Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition)

That said, I see no problems with the introduction of integration before differentiation, since most appreciative users will have been introduced by other texts. Far from all the modern books aimed at generations X, Y and Z everything remains axiomatic and mathematically thorough and no necessary proof is omitted in an attempt to cut corners.

A classic couple of books for those that need all their t's crossed.


take this simple quiz   July 28, 2004
mathwonk
21 out of 23 found this review helpful

if you are the kind of student who thinks the area of a triangle is: "Mmmm...(1/2)BH, or is it (1/3)BH? Oh well, who cares, I can always look it up anyway." then this book is probably not for you. But if you have wondered whether the number given by that formula changes when you change which of the three sides of the triangle you call the base, then this book is exactly what you have been looking for. The author of this book assumes you are bright and curious, the kind of student it was written for at Cal Tech. Professor Apostol has made an enormous and thoroughly successful effort to explain in intellectually honest detail exactly what is going on, and how everything is proven rigorously. In this same vein, Spivak's book is more fun, and Courant's has more physics and applications, but this one is the most scholarly. The linear algebra was an afterthought, added to the original work when that craze swept the subject in the 1960's. In general, great works are best in the first edition before the publisher convinces the author to modify his original vision. In my opinion the linear algebra does nothing to enhance the presentation of one variable calculus, and should have been left out, but it won't hurt you.


There is but one Apostol, and he is Tom.   August 11, 1997
Zachary Strider McGregor-Dorsey (Superior, CO)
32 out of 34 found this review helpful

Perhaps the best description for Calculus, by Tom M. Apostol, is simply its title. This text is Calculus. Like no other calculus book I have seen, it devotes itself totally to its subject matter, never compromising itself for the sake of understanding. By doing this, the reader is permitted to learn calculus completely.

So many calculus texts in the current market have a sort of misguided focus. Instead of explaining the subject they claim, all they offer is the tools for solving the rote calculus problems of Advanced Placement tests and engineering. This is fine for someone who cares nothing of mathematics, but is not sufficient for their claim of teaching calculus. Apostol's Calculus cares little about explaining the applications of calculus or preparing someone for yet another standardized test. Uncluttered by fancy computer-aided graphics and pages and pages of redundant examples, Apostol offers the basics of calculus with the prrofs behind the theorums. Never once is the reader left with questions as to what exactly integrals are or why any two nonequal numbers must have another number between them. Everything necessary for the reader to solve any single variable calculus problem is presented in text. Apostol's rigor knows no bounds, begining first with the proof of the positive integers and continuing to the finest points of integral calculus.

This text is not for the faint-hearted. If you just want to be able to solve calculus problems, you would have little use for this text. But if you want the tools and justifications for all of calculus, this is the book for you. It is a necessity for all mathmaticians' libraries.

See also Calculus 2 by Tom M. Apostle for multivariable calculus.


Great if a freshman tells you 'i want to do math'   February 23, 2004
bal gombak (Cambridge, MA USA)
13 out of 15 found this review helpful

"Tommy" is a good choice for first or second year students who have considerable talent and interest in math, as a bridge between the 'compulsary' freshman calculus and the rigor of mathematical analysis. The text is well written (as freshmen text ought to be) sans colorful diagrams and 'real life applications' prevailing in most calculus texts (those not written for math majors). The exercises are balanced between routine slog and rigorous proof. Notations are standard and consistent throughout. I recommend this as a textbook for honors calculus class, or as an in-depth self study for the non-math majors.