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Recommendation for an Advanced Calculus text

  1. Apr 17, 2012 #1
    Lookin' for a good text on Advanced Calculus for self-study. Thanks.
  2. jcsd
  3. Apr 17, 2012 #2
    What do you mean by advanced calculus? Do you mean the calculus of multivariable or vector-valued functions? Or do you mean real analysis? Or perhaps the calculus of complex variable functions or complex analysis? There are many topics that are referred to as advanced calculus, but they are not all contained in any single text that I know of.
  4. Apr 17, 2012 #3
    I guess that's my problem then. I've finished a course in linear algebra and all my (3 semesters) of calculus. So anything which would be accesable to me from this point would be good. Sorry for the ambiguity.
  5. Apr 17, 2012 #4
    In that case, you have probably covered basic vector calculus (the Gibbs formulation). You should probably study real analysis, which is the rigorous theory behind calculus, and the calculus of complex variables. These would both prepare you for rigorous courses in differential equations.
    A nice segue into real analysis is Spivak's text "Calculus", as it is rigorous where most other texts are not, and a very friendly read compared to some dense analysis texts, as it bases most of its theorems on ideas you already know from your calculus courses, but with more detail. A proper analysis text (that is, one that covers the fundamentals like measure theory and topology) would be Rudin's "Principles of Mathematical Analysis". If you have taken a proper theory-based course of linear algebra using proofs, you should be ready to work through this.
  6. Apr 17, 2012 #5
    Awesome. Thanks for the recs.
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