Customer Reviews

Essential Calculus

5 star:		(6)
4 star:		(5)
3 star:		(0)
2 star:		(3)
1 star:		(5)

 

 

When I received this book, my immediate reaction was one of joy and surprise. A textbook for differential and integral calculus that is less than 1000 pages is unheard of in the modern age. Then, I opened it to determine what the others have that this one does not.

*) There are not pages and pages of problems at the ends of the sections. When comparing other calculus books, it has appeared that there is some kind of arms race regarding the number of problems at the ends of the sections. Properly done, 20 -50 problems are enough, hence no loss.

*) There is little mention of a calculator or a symbolic mathematics program such as Mathematica. I applaud this because I don't use graphing calculators. Simple sketches are enough to grasp the ideas, so I don't miss this either.

*) The number of examples is reduced. It is impossible to anticipate all of the conceptual difficulties students will have, so any attempt to write an example for all possible scenarios is impossible. The role of instructors is to answer the questions textbook authors do not anticipate.

The coverage is that of the traditional calculus text, so there is no loss of fundamental content. I am not scheduled to teach introduction to calculus for some time, so at this time I have no need for this book. However, if I were teaching it next fall, this is the book that I would use.

"A three semester calculus book for scientists and engineers" is Stewart's stated goal, and "Essential Calculus" fulfills it without swelling into a back-breaking tome. The canonical topics are developed thoroughly enough for unity and direction, but also distinctly enough toward launching points for other important math classes in the intended audience's quadrivium, such as differential equations, analysis of algorithms, topology, and linear algebra.

Stewart develops the curriculum around functions and the limit. There are legitimate causes for praise and criticism here. This approach is very effective for a structured presentation; physics, computer science, and some engineering students will benefit greatly from the rigor. Future mathematicians might need more, chemists, biologists, and social scientists a lot less. "Essential Calculus" may not ideally serve the practical needs of everyone in the greater STEM community, but I doubt that any single approach can, and Stewart would be unfairly maligned for falling short here. On the contrary, to his credit, he keeps his inner mathematician from running rampant into pure analysis, and abstains from full formal proofs most of the time. Often he presents a basic outline to demonstrate the validity of important equations and refers the reader to appendices or the bibliography if he or she wishes to go deeper. It is sufficient and very appropriate. Key formulas are highlighted and examples are worked out in a sufficient number of steps with clear diagrams. Concepts are (correctly) taught from multiple abstract problems before moving to applications. My only significant gripe is that chapters 9 and 10 are major topic-changers, without any apparent connection to prior or subsequent concepts (including each other) at first. They require a patience that isn't rewarded until late in chapters 12 and 13 respectively. They would probably be better integrated piecemeal, perhaps with an increase in the overall chapter count to avoid unwieldiness. Currently they reflects the mess that is the standard American precalculus class, which in turn reflects the mess that is American mathematics education in general. If you're going through this book solo, it may be better to skip right to chapter 11 and come back as needed.

Section practice problems are superbly scaled. Even within each tier of difficulty, there are those that mimic the worked examples with minor modifications, those that require a better knowledge of procedure, and those which truly require a creative application. I do not like, however, that the separately sold student solutions manual does not work out the even-numbered problems. This supplement is misleadingly different from the full solutions manual, which I could not find bundled with the textbook.

Having cracked my teeth in university on "Essential Calculus," it will always have a special place in my heart. It is not perfect, but simultaneously condensed and nimble, it teaches the calculus core curriculum in a clear organized format on a function/limit foundation, emphasizing the major points in its judicious use and repetition of the important techniques and formulas.

Essential Calculus

Having taught from several different calculus books and been given many more by salespeople eager for me to make a decision to teach from their books, I will admit that I have a different viewpoint about calculus books than most.

There is no way around it. This is a bad textbook for any but the most gifted of students. It's not very good for them either. In general, students learn through doing and not through being "talked at". This is at best a skeleton of a book. The basic theory is covered but not in a way conducive to learning. Having taught more than a thousand calculus students, some who scored 780 - 800 on their math SATs and some who scored in the low 600s, I pity the poor engineering or science student stuck with this book. The explanations are, for the most part, poor, the examples few, and the problems insufficient for adequate reinforcement of knowledge. In reality, being one of those so-called elite students, one who rarely attended classes in calculus (other than those during which examinations were given), I taught myself from an excellent and long since defunct text, one which had more than an ample supply of examples and problems. A saleswoman sent me a copy of this book, I pored through it, and came to a simple conclusion. I cannot conceive of a class, either one of average students at a state university or the very elite of the Ivy League for whom I would choose this text. I have heard it praised to the skies by mathematicians, but those were mathematicians who either had never taught or who, in the case of professors and graduate students in mathematics, had never taught well. The two star rating was probably excessive, but Stewart does cover material skipped in other texts. It's does poorly, but it's done. The first star was required by Amazon for those who would write reviews, so consider this a one on a scale of zero to five.

