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Advanced Calculus Text: Apostol vs. Spivak vs. Courant.

Started by Mephisto, March 07, 2010, 02:13 PM

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Heh - wonder if anyone reads this forum anymore.

Has anyone studied, looked over or at least heard one way or the other about these three books?  I'm finishing up my last lower division courses this semester (differential equations and linear algebra) after completing our school's calculus sequence (differential, integral and vector/multivariable), and then transferring to UCLA's joint mathematics/economics undergrad major this Fall.  Despite having mostly excellent math professors the last couple of years (gotta love those Russian purists), our school used one of the least rigorous calculus texts I've ever read (Stewart 6th Ed. Early Transcendentals - I used as a supplement the slightly more rigorous Varberg/Rigdon/Purcell early transcendentals text).  And since I will be starting off with Real Analysis (Rudin - which I've heard is extremely difficult if you're not well prepared with proofs and the basic underlying theories of calculus beyond what standard texts teach) at UCLA this Fall, I want to prepare by reading through an advanced calculus/pre-analysis text, and heard these three are among the best ones (used at MIT, UChicago, CalTech, etc. in their honors calculus classes).

Any thoughts from anyone who has taken upper division mathematics?