Customer Reviews

Calculus: Graphical, Numerical, and Algebraic

5 star:		(3)
4 star:		(1)
3 star:		(3)
2 star:		(1)
1 star:		(3)

 

 

This text has simple examples that are only moderately easy to follow. The problems, on the other hand, are extremely difficult. There is no bridge between the two. The index is not particularly good. The explanations are obscure. The text spends too much time on theory that I suppose is interesting to mathematicians, but just gets in the way of learning about derivatives and integrals and their uses. I truly detest this book and find it a misery to deal with. My child's teacher was sick for the first half of the year, so I was thrust into the breach. I graduated from college magna cum laude with a Phi Beta Kappa key, I took Calculus and made an A (many years ago), I am a CPA with an MBA. My difficulties were not because I am dumb and not because I wasn't trying.

I used this textbook when I took AP Calculus. I recall not liking it very much -- my mathematics preparation was poor, and I struggled to understand the precise statements of definitions and theorems. It didn't help that at the time I was only concerned with what would be on the AP exam, naively believing that a 5 on the AP course represented mastery of an equivalent college course.

Revisiting this book years later, having taken college math classes where it's sink or swim -- and you sink if you don't read the textbook -- I appreciate this book a lot more. It is fairly rigorous but never too much so, and there are plenty of practice problems and examples. My only regret is not actually reading this book when I was in high school. Like many calculus students, I went into the AP exam very skilled at doing AP problems, but I didn't truly understand calculus. I could compute integrals or solve related rates problems with the best of them, but I wouldn't stand a chance if anyone were to press me on my foundations (luckily, the AP Calc exam didn't). It didn't help that my teacher knew very little calculus himself and let theory fall by the wayside in favor of computation. I hope that current AP Calculus students learn from my mistake and take things like the Mean Value Theorem and the Fundamental Theorem of Calculus seriously -- this book proves these theorems carefully, but it's all too easy to skip the proofs and jump to the examples.

I was not alone in finding this book difficult to read as a high school student -- my classmates then and my students now have expressed similar opinions. However, this text is much more informal and accessible than any mathematics text I used in college. Being able to read technical exposition on one's own is probably the most important preparation one can have for college, and the exposition in this textbook is fairly user friendly. Students will struggle at first if they, like me, are accustomed to being spoonfed formulas by their math teachers. Nonetheless, this book is accessible enough that a mature high school student who is not used to reading math textbooks CAN pick up the skill by reading it carefully.

As much as I find the explanations in this textbook perfectly clear now, I realize that it is easy to find something clear when you already understand it. I can sympathize with the high schooler who is seeing power series for the first time and trying to understand the terse explanations and notational subtleties in this text. Some of the concepts are crudely explained, and the book gets too carried away with graphical arguments at times. The ridiculous number of "try graphing this to see..." investigations come at the cost of additional examples and clarifications for students who actually want to use the text as a reference. I also don't understand why certain homework problems are marked as "Work in groups of two or three" when they seem no more conducive to groupwork than other problems.

The quality and depth of the coverage of topics vacillates. Ch. 1 reviews relevant algebra and pre-calculus topics, and is well-suited for summer work. Limits in Ch. 2 is treated exceptionally poorly -- the book provides the standard theorems about limits, but it fails to discuss any techniques for evaluating limits that are computationally useful. The limits in the exercises can be evaluated by direct substitution! Where, then, are students supposed to learn that you can cancel common factors in the numerator and denominator when evaluating limits -- a technique that is imperative for computing a derivative from the definition?

Chapters 3 and 4 do a great job of introducing the student to derivatives and then their applications, and Ch. 5 is an excellent treatment of the theory behind the Riemann integral. Ch. 6, however, is where it begins to fall apart. The chapter is titled "Differential Equations and Mathematical Modeling," but its sections include "Integration by Substitution" and "Integration by Parts," which don't seem particularly relevant to differential equations -- or mathematical modeling, for that matter. I would have preferred that these techniques of integration be grouped with the others, such as partial fractions and trig substitution, which somehow ended up in Chapter 8. Ch. 8 is another oddball -- what exactly is the unifying element of a chapter entitled "L'Hopital's Rule, Improper Integrals, and Partial Fractions"? It's almost as if the authors realized at the last minute that they forgot to cover these three topics and threw them into one chapter.

I am nitpicking, and really, I do quite like this book. It doesn't try to dumb down the math like some recent calculus textbooks (I especially like the appendix on epsilon-deltas!), and the exposition is quite clear. Nonetheless, this book would be much improved if it abandoned the gimmicks, stuck to the math, and presented the material in a more methodical fashion.

a very nice book if you are using it in a course, but not a good choice for self learning. The contents are solid but lack of explanations.

