Customer Reviews

Single Variable Calculus (Stewart's Calculus Series)

5 star:		(11)
4 star:		(12)
3 star:		(6)
2 star:		(3)
1 star:		(6)

 

 

This book covers the first twelve chapters of the full edition of Calculus by Stewart. I would actually recommend buying that book instead of this one if you are planning on taking up to Calc. 3 because they are similar in price but the full version includes Calc 1, 2, and 3 material.

Anyway, I used this text for both Calculus 1 and 2 in college. The first six chapters cover the course material for Calculus 1: Introductory Analytical Geometry, Limits, Derivatives, Applications of Derivatives, Integrals, and Applications of Intergrals. Chapters 7-12 covers course material normal for Calculus 2: Inverse functions/Derivatives and integrals of exponential and logarithmic functions, Techniques of Integrations, Applications of Integration to Physics/Engineering, Differiential Equations (which we didn't cover), Parametric Equations/Polar Coordinates, and Series. For some reason chapter seven includes different verisons of certain sections but they are basically the same anyway.

Unlike other reviewers, I think that this book was very helpful. It is possible to learn the material if you put a lot of effort into it, which you need to do if you really want to learn Calculus.

I can see why reviewers would find this book difficult to use though. Truthfully, I found the Calc 1 material much more difficult than the Calc 2 material, probably because more of the calc 1 material is based on theory. The section about graphing fuctions using derivatives is especially difficult. It is extremely difficult to take the derivatives of some of the functions the book gives you, let alone find the critical points, etc. Also, some of the maximinization problems are virtually impossible to solve and a number of the related rate problems are very tricky. Finally, I think that I can truthfully say that I rarely solved integrals correctly by the long way (using summations).

Some people think that Calc 2 is the hardest math subject in the world, but I found the calc 2 material much easier than the calc 1 material. The calc 2 chapters deal more with just solving problems particularly limits, integrals, and series, and the "proofs" for equations are just given on the side or in the appendex. You should already know the basics, so there is nothing really tricky here (except maybe integration by partial fractions) and if you put the effort into working problems, you will probably do ok. Calc 2 is all about 1) Learning how to solve problems by recognizing trends and 2) Commiting some formulas and equalities to memory in order to solve problems and learn about applications of math. As far as I can see, Stewart's problems are as good as any to learn Calc 2.

If you plan on studying Calculus in college, I would suggest first buying the book "Calculus the Easy Way" to look over first. It is pretty good; it covers all Calc 1 material and a good chunk of Calc 2 material. I would also suggest buying the solutions manuel to Stewart's text because it is helpful to see how the problems are worked out. My advice is to just put a lot of time into Calculus (no matter what book you use) and you should do ok. Its just math.

Specifically, This book...

Contains many errors, which have been discovered by students.

Offers far too few examples for the student to learn from.

Generally, students who use this book need to consult other books to learn the material.

In the world of introductory physics, there is clearly a division: those who hate Stewart, and those who love Stewart. I, frankly, am neither: but I realize that Stewart's many strong points outweigh the weak points.

Beginners often will find pure theory and proofs alien to their minds, as they are just trying to grasp how to apply what they are learning --- like how they may go about obtaining derivatives and plotting periodic functions. Stewart handles this well: while providing a good theoretical background (he states theorems and proves most of them quite clearly and succintly) he does not inundate the wide-eyed innocent with epsilons and other frightening Greek characters. Stewart stresses some very important and difficult concepts to grasp --- like the many methods on integration involving 'guessing' substitution methods and others ways of integrating which involve understanding what the answer might be in advance by scanning the integral first, etc. Stewart also introduces some differential equations and has a wonderfully long section on series which stress their most useful applications -- the convergence and divergence of series and the Taylor and Maclaurin series representations of functions.

Stewart's text is clear and easy for the student to work through either in a class setting or independently. I should know -- I taught myself Calc II (integration to series) using this book, and now I am doing quite well in advanced calc (integral transforms, partial differential equations, etc). Stewart sets the stage for success.

This book can be easily used by students at any age who have had up to the level of trigonometry.

I feel sorry for the non-math inclined person who has to take an online Calculus course using this textbook. Math teachers rarely teach math the way the math textbook they use explains the topic. Typically a math teacher shows you how to solve problems then (sometimes) shows you why things work that way. This book, like typical math texts, gives a short written introduction to each topic then dives right into full-blown examples with the whys and hows all jumbled together. As a math person, this is workable for me as I can pull it all apart and reprocess it back together and I appreciate the in-depth analysis, but a non-math major could get lost very quickly.

I think the author of this book tries his hardest to make the problems as confusing as possible. Especially the even ones. There are many times when an even numbered problem is extremely difficult, but there is no similar example out of any of the explained odd problems in the text. The only thing I would say is good about this book is possibly one or two of the earliest sections and the cd, which isn't even all that good as far as text book cds go. I guess the people who rated it well must have already had a pretty good handle on the concepts already, but for someone who has never had calc and who is not the best at math, this book just makes things more confusing. Your best bet would be to hope you have a very good teacher, and maybe to join a study group because the book definitely is no help.

this text is hard to understand. A lot of the stuff is unclear. Make sure to get a good professor to explain the book! The book doesn't hold up its own end of the deal.

