<p>Has anyone here ever worked through Spivak's Calc? What are your thoughts on it?</p>
<p>Out of Courant, Spivak, and Apostol, which would you recommend for a rigorous introduction to real analysis?</p>
<p>Oh, Spivak, undoubtedly. It's absolutely wonderful for pure mathematics, and indeed the title of the book is itself misleading, as it essentially builds from the foundation of real numbers into real analysis. It's also a joy to read. The tone is conversational, but it is mathematically rigorous and never boring. Most of the learning, however, is in the problems. They can be devilishly difficult to solve, but it's absolutely worth it. I used it in tenth grade, and it took an immense amount of effort and discipline to work through it. </p>
<p>I would advise getting Courant or Apostol in addition to Spivak, because the Spivak book is lacking in applications to physics (thought chapter 17 of the third edition is focused on planetary motions and the like). I'm not saying this is a bad thing, in fact, the pure mathematics bent is one of Spivak's advantages, but the joint learning of physics and calculus has a certain pedagogical value that is not to be underestimated.</p>
<p>I've heard Spivak is the best out of the three, however I only used Apostol in High school. Apostol seemed to be a good introduction to Real Analysis and was an enjoyable text for Calculus (I've only read the Volume I. I used other texts for Multivariable Calc and Linear Algebra. I plan on getting Spivak and Apostol Volume II eventually.), and was far more interesting than a textbook like Stewart's Calculus. I need to go get my hands on a copy of Spivak some day.</p>
<p>How expensive is a copy of Spivak's Calculus?</p>
<p>Spivak runs about 75 bucks most places. Check on <a href="http://www.abebooks.com%5B/url%5D">www.abebooks.com</a> for a cheaper copy. Getting a copy of the solutions manual is a good idea, as well. </p>
<p>(Here's a cheap copy: <a href="http://www.abebooks.com/servlet/BookDetailsPL?bi=753922465&searchurl=sts%3Dt%26an%3Dspivak%26y%3D0%26tn%3Dcalculus%26x%3D0%5B/url%5D">http://www.abebooks.com/servlet/BookDetailsPL?bi=753922465&searchurl=sts%3Dt%26an%3Dspivak%26y%3D0%26tn%3Dcalculus%26x%3D0</a>)</p>
<p>Apostol is a lot more widespread, so there's a better chance of getting a cheap copy. For example, I bought both volumes for about 25 dollars, which was a great steal. They served really well for multi-variable calculus and linear algebra, and were far better to use while studying physics than Spivak. </p>
<p>By the way, EbolaPox, any chance you frequent physicsforums.com? I swear I saw the same username there.</p>
<p>Thanks a lot Quark!</p>
<p>Indeed, I do go to PhysicsForums often. Love the site, and they have great advice for people going into Math and Physics. I also love being able to help people out with calc problems and the such on physicsforums.</p>
<p>Thanks for the link to the cheap copy of Spivak. I may just buy that soon.</p>
<p>which forum is that? what's the website?</p>
<p><a href="http://www.physicsforums.com%5B/url%5D">www.physicsforums.com</a> </p>
<p>Great advice for High School , Undergrad and graduate students. The people there offer assistance with math/science/engineering. Academic Advice and Homework boards are really useful. They also have good book suggestions.</p>