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Callahan vs. Fleming

  • #1
103
7

Main Question or Discussion Point

I have a knowledge of Calculus, Differential Equations, and Linear Algebra, I want to learn advanced calculus, but I'm wondering what book is the best choice, I want to learn it rigorously "enough" but not to the point where someone would call me a mathematician i.e. Calculus by Lang vs Calculus by Spivak, certainly Lang is rigorous but Spivak is at a higher level, though Lang is enough for physicist. I also want to learn it in differential forms approach after, i.e, Advanced Calculus: A Differential Forms Approach by Edwards. I have to choices,

Advanced Calculus by Callahan - longer but has more geometric arguments and diagrams
Functions of Several Variables by Fleming - shorter but harder?

I think Fleming has an advantage because it is shorter, but Callahan is newer and might have some topics that are not in Fleming's book, it also has more explanations and diagrams. Which do you think suits me best? Do you think if I read Fleming instead of Callahan I'll miss some important discussions in Callahan? As of now I'm more into Fleming since it's shorter. I don't have much time to read two books fully, so I just need to choose one and concentrate on that.
 
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Answers and Replies

  • #2
317
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Fleming's book isn't especially short. I'd like the sections on differential forms to be a bit more fleshed out, but even there it's more verbose than Spivak's Calculus on Manifolds.

I'd recommend Fleming because of the applied topology and Lebesgue integration on [itex]\mathbb{R}^n[/itex].
 

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