Customer Reviews

Calculus: Single and Multivariable

5 star:		(6)
4 star:		(3)
3 star:		(5)
2 star:		(4)
1 star:		(7)

 

 

I have a Ph.D. in math and teach at a college in California. I compared the Hughes-Hallett book with 7 other calculus books: Anton, Edwards, Larson, Rogawski, Smith, Stewart, Thomas. Here are some concerns with the Hughes-Hallett book.

This book is missing the following topics: reciprocal trigonometric functions (sec x, csc x, cot x), squeeze theorem, logarithmic differentiation, sketching graphs by hand by using derivatives, telescoping series, curvature, tangential and normal components of acceleration, line and surface integrals over scalar fields. All the other 7 books include these topics.

Six series tests are crammed into section 9.4. None of the other 7 books cram all six of these series tests into one section.

The Root Test for series is embedded into two homework problems. All of the other 7 books include the Root Test in a box within a section.

Planes (12.4) are discussed before talking about vectors (chapter 13). All the other 7 books discuss vectors first and then use vectors to develop planes.

Center of mass multiple integral formulas are embedded into the homework problems. All the other 7 books explain center of mass multiple integral formulas within a section.

The preface reads, "Students are expected to use their own judgment to determine where technology is useful." All the other 7 books make it clear when the students should use technology.

The preface reads, "There are very few examples in the text that are exactly like the homework problems. This means that you can't just look at a homework problem and search for a similar-looking `worked out' example." Many students learn calculus by seeing `worked out' examples.

Instructors: If you are considering adopting this book, then you've been warned.

Students: If you have to use this book, then go to class, do your homework, and good luck.

Hope this information helps.

Dr. Chuck

(Commentary below refers to soft cover Third Edition.)

For those of us who learn by example and who need more active guidance through difficult material, this book falls short. It appears to be a deliberate design strategy of this book, to under-explain then over-exercise. This is tolerable until one gets to integration, where the sink-or-swim approach will result in many unnecessary drownings.

Stewart seems at least a little better in this regard, and I note that it is replacing Hughes-Hallett in my school.

One could hope some day for a text written by someone who had enough trouble learning the subject, to be able to remember the value of a patient explanation.

No, 8 pages (including the exercises) are NOT sufficient to explain algebraic identities and trigonometric substitution in integration, except to a bright student with a fresh memory of trigonometry.

The physical weight of this book is burdensome, and the price is symptomatic of the shameless shakedown racket that American textbook publishing has become. Some Web research reveals that a typical price for a German university mathematics text is under $50 equivalent.

I teach mathematics and computer science at a small college, so I examined this book for possible adoption as a text in our three class sequence in calculus. Since it does cover calculus all the way through flux integrals and the calculus of vector fields, there is certainly enough material for the sequence. One characteristic that I approved of was the lack of "using technology" segments.

In this area, I will be the first to admit that I am of the old school, even though I have taught a course in programming with Maple and am a heavy user of Mathematica. The reason why I disapprove of using these programs in calculus is that the students have enough on their minds without having to learn how to program a symbolic mathematics package. Learning calculus is very hard, all mathematics, especially calculus, is not a spectator sport. Some people liken it to a contact sport, as it can be very exhausting to learn it. Forcing the students to simultaneously learn programming is in my opinion too much to ask. There are plenty of exercises and solutions to the odd-numbered ones are included.

However, I will not be adopting this book or recommending that it be adopted. I do not think the depth of the explanations is adequate. For example, on page 50 there is the epsilon-delta definition of a limit. After that, there is only one example (limit of 2x as x goes to 3) of how this definition is used to determine a limit. On the next page there is a theorem listing many of the properties of limits but no explanations as to why they are true. Proofs are largely nonexistent, the pedagogical style is to say, "here is something that is true" and then go immediately to an example of how it is used.

I will readily concede that if that is your style of teaching calculus, then this book will work for you. However, if you want to occasionally give a true proof-style explanation as to why a property holds, then you are on your own.

This book was written to make the teachers job easier by providing large sets of problems and lots of questions. The real issue is that most schools, or students for that matter, do not have the time or resources to ask or answer the number of questions, mostly in the form of grey areas, which this book introduces.

