be Rudin 'principles of mathematical analysis', it covers the slightly more advanced way of thinking about series/multivariable calculus and so forth, as well as some numerical methods.

I absolutely guarentee you won't be able to derive something new unless you have the material in this book second nature.

You might consider taking a course on this material, if you are serious about it, its really one of the harder classes you'll find in college and somewhat of a weedout event for math majors.
 
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