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Editorial Review Product Description
Aimed at first and second year undergraduate students in mathematics, the physical sciences, and engineering, and written by two authorities in the field, this book will be required reading for courses that follow a 'problem-solving' approach to teaching calculus. The main philosophy of calculus is presented through many examples and applications to explain its abstract notions and concepts. A solutions manual demonstrating the workings of each example accompanies the book. ... Read more Customer Reviews (4) 
improvements in the 2ed
This 2ed (2002) of Saxon's calculus text is a big improvement over their first.The biggest improvement is in the expanded content to include better coverage of AP calculus test subjects.Some subjects (like the treatments & tests for series, Taylor series & polynomials) that were omitted entirely in the first edition are included here, and some that were in the first edition are earlier in this one.Where I was having to augment my calculus lesson material in the first edition, this one seems to fill all those gaps.Some criticisms will still live on, such as my students' frustration that some lessons only include two or three problems from the freshly taught material of that day.That seems to still be true for some lessons in the 2ed as well, but other lessons provide an ample supply of the new problems, somewhat softening the criticism.For those who are excited about graphing calculator usage on exams (a reality we teachers are compelled to take advantage of) this text gives some instruction in that regard. And, as usual, the text wastes no ink on big glossy culturally correct pictures & entertainment; (Saxon is NOT for you if you are looking for visual entertainment in your texts --magazines or internet will serve you better if you have a need to look at pretty pictures).Here you will find solid experiential based calculus instruction --not perfect-- but mostly just as it should be.Those who don't like the spiraling instruction (not arranged in topical units) will continue to not like this book.Saxon adheres to their basic philosophy in this regard; and while I haven't found their approach to be any magic pill for cognitive retention, nor have I found any textbook (traditional or otherwise) to solve that problem satisfactorily. But anyone who has already found Saxon's earlier books to be an adequate help for instructional purposes, should find this edition even more so.It is longer and will probably not get packed into a single high school year, but this does afford a teacher more selection for the classroom time they have.Saxon must have done a good job listening to criticisms of their first calculus book.
--Merv Bitikofer
Saxon is a calculus student's best friend.
Saxon textbooks make learning mathematics easier than alternative approaches. Saxon leverages fundamental pedagogical principles well known to psychologists. Most students can retain no more than a handful of facts at one time. Repeated exposure is required to transfer facts from short-term to long-term memory. Long-term memory forms the foundation of knowledge. Subject mastery relies on knowledge. Problem solving practice is the sine qua non of that mastery, and mastery is the prerequisite for abstraction. Virtually all of mathematics is some form of abstraction.
Unfortunately some teachers and textbook authors ignore these principles, or misunderstand their effective use. Perhaps the best example of this is the misapplication of rigor. Rigor is important to ensure that mathematical propositions are true, but for learning elementary calculus it is an impediment. The reason for this is that the formal definitions, theorems and proofs used are almost always inaccessible to the novice. Basic problem solving is interwoven with the dense, sophisticated notational system of mathematical logic. Often prior knowledge is assumed, and the student has no way to acquire it.
For example, a rigorous description of limits is not necessary to learn calculus. The seventeenth-century discovery of calculus by Newton and Leibniz testify to this fact. The rigorous definition of limits did not appear until the nineteenth century.
This is not a new phenomenon. As Silvanus Thompson wrote in "Calculus Made Easy" a century ago, "The fools who write the text-books of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way." Probably Thompson meant this as hyperbole, but he does identify the rigor problem.
For these reasons, I assign five stars to Saxon Calculus as an introductory calculus textbook.
Great Book
From the standpoint of a 15 y/o homeschooled student: I enjoyed taking this book very much, I was able to understand the whole book without having to look elseware for any instruction from anybody. The only thing I would reccomend for it would be more examples in the explinations.
Unusual in structure, content and order of presentation.
This is a very unusual calculus textbook, in structure, content and order of presentation. In terms of structure, the sections are very short with a large number of problems at the ends of the sections. What is unusual about the problem sets is that explicit review problems over previous sections are included. For example, at the end of section 69 there are problems from sections 47, 26, 68, 50 12 and 18. Since the subject of section 69 is integration by parts and the problem from section 26 deals with interest computation, there does not need to be a logical connection between the two. This is most unusual and I am not convinced that it is of value, in fact I consider it detrimental.
The content is also weak, most of the explanations do not extend beyond the basics. Instructors attempting to provide a rigorous explanation of the principles of calculus will most likely need to find some supplemental material.
Finally, the order of presentation is unusual. For example, lesson 70, which starts on page 361, covers the properties of limits. Rules such as "The limit of the (sum, difference, product, quotient) of two functions is the (sum, difference, product, quotient) of the limits of the functions", are mentioned in this lesson. Since this lesson comes after derivatives and integrals, which are based on limits, have been used for some time, I found the order very odd.
In conclusion, you can teach non-rigorous calculus classes using this book, but the unusual features mean that I would not consider using it as a textbook.
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