Reviews for Calculus: Beginner to Advanced, and Everything in Between

The average rating for Calculus: Beginner to Advanced, and Everything in Between based on 2 reviews is 3.5 stars.

Review # 1 was written on 2011-08-03 00:00:00 ROBERT RANDALL A very basic introduction to calculus. Most of the method I remember from high school maths class, except for the clearly described theory of boundaries. Boundaries and limit theory are the roots of Calculus, and I fear that my high school classwork covered these insufficiently. Calculus, like any mathematics or science, is based on several assumptions (which assures us, by the way, that science cannot solve every question, even if we wished that it could; the ones it cannot or does not wish to it pushes away by refusing to consider them). Functions and their derivatives cannot be defined until all anomalies and unwanted ripples are eliminated using boundaries. I will advise readers to go carefully over the text and perhaps familiar methodology, if only to relearn the theory of boundary conditions. This book is very well presented, clear and concise. If the pages had been finer, the weight of the book and its size may have been reduced.

Review # 2 was written on 2012-04-26 00:00:00 Walter Harris In writing "A Tour of the Calculus", there are three things that David Berlinski would like you to know, in order: 1. David Berlinski has read more books than you. 2. David Berlinski is well regarded among mathematicians. 3. The motivations and concepts that support calculus as a foundational achievement of modern thought. Let me offer this praise: Berlinski faithfully and artfully expresses what almost every math teacher misses; The motivation for creating calculus was to understand a world of varying forces, flows, and influences. Questions like "Why do the planets move like they do?", "How fast is a cannonball moving in mid-flight?", and "How much concrete will I need to dam this river?" were not really answerable before calculus. Calculus gives us a way to quantify the nuances of natural phenomenon that was never available before in history. This is exciting, and the author communicates this excitement in the mirror of his own excitement. This enthusiasm is quickly buried, however, in a mountain of cheeky literary references and irrelevant, boring asides. The author tries to bind all these together with metaphors, which are stretched to ludicrous lengths and ultimately break. These overlong side trips are neither explanatory nor entertaining. Don't get me wrong. I do not wish mathematics to remain dry and unattainable. Ostensibly, neither does David Berlinski. I so wanted to be able to point to this book and tell others, "See, this is why calculus exists. This is why math is central to every aspect of modern life!" Alas, the book fails in this regard. It fails also in its stated mission to illustrate the formal, stuffy proofs that underpin calculus in a down-to-earth way. Every time such an illustration is attempted, it turns into a bizarre shaggy dog story that is a blend of historical fiction and motorcycle rides. I cannot recommend this book; either as a calculus tutorial, or as entertainment.