Are Gilbert Strang's books on calculus and linear algebra suitable for math majors? I would like to know what are the best resources to use to teach and learn elementary subjects (calculus, linear algebra). I remember when learning calculus, I used Spivak's book, which had wonderful problems, but the explanations were not really memorable, the illustrations weren't that appealing and it didn't have enough applications. I would like to know the mathematician's opinion on Strang's books on calculus and linear algebra and the others. Are they not fit to be recommended to math majors? Are they rigorous on any level? What other books do you recommend that have what these don't?
Also, I think that learning through examples first and some visualisation is superior to putting generalities upfront with countless formulas Therefore if you know any book that's written in this vein, please post it.
P.S. Strang's books stress the importance of matrix notation. Is that good? Does it add any insight?
 A: I consider both of Strang's books must-reads for undergraduates. These are what applied mathematics books should look like. There's a perception that applied books are merely rote procedural texts, where proofs are omitted and they basically give toolbox approaches to the material. Bad applied books do this—good ones like Strang's don't omit proofs, but they merely downplay them. They are both rich with relevant applications—that is, applications that are currently being used in research and practice by applied mathematicians and other professionals—beautifully written and conceptually careful. The Calculus book has the added bonus of being available online for free at Strang's website. Don't be fooled into spending all your money on the second edition of the calculus book—it's no different from the first, it merely contains Strang's "Highlights of Calculus" in addition, which is good but doesn't really add anything to the book's quality.  
A word of warning: There are several versions of Strang's linear algebra texts. The one you really want to read is Linear Algebra And Its Applications. The other book-Introduction To Linear Algebra-is a dramatically watered down version of this book and it's missing many of Strang's wonderful sidebars and digressions. So the "non-introduction" version is the one you want.
