Calculus: One Variable

One variable calculus books are almost identical in content and organization. In terms of organization, there is a brief explanation of the new topic of the section, any new definitions or theorems pertaining to the topic, several examples followed by worked solutions and the section ends with a set of exercises. Solutions to the odd-numbered exercises are given in an appendix at the end of the book. This book does not deviate from that organization. In terms of content, the chapters in this book are: *) Precalculus review *) Limits and continuity *) Differentiation *) The mean-value theorem and applications *) Integration *) Applications of the integral *) The transcendental functions *) Techniques of integration *) The conic sections; polar coordinates; parametric equations *) Sequences; indeterminate forms; improper integrals *) Infinite series As can be seen, the content is routine, both in order and in topics. Therefore, the obvious question to ask is, "What if anything, differentiates this book from the other calculus books?" There is no overwhelming answer to this question, just a few minor differentiating factors. *) There is not a great deal of time spent under any heading resembling "Using technology." A few problems at the end of the sections are noted with a calculator symbol, but there is no time spent on teaching how an item of technology is used to solve the calculus problems. While others may not agree, in my opinion this is a major positive. The goal is to teach the principles of calculus. With the large number of topics that need to be introduced in the first two semesters, and the difficulties that some of the students have, spending time on technology solutions is largely a waste of time. *) This book contains only single variable calculus. This makes it easier on the students as calculus books are rapidly reaching the point where they could be used as weights by members of the football team. *) The authors do not engage in exercise overkill, where the exercises at the end of the sections seem to go on and one. Simply adding additional exercises that cover the same material is not an improvement. As a consequence of these positive aspects that differentiate it, this is a book that I will consider adopting the next time that I am scheduled to teach calculus.

Had no experience in calc until freshman year, where I learned from this book. My teachers for Calc I and II both commented about how they felt this was the clearest most concise one variable book they'd taught from. Without a doubt, this book is taught at a very high level. The math isn't about manipulating equations, but building theoretical understanding and providing a solid background for future math study. My university offered two first year calc courses, and this book was used for the one which was intended for expected science/math majors. Through the semesters I spent a lot of time with this book, and while I haven't studied calc with any other real textbook, I have had nothing but great results from this book and would immediately recommend it. Just a word of warning, however; if you do not spend enough time with a text such as this, you will never be able to appreciate what distinguishes it from other books. Be prepared to take your time with the sections.

I got this book (eigth edition) in 1998 and it took me several years to fully appreciate it's contents. I'm not sure what's changed in the 9th besides reordering the problems. This book is for beginners of calculus, but it assumes that a certain level of mathematical maturity has been reached. The authors assume you understand mathematics, not just manipulating equations. The proofs are not that hard to understand IF you understand the mathematical argument. When I first started this book, it made very little sense. Persistance paid off for me and it will pay off for you. You will obtain a deeper understanding of calculus that won't go away after you complete the course. If you're having difficulty understanding the material in this book, you need to take a step back and visualize what the book is saying. As the book says in the beginning, calculus is just high school math with limits.The solutions manual is useful if you get stumped.

Despite the highly theoretical way of writing, this book acts as an excellent supplement either as a review, or as part of a class. The examples are concise and clear. There are many examples detailing how a certain problem should be done. The problems at the end of each section vary between relatively easy and incredibly difficult.