Returning to school after many years' absence, the university required me to re-take calculus and other courses to prove that I could keep up. Having received an "A" in two calculus courses, a "B" in another, I re-started the series without too much worry. WRONG. This text does not explain fully, let alone in depth, any concept so far this semester. The few examples that are covered often do not match the problems presented at the end of the section. Thompson's claim of having taken material out of his text and put that material on his website is a joke at best. Skeletonized is the best word I can think of for both the text and the offerings on the web. Thank goodness I had a couple old texts laying around that offered clear, concise explainations of concepts and to-the-point examples.

Perhaps all of this could have been dealt with if the professor had presented examples of problems during class time or gone over the homework once it was returned. That is not his policy. His only suggestion was to go to the Engineering Tutoring Center and do my homework there. With four children and a husband at home, and a job, that was not an option.

So, all in all, I gave the book a 1. Maybe an E for Effort, but you can never have too many examples nor too many problems to practice on before an exam. Thompson's text left you wanting.

I'm not the best math guy in the world but I want to learn and this is not the book to learn with. Calculus in not easy to begin with and it helps if you have a good instructor, but this book treats the student as if they have mastered the subject. The examples are nowhere close to the exercises and there is not a lot of explaination. I like to to see A, B, C, and D, not just jumping from A to D. I still go back to my old calc books for reference. This book may be smaller than my first calc book but is sure lacks the material!!!

This book is not student friendly. The examples in the book are not worked out completely; for ex, they will ask a question, and show you about 10% of the steps you need to take to arrive at the solution. So if you are not very good in math, you will not see all the steps they took to get to the end, leaving you lost and frustrated. This book does a poor job at explaining everything.

I'm not good in math but I was willing to put in the effort and the only way I passed Calculus was from going to the math lab everday and studying with tutors at my school, not from this textbook.

I can't help think that people who write negative reviews for this book wouldn't like any calculus book. Perhaps they do not appreciate that calculus is one of the most challenging endeavors of the human intellect and requires extensive time and sophisticated thinking to properly digest.

I've read multiple calculus books (Stewart, Thomas, Edwards & Penny) and Stewart, even in this compact version, is the best at clearly revealing details of the subject.

The book sucks in every way, shape, and form.It doesn't go in depth and make sure you understand concepts. It just presents ideas and moves on to the next one. Don't waste your money. If you want a good calculus book, buy anything written by Larson.

I bought this book for my Calculus I class, which I was very excited to take. I eventually dropped the class to take a different section where the professor didn't use this book. Smartest decision I've ever made. Since then, I've found out that my current professor is considered the hardest in the mathematics department, and even so, I've got an 'A' in his calculus I course. I doubt I would have made a 'C' in the other class using this book.

The book just doesn't relay the information very well. I can read the same sentence five times and still not get what the author is trying to say.

He focuses a lot of time on proofs and theorems, and very little time on application.

This book is probably great for pure mathematics majors, as I think that's the audience this book is geared towards. However, I would NOT recommend this book for any science or engineering majors, such as physics, chemistry, chem. e., m.e., e.e., etc.

I am a chemistry major, so I have to give this book two stars. If I were a mathematics major whose main joy in life was proving things, this book would probably get a much higher rating.

Basically, if you need to know how to use calculus, then do not buy this book, but if all you need to do is prove that the theorems are true, then this book is great for that.

Frankly, I'm not sure what significant differences Stewart has made, compared to his other books, as I've not encountered those. But considering this book as a standalone entity, then the material is skilfully presented. With ample examples that are thoroughly worked out. Plus, there is a plentitude of exercises that the reader is urged to tackle.

The rigour of the theorems is not at the level of Spivak or Apostol's texts on introductory calculus. But those are aimed at maths majors. Stewart's work is best suited for students going off to major in science or engineering. It lacks the epsilon-delta approach pioneered in the 19th century. But the infinitesimals viewpoint is perfectly adequate, and is probably more intuitive to many readers anyway.