All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides)

Having left school and education many years ago I wanted to revisit the calculus. I found that this book explained it in a way which encompassed the thoughts and perspective of a maths lecturer to the subject. His explanation of how you analyze a problem and what treatments you should use are enlightening. I cannot say how closely this book corresponds to any specific curriculum but I imagine its coverage sufficient to explain most if not all topics within single variable calculus. If you need to get a good feel as to the authors teaching style watching the accompanying videos first might be useful. If I have any criticism it would be with the typos in the eBook version. Other than that it is extremely legible on my kindle and I have no regrets with my purchase.

Adrain probably fixed a lot of issues many writers have, they just write with no understanding. Personally, I don't like to take things at face value, lets say I am slow, so I like concepts explained, there a few people like Adrain who are concerened about really explaining things, I wish I have had this book 10 years ago, thanks Adrain for standing out! I strongly recommend this book, actually, I think it is the only Calculus Book you will ever need. Very impressed with the detailed work as you can see.

CNortey

Disappointed in the limited help offered on my topic of interest, and in his effort for simplicity, the explanation was too simplistic. But this is a bit unfair since my use of the text was very limited.

Awesome book! Being quite rusty in math this has been just the sort of guidance I have been seeking. As I prepare for Calculus in school I am sure I will have a "leg up" on the younger folks in my class. I also own the Calculus problem solvers book which allows me to test my knowledge learned from The Calculus Lifesaver. Overall, Dr. Banner has a great product which allows math to be an easy read and enjoyable experience.

Please note that I bought this book for self study. When it comes to math, I'd like to have 3 things stated objectively:

1. What we are doing.
2. Why we are doing this.
3. How do we do it.

Instead, this book rambles on from example to example, only stopping to tell us what we're doing whenever it pleases; the why's are structured at the end of every point, as if that would lead us to an ah-ha moment. This book is too wordy, not that it is eloquent or gracious in its vocabulary, or that the author seems infatuated with his own delivery, but that it is repetitive and unstructured: the author literally restates very obvious observations multiple times in similar wording, and when I attempt to speed-read through all the excess, superfluous words I tend to miss the meat of the subject which is buried somewhere, one very straight-forward line lost in the details amidst an entire page of nonsense.

I'm beginning to feel that it is books like these that made me require a book like this in the first place. A typical math student reads through 20 pages of head-scratching, seemingly purposeless examples of limit problems leading up to the Intermediate Value Theorem (IVT), thinking what the hell is the point of all this? What am I missing? If x approaches a and f(x) = f(a) and the line is continuous -- what?

It turns out those 20 pages was inserted just to feed some mathematician's ego when he tries to convince you that if a continuous line is drawn between 2 numbers, it must cross all the intermediate numbers! DUH! Well, mission accomplished, I am thoroughly impressed by how hard you've made Calculus out to be.

I'll provide a couple excerpts that I've randomly picked out of the book (the style is consistent throughout).

In this first excerpt, the book tells us how to intuit: "We'll start off by looking at what it means for a function to be continuous. As I said above, the intuition is that you can draw the graph of a the function in one piece, without lifting your pen off the page. This is all very well for something like y=x^2, but it's a little unfair for something like y=1/x. This would have had a graph in one piece except for the vertical asymptote at x=0, which breaks it into two. In fact, if f(x)=1/x, then we want to say that f is continuous everywhere except at x=0. So we have to understand what it means to be continuous at a point, and then we'll worry about continuity over larger regions like intervals. Let's start with a function f and a point a on the x-axis which is in the domain of f. When we draw the graph of y=f(x), we don't want to lift up the pen as we pass through the point (a, f(a)) on the graph. It doesn't matter if we have to lift up the pen elsewhere, as long as we don't lift it up near (a, f(a)). This means that we want a stream of points (x, f(x)) which get closer and closer--arbitrarily close, in fact--to the point (a, f(a)). In other words, as x -> a, we need f(x) -> f(a). Yes, ladies of gentlemen, we're dealing with limits here."

