Essential Calculus with Applications

The book is nicely, and concisely, organized. Based on the topics covered and the explanations presented, I would place it somewhere between typical calculus service course texts and introductory texts on real analysis. As a result it can be used for self-study in preparation for a more applications-oriented calculus course, a prelude to a real analysis course, or a short refresher for those who've had calculus in the past. There is a brief introductory chapter (35 pages) before the chapter on Differential Calculus begins. Subsequent chapters are Differentiation as a Tool, Integral Calculus, and Integration as a Tool. The text concludes with a chapter on Functions of Several Variables. Although this Dover edition includes additional answers not available in the original, the solution section was not retyped. The additional answers are not integrated into the original answer section; they are included, in a different font, as a separate section after the original. This is only a minor issue, but it does require some extra 'page flipping' as answers are checked. However, the additional answer section is of real value for self-study, probably the most likely reason this book will be purchased. Questions range from easy to hard, with harder questions marked by asterisks. Asterisked questions ask the reader to solve problems that are only peripherally related to the section's topic, or where no problem solving exemplar had been previously presented. For example, the reader is asked to find the rational number representations for a set of repeating decimal numbers when the procedure to do this had not yet been discussed. Fortunately, in many of these cases problems have been sequenced so that the results of earlier questions can provide insight into solving later ones. This book was written before the "questions proliferation" juggernaut of recent times. So, although there is the occasional section with thirty or so questions, most sections contain twenty of less well chosen questions reinforcing the section's core concepts, with asterisked questions asking the reader to consider new material. Thus, readers can consider all problems and still complete the book within a reasonable period. In proofs, the author often takes the interesting approach of returning to basic definitions rather than using theorems previously proven. For example, the section on inequalities presents theorems with algebraic proofs that multiplying both sides of an inequality by the same positive (negative) quantity does not (does) change the sense of the inequality. However, in the solutions section, the author often returns to basic definitions for proofs, e.g., a > b means a - b > 0, even where the use of previously proven theorems would have produced more concise results. <br /> <br />There are some minor additional issues: In the section on sets, Venn diagrams are unfortunately missing. These usually prove helpful to those new to this topic. Occasionally,

This is a very neat little introduction to basic single variable calculus that also includes a final chapter on partial differentiation. It's fairly rigorous and would lead naturally into a first course in real analysis. The problems are all fairly easy and many can be `done in your head' (so saving paper) but they are typically not as boring as the usual `follow the method' type problems you see in many of the big introductory calculus texts. Some problems even ask you to construct proofs of simple theorems. This is all good stuff and for the money, who can argue? Given the aims, coverage and price, I don't see how it could be much better - five stars from me.

Silverman's book is much clearer than other books on calculus that I have seen recently. Everything is concise and there is no extra "fluff". Some may wonder about some seemengly strange orderings in the book such as introducing the differential before introducing limits but this serves to help create an intuitive understanding of limits before explaining their mathematical meaning. Otherwise, the problems range from extremely simple to challenging. All of the problems are reachable by just having read the previous section and are not out of the reach of a careful reader. Most of the problems have solutions and / or hints at the back of the book. The book's title includes the word "applications" and the book indeed does contain them. After each chapter on a new topic, the following chapter contains applications. In addition, the last two chapters on differential equations and multi variable calculus are better than in most introductory books. Essential Calculus is suited for class study or for self study and should be accessable to all with high school mathematics under their belt.

I am a graduate student in computer science, and I've forgotten quite a bit of math from college. I picked up this book and made a point to read it over the summer and do as many problems as I could. It is a very "tight" book, in the sense that there is not a lot of fluff (hence the "essential" in the title). The book seemed to maintain a nice balance between too hard and too easy so that I was always challenged. It is a very good book for me, and has a sufficient level of rigor so that I feel like I get some practice in that area as well. I would highly recommend it to someone wishing to learn calculus. In addition, it's always nice to find an author you like, because it usually means other books by that author will be good. As a bonus, it has solutions (or hints) to all the exercises so you can check your progress.

It is awesome that I can find most of the important calculus theorems and their proofs in only 250 pages. The author really shows all the proof clearly. This book is much better than the calculus book that I am using in my class. It is definitely worth more than 10 bucks!