If this were a novel, I'd love its exposition: all show, no tell. Sadly, this is a Calculus textbook that gives examples, but seems not to care about explaining the topic. If it just did a poor job with its explanations, that'd be one thing, but it seems to leave them out altogether at certain points, and at others, presents a concept via an example before the explanation.

I am currently a senior in High School, and I am in Advanced Placement Calculus. The textbook we use is the next edition of this text, but the textbooks are pratically identical, so i decided to comment here. This text is designed to be an introductary text. Introductary texts teach you concepts that you should be able to understand how to use. A lot of these concepts are too advanced to be explained in an introductary course, so they are omitted from the text. Learning math is just like learning anything else. You must first learn how to do it, and then you must learn why you do it. This text tells you what to do with minimal explations because long explainations make readers lose attention and the why would be gone anyway. One other thing that this book does is it gives previews into the next section. Obviously, concepts build upon one another, so some of the problems in the exercises are designed to try and make you think outside the box and get a glimpse into the next section.

This book is extremely clear and concise in explaining the basic level calculus. The addded instruction on how to use calculus on a calculator is a nice touch and ensures that the book is up to date. the organization of the material is logical and the difficulty level is perfect for a teacher to teach. It is a good text.

Calculus is far from difficult. It's different, but not difficult. In an attempt to be terse, this book loses all of the things essential to getting a student to understand calculus: good examples, explanations, and a logical progression of difficulty. There are many ways to explain a mathematical concept, but you're lucky if you get a single coherent one out of this book. It needs to be supplemented so much -- to the point of it being just plain useless. I'm all for lighter, briefer textbooks, but not when brevity impedes on quality. It's sufficient for getting a student to pass the AP exam, in some cases, but that's not the goal. The goal is for students to understand calculus and, more importantly, better understand mathematics as a whole.

I am currently a senior in high school working my way through this book for my AB Calculus class. All I can say is that this is the crappiest textbook I've ever come across in my life, and I mean it. The concepts are presented poorly with very few examples. The examples that they do give are hard to follow and often times will not help you with the problems you will soon encounter. As life would have it, my math teacher is of no help either, which only makes things worse. If you know you will have this textbook for Calc beforehand, heed my warnings and learn from a different book if you can. Save yourself from this nightmare that will haunt you for the rest of your life.

If this book were just merely a math workbook, I would rate it five stars.It is obvious that the professors who wrote this book are geniuses and truly appreciate and love math. However, they made the mistake by assuming that all their readers are also experienced with math. Math teachers, professors, and Einstein will appreciate this book- not average students who are taking calculus for the first time.

The examples given by the book are few, and what few it does give focuses on the simplest problems while the work problems are very difficult. Don't get me wrong- I'm not complaining about the difficulty of the problems. I know we have to be challenged to do well. HOWEVER, if the authors put in such difficult problems, they should at least provide more examples! This book is confounding and frustrating. It will guarantee that students get stuck.

This book also does something very very funny, which is why I say Math teachers and Math professors are the ones who will enjoy this book- this book gives more proofs than examples! That's right, it wastes space on giving students PROOFS instead of EXAMPLES. That's great, but calculus class was designed to teach students how to solve calculus problems, not to learn how to prove or create equations.

In other words, this book was written for Einstein. I would rate this book one star if it didn't give such great work problems. It would make a great work book, but not a text book.

This book seems tailored to the AP Calculus examination (the preface clearly states the content of the book reflects the AP philosophy), but it seems to be the equivalent of Calc I and II courses.

The explanations, as another reviewer mentioned, are practically nonexistent. Rather, this book relies essentially on a few meager examples to "explain" the methods of calculus with a few explanations of the examples. While this isn't horribly bad for all topics of calculus, I do believe some of the more difficult topics (for instance, Taylor and Maclaurin series) could have been explained better.

The exercises are variable for the most part. They range from the routine to the fairly challenging. There were some problems however, especially in the series section, that NOBODY in my AP Calculus BC class (even us with 750+ Math SAT scores and A's in the class) could solve. I understand that exercises are meant to challenge the student and make him/her make new and interesting connections, but the main problem is that this book doesn't even lay a foundation down for those connections to be made.

So I say to all potential self-studiers and teachers looking to pick out a textbook for their caluclus class to NOT buy this book. The equivalent to this book, "Calculus of a Single Variable: Early Transcendentals" by Stewart, is a much better book with better explanations, better exercises, and is just going to give a much better foundation in calculus to the diligent student.

I gave it 3 stars because I feel that it is "competent" and will probably work fine, but you can do better if you're going to hand over $100 for a textbook.