Notice how the author loves prepositional phrases acknowledging his redundancy, such as "as I said above" or "in other words". Notice how he repeated the phrase "without lifting your pen off the page" multiple times within the same paragraph. Note that the formal definition for function continuity follows this paragraph; instead of defining a clear objective at the outset, we are led through labyrinths of unnecessarily complex examples and exceptions, with inexact observations before the author feels like enlightening us with a rule.

Here's another random excerpt that occurs 7 pages after the last: "Let's move on to the second benefit of knowing that a function is continuous. Suppose we have a function f which we know is continuous on the closed interval [a,b]. That means that we put our pen down at the point (a, f(a)) and draw a curve that ends up at (b, f(b)) without taking our pen off the paper. The question is, how high we can we go? In other words, is there any limit to how high up this curve could go? The answer is yes: there must be a highest point..."

As far as I'm concerned, the first 3 sentences are fluff and the last 3 sentences say exactly the same thing. A college student, the intended audience, definitely does not need to be reminded that a continuous line means that we can't take our pens off the page for 7 straight pages and more. It could have been stated more succinctly, as so: "Every continuous line must have a maxima, the highest point in the curve; and a minima, the lowest point in the curve. It is impossible to pinpoint the maxima or minima when they occur on the end points in open intervals." There, I just summarized the next 3 pages in 2 sentences. In other words, the next 3 pages of the book has just been summarized in 2 sentences!

Adrian really went all out when he wrote this book. He effortlessly explains important, and often difficult to understand, concepts, as if he were teaching calculus to an elementary school child.

Central to the outline of this book is a clear explanation of proofs, theories, and conceptual topics. Yet Mr. Banner does not forgo some typical problems you might see on a test (after all, the book was written out of a collection of notes to help students on calculus exams at Princeton University, or so the story goes).

The book alone really does deserve 5 stars. It is too clearly written to confuse anyone. (I have long come to the conclusion that anyone who does not understand calculus after reading this book is either illiterate or incredibly developmentally challenged.) However, if you buy this book, you just can't forgo the video lectures Mr. Banner has posted on the book's companion website. In his videos, Mr. Banner dissects the whole book, going through each chapter and giving the best explanations one can give on such a difficult subject. Not to mention, the lectures are enjoyable to watch just for his incredible sense of humor. What other professor will claim to be possessed by Isaac Newton?

Overall, the book is great. However, a few words of caution are in order. First, this book only covers topics from typical differential and integral calculus courses (close in relation to Princeton's univariable calculus courses, I imagine). So, unfortunately, there is no multivariable or vector calculus involved (perhaps we need to write Mr. Banner on getting a book out for that, too). Second, this really is not ideal for self-study. However, if you've seen calculus before and want to review, or if you're taking a calculus course now, this books is a great supplement. Third, this book will give you the best conceptual and intuitive understanding of calculus money can buy. However, beware that reading this book alone will not help you pass many of the typical "plug and chug" calculus courses you might see today. These extruded calculus courses at the less prestigious colleges and universities strip away much of the need for a firm understanding of what calculus really is or does, so they rely solely on rote computation which you must master through doing many problems on your own. For other usually more rigorous and conceptually intense calculus courses at the more prestigious universities, this book really is A Calculus Lifesaver!

This is the best book ever written on calculus.
The author presents and explains each and every concept in a playful and easy to understand manner.
You have to try hard to fail in calculus with this book in your arsenal.

Thank you Adrian Banner, you're a legend.

I bought a simplified Chinese version of this book (it's a shame that there is no traditional Chinese version), and I still want to buy this one, it is just great.

Of course it is not an textbook, so you can't judge it as a textbook(see those 3 star reviews). It is problem solving oriented book, which is very important, because I believe every calculus student, after they learned some theorem, they still don't have a clue to how to solve any problems(except for trivial ones). This book helps you solve problems, and it is the best one I have ever seen.

But this book alone is not enough, students still need a good textbook, and some problem books. If you don't practice, even this book won't help you. From here on, you can move on to advanced Calculus with ease.