So back to what everyone else is saying about this book. It's missing patient examples with fine grain explanations of how to apply sometimes convoluted steps in solving a problem. I don't feel the material sticks as well when my own theory of the material is the only supporting detail. I am sure the author thinks it's the teacher's sole responsibility to provide the details where they are not given in the book but this is back to paragraph A) of my review. I have learned many programming languages and material by reading books and apply what I learned in those books to real world problems or inferring a solution to a problem from what I learned out of the book. Learning and understanding key concepts is the first step, then throw us into the water.

My best advice for students that are required to use this book is to find the tutor's solutions in PDF form, if you can. The tutor's solutions have the full solutions to ALL of the problems in the book (even odd) and the solutions are very well written. The solutions PDF has been the most valuable tool in cracking the enigma.

I was required to buy this book because of my Calc II class, and I must say it was rather horrible. As my teacher was incompetent and simply took samples out of the book and did them on the board, I found myself relying on teaching myself the material out of the book. Unfortunately, the amount of explanation in the text is... minimal, at best. It usually just says "This is what you do, and it works because it's MATH." The examples skip a fair number of algebraic steps--great, if you remember every bit of your middle and high school math classes, but very confusing if you forget anything. I ended up failing the class because I couldn't learn an adequate amount out of this book.

I used a different book for Calc I, and this can't hold a candle to it. If I was unsure of something, I could read the start of a chapter and understand it. This book, more often than not, leaves me more confused than when I started.

It was a nice value, having bought the book new, that I was able to use it for three classes. The book itself, however, needs a lot of help. I agree that it does under explain and then do a lot of examples. The problem is that the examples are often nothing like the exercises in the book. They are often oversimplified or overly complicated compared to the exercises used as homework. The student solution manual is good for what problems it has. But with only every other odd, there are not nearly enough.

Mathmatica is used with this book. Which is nice, if you enjoy using a computer program that is not as good at a TI-89 graphing calculator.

I used this book to teach myself.

It was very difficult going. Concepts are introduced, then some examples are shown. Then comes the hard part - extensive questions of ever increasing difficulty which ultimately require the student to think, and think hard and then think very hard. In particular the solution to problems is not necessarily given in the text, so that you cannot simply flip back a few pages and find out how to solve a problem. The means to deduce the solution is given, but the student will have to carefully think through what is known and what is not to find answers to the exercises.

The exercises themselves cover many disciplines - pure math, physics, social sciences, medicine, etc. As a consequence, the student gets a sense of the usefulness of calculus in solving problems over a wide spectrum of applications.

I would not recommend this book if you are at all shaky in pre-calculus concepts. It does not spend much time on these, and you could easily find yourself at sea with the more difficult questions.

The price is a [bleep]ing outrage.

If you're buying this book for a class, my advice is that you attend your class everyday, take notes and pray for an awesome professor. This textbook has terrible explanations for everything and the examples they use to help you learn usually do not apply to the problems they provide you. Do not buy this book if you plan on teaching yourself calculus. The only nice thing about this book is the large variety of problems they provide you with for each chapter. I think the chapters on derivatives and integrals will give you about a hundred problems each to work on.

If you are looking for access to WileyPlus to be included with this book, do not purchase this item.

Even though the product description clearly states, "Readers will also gain access to WileyPLUS", they do not give you access. It does not say that Readers may also gain access for a fee. There is nothing in the listing of this book that says anything about purchasing WileyPlus separately.

Amazon will not stand by their product description.

In fairness to Amazon, they did offer to give me a refund. Since my son is at college now and needs the book, our options are limited and we will not be able to return it for a refund.

Since I can not count on Amazon to describe their products accurately, I have no other option than to look other places for products.

If I had to learn solely from this book, I would not know anything about calculus. This book is a great tool for professors to supplement their teachings, but not very good as a stand alone if you are trying to learn on your own. There are lots of examples throughout many of the chapters that skip crucial steps and of course the even problems are much harder than the odds which have answers in the back. I'm mostly glad that this book covers three semesters of math credit at my community college.