This is one of the most user-unfriendly textbooks I have encountered. Stewart often presents complex concepts very quickly, with only the simplest of worked examples. This often makes the end-of-section problems bewildering, as the reader has not seen how to approach a given type of problem. Of course, there's nothing wrong with a textbook presenting some problems that require "outside the box" thinking and extension of chapter material, but I think it's a sign of shoddy writing when one's given such little guidance on how to do even simple problems. The book is serviceable for Calc I and very early Calc II (chapters 1-7), since Calc I material isn't nearly as difficult as Calc II. But the later chapters really suffer from Stewart's spartan presentation. Especially badly done are the sections on centers of mass, polar coordinates (especially the area between two polar curves), Taylor's Inequality, and the multiplication/division of power series. I was lucky to have a good professor who cleared up much of the material in lecture, but autodidacts are out of luck. I give this book two stars only because it's written in complete, grammatical sentences, and it does not contain glaring errors.

I was asked to serve on the calculus adoption committee this spring. Over the holidays, I examined some of the texts submitted for our consideration. With each, I started with the presentation of the Mean Value Theorem because this theorem is fundamental to the understanding of Freshman calculus. I was disappointed at the poor presentation of this material in Stewart.

4.2 Mean Value Theorem, pages 234-239

p. 234 Stewart says that "to arrive at the Mean Value Theorem we first need" Rolle's Theorem. This is not true. There are many ways to prove the Mean Value Theorem. I don't like a text that tells my students there is only one way to prove a certain result.

p. 235 The margin comment seems to imply that a student can trust the graph shown by a graphing calculator. The section gives no example to demonstrate possible pitfalls of graphing technology.

p. 235 Stewart says that Joseph-Louis Lagrange was French. This is not true. He was born in Italy and baptized in the name of Giuseppe Lodovico Lagrangia. His great-grandfather on his father's side was French and Lagrange leaned toward his French ancestry. A college text should be more careful when discussing historical facts.

p. 235 The text gives students no idea about the meaning of the word "mean" in the Mean Value Theorem.

p. 235 I find the use of "we" and "let's" throughout the text to be old fashioned and presumptuous. When the author says to a student "we can see" (last paragraph) he is assuming that he and his reader have similar backgrounds. Overall, the writing style is uninviting.

p. 236 Again, in the proof of the Mean Value Theorem, the author claims that "First we must verify that h satisfies the three hypotheses of Rolle's Theorem." As a mathematician, this offends me.

p. 237 I consider the Mean Value Theorem to be the most important theorem in Freshman calculus. The author's statement about the "main significance of the Mean Value Theorem" gives students no idea about the fundamental importance of the theorem.

p. 237 The numbering system in the book would be awkward to use in class. Each section begins anew with Figure 1 and Theorem 1 and Equation 1. The standard convention is mathematics texts is to number Figures and Theorems by chapter, as in Figure 4.1.

p. 238 The exercise set is short --- only 34 exercises. Of these, there are only 3 exercises dealing with trigonometric functions (Exercises 3, 18, and 29.)

p. 239 Exercise 9 I don't like the wording in part (c) of this exercise. As a student, how am I to verify to my instructor that I have "noticed that the tangent line is parallel to the secant line?" I would prefer something more challenging, such as "show that the tangent line is parallel to the secant line."

p. 239 Exercise 22 Stewart refers to a function having "roots." I checked this in the James and James Mathematics Dictionary and Stewart's use of the word is incorrect. Equations have roots, graphs have intercepts, and functions have zeros.

p. 239 I have heard that Stewart has challenging exercises. Yet, I see that two of the more challenging exercises in this set are accompanied by "Hints" that give the solution away.

p. 239 Exercise 33 This exercise is nonsense. On page 118 the author defines "position function" to refer to straight line motion. Yet, it is not given that runners are traveling in a straight line. Don't runners commonly run around an oval track? In such a case, what does the author mean by the term "velocity?" Does he really mean "speed?" The author makes a point of saying the runners "start at the same time." The point of the using the Mean Value Theorem is that the runners travel the same distance during the same interval of time.

Rate a 4 since it is needed (no ESSENTIAL - no punn intended) to accompany the horrible textbook. If your unlucky enough to have your teacher choose this text, then at least you should get this guide - so that you can learn some application of solutions. The solutions manual could be more explanitory - not just expository. An Excellent (5 rating) solutions manual would have provided reinforcement of text discussion (and reference). Unfortunately, this one does not so it gets a 4 rating. ALSO NOTE: only odd number problems are provided (just like the answer guide at the end of the book).

That said, do not attempt this class without this guide - suffer two weekends without beer for the money difference and do your self a favor. GET IT!!!

The Stewart Calculus sequence features worked out examples in the text. The Solutions Manual is important since it gives feedback after trying to solve problems on your own. The Study Guide is also valuable in terms of practice and feedback. The philosophy of the Stewart sequence is, I believe, to combine theory, proofs along with applications and problem-solving. The feedback in the Student Solutions and the Study Guide provides a way to keep the student moving in the right direction. Michael Macaluso, Flossmoor, Illinois.
(These books were puchased at Amazon.)