Customer Reviews

Advanced Calculus Demystified

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

 

 

This book deserves 10 stars. It is simply the clearest and easiest to understand math book on a difficult topic that I've ever seen. Out of the over 1300 things that I have reviewed on Amazon, I would give this book the highest rating. I completely agree with Darkman in his earlier review, that the book is so good that you can just pick up anywhere and understand what is being said. I've seen a lot of math books over the years that purported to be what this one is, and were not, most of them not by any stretch of the imagination. As he says, most just cover proofs, which isn't that useful for most people, or try to teach the applied practical side but just make it too difficult.

The problem is that most people who are good at math, good enough to get a Ph.D. and write a book like this, are so good at it that they just don't understand the average college student who doesn't. For some amazing reason, Bachman does, and if all math teachers were like him, math would actually be, if not a popular subject, at least far more than it is now. If you are considering this book, just pick it up and start reading anywhere and you'll see what we mean. It's truly an amazing feat of writing and math teaching and the book is worth 10 times the actual purchase price, in my opinion, in all the time it will save you and all the hassle you'll avoid trying to understand difficult concepts.

Not only that, but the way Bachman presents the subject, despite the overall technical level, he is still able to show you the beauty and elegance of the language of advanced calculus despite that.

Finally, the worked problems are well chosen and very clearly solved and illustrated. I just can't say enough good about this book. I've looked for a math book this clear for advanced calculus and other advanced math topics for almost 35 years. I'm so excited by this book that words don't really do justice, and at my age there's not a whole lot that I get really excited about anymore. They should inaugurate a new Nobel Prize for teaching excellence and give the first one to Bachman so he can retire from day to day college teaching and continue to write books like this.

It's been a long time since I'd learned Calculus in H.S. and a bit in College -- when I needed a quick review, to do a couple of problems that cropped up at work, I stumbled across this book, and boy am I glad of that. Everything is explained clearly -- really clearly -- and sometimes with a touch of humor thrown in that makes the book so much more enjoyable to read.

It was organized so well that I could immediately zoom in on just what I needed, and once I got to the right chapter, the info was well organized, well written, enabling me to review, get my answers, and apply it to the things I needed.

Skimming other Calculus books in the bookstore, they were either too didactic, doing endless proofs (which I didn't really need...) or they were written so poorly that they didn't really help much. (Best way to compare books -- choose one topic, read about it in several books, see which book explains it best... this one did!) It stays true to the title "Demystified".

If you're a bit beyond the intro level, such as in college, taking a math course or a few, this would be a great way to review before an exam, or a great way to get "another viewpoint" that might help you figure out what you're not getting from your dry, dessicated textbook. You should know that this book covers more advanced material than the very simple stuff, but frankly, it handles it so well that I didn't need to review the simple stuff to understand what I needed to. Imagine that -- a math book so clear that you can pretty much pick it up anywhere and just start reading! If you're a student taking "calculus I" in high school, much of this book will be beyond what you want, but you'll be able to understand it.

What's more, I'd recommend it to anyone who is in a field who might stumble across a Calculus idea or problem, such as computer geeks (such as myself), or engineering professionals, etc. Pick it up & if you can't read it now, put it on the shelf -- you'll be glad it's there when the need arises. An excellent book, that "hits" just the right level of review and learning so you can really understand it, and use it.

When you're studying Advanced Calculus on your own you need three things (apart from work and the right mindset, of course:)
-A good intuition about the nuts and bolts of the problems.
-Many, many exercises.
-A source for formalism and other theorems that are important.

David Bachman's book is amazing in that it is the first book i know that can give you the first point and a bit of the second. But! Do not expect to learn Adv. Calculus using this book alone.

Firstly there simply are not enough exercises. Secondly, it has some important omissions (there is nothing about the Implicit Function and Envelope Theorems, which are essential in Differential Calculus).

But if you arm yourself with this wonderful little book (They DO say it's a companion for more advanced texts in the cover), with a good source of solved problems and any regular Calculus textbook and work them over you should be in good shape.

I took a course in vector calculus and linear algebra 15 years ago but was forced to drop out of college and have forgotten most of the material. I am preparing to go back to college and complete a degree, so I want to get caught up. This is not a bad book as a supplement to a good text, but it's not a good text book on its own. I thought I'd be able to use this by itself, but I ended up using my calculus textbook to actually learn the subject matter, then I used this text to fill in the gaps and review.

In relatively few words, and quite painlessly, this book can teach you the core of advanced calculus. The examples are easy at first and never "jump" to an incomprehensible level. The exercises are numerous enough to ensure you get the point.

Not a thorough treatment, of course. That is not the purpose. This book will take away the initial horrors and set you on a course of comfortable understanding. You will "get it". And quickly.

Buy it now.

I bought this book to better understand my calculus textbook, and ended up using my calculus textbook to better understand this book!

The practice problems are very hard to understand. 90% of the problems in this book are worded in such a way that I could not even figure out what I was even being asked to solve. The wording of the problems is very hard to follow, it is very unclear how the information that he is giving you fits into the formulas that are there.

This is a good compact introduction to multivariable calculus. It covers just the essentials, gives barely enough excercises (but you might actually like this) and gives you enough to face the world of applications like physics.
It doesnt provide many rigorous proofs and concentrates on the intuitions.
Personnally I liked most of the explanations, even if they were rather condensed.
I could imagine someone being led by the hand in more detail (if you want more detail try Stroud's book).
Here are my little gripes:
1) I wish the diagrams were more polished. There is lots of wonderful software around there to make the 3D aspect of surfaces stand out really well, the author hasnt used them enough in my opinion. In fact I think a lot of this should be supplemented with videos, printed pages don't do justice to the concepts.
2) I was raised to think of functions as first class objects so that I dont like it when somebody says the function f(x). I prefer talking of the function f. I guess you cant change the curriculum overnight on this point, but I still think it's a valid point.
3) There are a few typos that will irritate the reader.

So it's a fast moving book that covers the field that you could use on its own, but you might want more exercises.

I rarely ever review a product, but this book has so many mistakes that it is driving me nuts. I feel like I spend half my time checking the solutions for errors. Point blank, this book is good for reviewing general concepts and a quick brush-up, but don't pay too much attention to the problems and their "supposed answers"

I can say this because I'm taking Multi-Variable Calculus now and thought I would use this book as a review for the final.

I bought this book to help me in multi-variable calculus calculus class. The subjects that were in the book were great and very helpful, unfortunately there were a lot of things left out. This book would probably be better for a class that combines linear algebra with multi-variable calculus, at my school they are separate classes. We covered a lot of things that were not even mentioned in the book. If you are considering this book make sure to take a good look over the table of contents and make sure it's worth it.

5 stars for quality minus 1 star for quantity.