Calculus
I don't know anything about Apostol's Mathematical Analysis. My guess would be that it demands a fairly sophisticated background of the reader, and does an excellent job of covering calculus from an extremely rigorous point of view. I have heard that Apostol's Calculus is an excellent choice, probably somewhat more accessible to beginners, but still offering a rigorous, highbrow perspective. I've also heard the same of Spivak. I'd probably opt for one or both of these.
In 1976 I bought copies of Apostol's "Calculus" for $19 for each volume new at the Caltech bookstore. These were published by Wiley. That was for the 2nd edition of Volume 1, which came out in 1967, and for the 2nd edition of Volume 2, which came out in 1969. $19 in 1976 dollars is about $86 in 2019 dollars. Apostol's "Calculus" is still available from Wiley, and is still used in a few schools for their proof-oriented calculus courses (Caltech, MIT, Stanford, for example). Wiley wants $283.95 for the current edition of each volume. Guess what edition they are up to now? The answer is…
Thanks! I think I am either going to go by Apostol or Spivak. I have had calculus years ago. I remember the mechanics faintly. I need a solid revision with the associated theory behind it. The only problem with Spivak is that it covers single variable while Apostol's two volumes cover much much more.
Glad to help! Posting about this inspired me to review all the calculus that I've barely touched in a decade, so I checked out a library copy of Apostol for myself :)
Apostol's text is less a Calculus text and more an introduction to real analysis. I would not recommend it to someone seeking a refresher on practical methods.
You can probably skip Volume I.
Calculus by Tom Apostol
>As someone who has done a PhD, done research in math, done research in computing, worked in research and development in industry, taught math Me too so now what? I don't think your credentials give you any real authority but just make you look like you're gatekeeping. >Doing the exercises is playing with the objects to try to answer specific questions. Great so then we're in agreement: playing with the object is doing the exercise. The funny thing is that at one time I actually did all of the exercises in volume 1 of apóstol's calculus. You know what effect on me it had? I was so bored I…