Before I even start talking about the actual book, let me just tell you that this is a steal. I don't know what the publisher was thinking, but a 750 page, recently published book on Calculus never sells for such a low price. On the store it sells for $16, which is a ridiculously low price for this 5 star tome. The average Calculus book is far from cheap, so this excellent guide is a pure bargain. Now, let's talk about the content of the book.

I'm very exigent when it comes to Calculus books and usually like a very formal and rigorous style. Most people don't. Many tend to like accessible books that speak to them in plain English. And this book is marketed as such. This is supposed to be an extra aid, on top of a regular textbook, to make Calculus more accessible. However, it stands on its own, thanks to its comprehensiveness and clarity. If commonly adopted Calculus books puzzle you, or if you are studying on your own, this is the book for you. Every step is clearly explained and it doesn't fail when it comes to covering all the pre-requisites/fundamentals. Thanks to its style and approach, pretty much anyone who's willing to learn, will. I'd even recommend it to high school students who wish to learn more about this subject, because I don't think they would have any trouble following along. The tone is informal, friendly and often even funny, making it one of the least boring math books I've ever read. I highly recommend it to those who are struggling and would like to really understand the subject.

I have reviewed dozens of calculus textbooks, and all are noble attempts at communicating something that is problematic for many students in simple-enough terms to be comprehensible. But most calculus textbooks books fail in their effort at simple communication. This book succeeds in that effort marvelously. The examples are worked through thoroughly so that when the reader has finished a section, he actually understands it. The concept of a function is explained as a sort of "machine" that transforms an input into an output. The concept of a limit is again clearly explained more simply and straightforwardly than I have seen it explained anywhere. The book is nevertheless non-trivial; it is solid and certainly not a "Calculus for Dummies" book. It is an easily understood but substantive introduction to calculus. If you've tried calculus several times using other books and in the end given up because the authors inevitably lost you at some unmarked turn in the road, get this book and give it a one more try. I think you'll find you are impressed with the resulting clarity of your understanding. Adrian Banner is gifted at explaining calculus.

This book is eminiently readable. It's well organized, clear, and even entertaining at times. Its fundamental weakness, however, is its lack of problems. But if you have access to problems/solutions such as in schaums, this book can be very useful. There is also a set of video lectures that are available for free. I watched a few. They are time consuming but provide a painless introduction to the material. If you're learning Calc on your own, the videos following by reading the book would be an effective 1-2 punch.

An outstanding job by the author in explaining the complex subject of Calculus in a simple step by step manner. The narration and graphic detail is impressive. Students of the subject need this book as a supplement to any course textbook because it does a much better job of explaining everything in detail. Many Calculus textbooks are notorious for leaving out details thus leaving many students confused and frustrated. This book is really a gem and deserves the best rating available - five stars.

I am a freshman engineering student and I used this book to help me get through Calculus II. The concepts are explained really well and you don't necessary need to be great at math to understand his simple language. The book was interesting to read and covers everything in the first two semesters of calculus. I highly recommend this book.

Many calculus textbooks are dry and teach calculus without giving the background motivation of why certain concepts have been discovered in a certain order in time and also how these concepts all relate to each other. Dr. Banner has done a great job at shedding light on the topic of calculus as it should be seen by anyone who really wants to understand the subject and walk away confident in their knowledge.

I am taking calculus next year in college and wanted to be a step ahead. I found myself actually enjoying this book and understanding not just concepts but how they were developed. I hope to crush calculus next year with this book in hand.

When it came the shell and disk methods of finding volume this book was far more complicated and left out quite a bit of explanation. It also didn't show you that if you solve for x the disk method is almost always easier than the shell. It's formulas were more complicated and less well explained than my current textbook (Calculus: Early Transcendental Functions). Save your money and get a tutor or a different book.

Awesome book! Being quite rusty in math this has been just the sort of guidance I have been seeking. As I prepare for Calculus in school I am sure I will have a "leg up" on the younger folks in my class. I also own the Calculus problem solvers book which allows me to test my knowledge learned from The Calculus Lifesaver. Overall, Dr. Banner has a great product which allows math to be an easy read and enjoyable experience.