This is the early transcendentals version of Stewart's calculus. The title of the book is quite appropriate, in that to learn calculus well, one must transcend the Stewart approach early and often. I found my self reading another text (Simmon's Calculus and Analytic Geometry) as an antidote to this dry, disjointed, lifeless tome.
Stewart takes an inconsistent (sometimes rigorous, sometimes intuitive) approach toward teaching the calculus. It seems as if he has attempted to be all things to all people. Though he may have attempted to present the subject in both an intuitive (to motivate the typical student) and rigorous (to satisfy the professor) manner, he failed to deliver on either.
The text is replete with pretty diagrams and some historical diversions, which read as canned, trivial snippets. In spite of this eye candy, the mathematical exposition is poor. Most proofs read as shorthand notes to one who already understands the subject. Is it analysis or basic calculus? Stewart seems to have a schizophrenic writing manner. On the one hand, he presents examples in "workbook" (i.e. Schaum's outline) form, so that if one wishes to solve a particular sort of problem, one might find it here. He does not seem able, however, to meld problem solving with rigor in a coherent manner. So an abbreviated proof is done, with several relevant steps (relevant, that is, to the beginner) omitted. What function does this serve for a pre-analysis student? A proof that might take 10 steps is presented in 4. What is the point of this approach? Perhaps so as to ward off accusations that a particular subject was not touched upon.
The book is expensive and bloated. Though the "official" rendering of the page numbers is 781, there are approximately 130 other pages devoted to appendices (some as advertisements for other, i.e. ancillary, materials). Note, this text is intended for a 2 semester Calculus sequence. It seems inappropriate, perhaps fraudulent,that Stewart devoted 900+ pages for this task, and yet failed to present the material in an interesting and efficient manner.
Given his insistence upon this secondary material, I ask Stewart - did you ever intend for this book to be relatively self-contained for the serious first year scholar, or did you expect the professor or CD-ROM to fill in the gaps in your exposition? In spite of the suggestion to buy expensive ancillaries, I diverted myself to the library where I discovered Simmons' brilliant exposition. This text provides what Stewart does not - a good, efficient foundation of the basic calculus in the context of intellectual breadth. When a calculus first-timer reads Simmons, he or she will likely understand exactly why a calculation is being done, as opposed to the Stewart "willy-nilly" approach, as if one is simply calculating for calculations sake, much like working glorified accountancy problems. Calculus is an intellectual masterpiece, but Stewart presents it as disjointed, purposeless exercise solving. I suggest that serious freshman mathematics scholars avoid Stewart. Compare the Stewart text to others in your school library if possible, buy used if necessary, and read something else if the exposition seems problematic.
I recommend most highly the George F. Simmon's text Calculus and Analytic Geometry (either the first or second edition). Another promising text is Anton's Calculus: A New Horizon, as more efficient, focused alternatives. These texts allow one to learn first year calculus on one's own, and if one has the benefit of a decent professor, so much the better for one's edification. After Simmons or Anton, one should be well prepared to move on to introductory analysis, such as the work of Michael Spivak (Spivak's Calculus).