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

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5 Reviews

1. With a week to go in Calculus II, I needed something to supplement my course’s required textbook in order to be successful in the course. The textbook for the course seemed to focus too much on reinforcing concepts from previous chapters at the expense of learning new concepts. For example, when learning Sequences and Series, my course’s text would put in challenging integration by parts of trig functions when demonstrating how to use the integral test for evaluating the limit. It is great to have challenging exercises to reinforce technique, but I would prefer a few more less challenging problems that demonstrate new concepts before making them more challenging.

   By enormous contrast, Prof. Banner’s book is concise and to-the-point when explaining new concepts. When there are prerequisite skills needed, he cross-references earlier parts of his book. In his introductory material, he has a table of what sections to focus on in case you have an upcoming test (this is what saved me).

   After checking this book out at my university library, I went to his website and discovered several videos that summarize his book. The videos are in the same style that you might find at MIT’s Open CourseWare site. The fact the Prof. Banner and Princeton University put these videos out to the world for free is the full reason I decided to purchase his book. It is least I can do to thank him for his talent and selflessness.

2. This book helped a lot for my calc class in college! very happy i purchased it!

3. Fantastic book for any calculus student. I found the explanations far superior to any I found anywhere else, including 4 different calculus textbooks. Highly recommended!!!!!

4. There are a few things to note about this book:

   1) It covers two semesters of calculus (math 103 and 104 equiv. at Princeton).
   2) It’s accompanied by about 48 hours of online video lectures, available at the book’s website, via princeton.edu. These lectures are of a “calculus review” nature, and are not the primary lectures for a calculus 1 or 2 course.
   3) Those seeking a calculus review or a supplemental helper to an existing calculus course will benefit most; those doing self-study will likely need additional material, especially for practice and skill building.

   STRENGTHS:

   – Comes with ~48 hours of online video supplement.

   – Explains most first year calculus concepts in an accessible manner; there are a full two semesters of material in this book.

   – Concepts are accompanied by worked examples.

   – A value at twice the price for anyone seeking a calculus refresher or a supplement to an existing course/text.

   WEAKNESSES:

   – Lacks progressive reinforcement of many concepts; the reader is generally referred to previous chapters/sections for review.

   – No practice problems or skill building exercises; only one worked exercise per variation is usually provided.

   – Could benefit from a few more diagrams amidst descriptions and notation.

   BOTTOM LINE:

   – If you are currently enrolled in calculus or looking for a review or a reference, chances are you’ll love this book (note the 5 star reviewers).

   – If you are a solo student looking for a replacement for classroom study, you may find this book a little less than satisfying.

   It’s from the perspective of self-study that I write this review; I used this book as a primary source for learning calculus. In the interest of full disclosure, I’m still about 50 pages from finishing.

   While The Calculus Lifesaver definitely teaches the material in an often accessible manner, there are some issues. The main drawback is a lack of practice problems. While there are lots of examples, many of which are dealt with in a step by step manner, typically there is only one example given for each variation or problem type. This means that the reader will sometimes be plunged headlong into a problem type, when a gentler approach would have been more helpful. Fortunately following the online video lectures will ease much of this.

   Let me just say that calculus is hard. It is hard but not impossible. This is coming from someone who began with basic algebra less than two years ago. Often calculus subjects take time to sink in, so expecting to cover 20-30 pages per day is not reasonable for anyone broaching calculus for the first time (some days I could barely do 5). Be patient and give concepts time to assimilate. Often a day or two after banging your head against the wall can make all the difference. If you’re having trouble with the material in the book, shift gears to the video lectures. For me, this often made a big difference in my ability to digest the material. I prefer seeing and hearing first (then sleeping) then review and problem solving via the book.

   A review like this will generally depend on how well the reader believes they are learning, even mastering the material. For me, working through The Calculus Lifesaver cover to cover, I often found myself lacking confidence in my ability to solve calculus problems. And although there are many diagrams, more would have been justified. Often I had trouble following the descriptions and notation, where most likely a few more illustrations would have helped. For the first part of the book, chapters 1-17, I followed up by studying Paul Dawkins’ online calculus notes, available at tutorial.math.lamar.edu. These were very helpful for practice problems, not to mention a different perspective on notation and proofs — there are also cheat sheets for trig identities, derivatives, and much more, and everything is available in PDF format. I intend to use Paul’s notes for calculus 2 as well (essentially chapters 18-30 in TCL) which I’ll begin shortly.

   There is no doubt that The Calculus Lifesaver will teach you the concepts of calculus, and make digesting other calculus material much easier. However, it’s unlikely to be sufficient as a solo guide unless you’ve taken the subject in the past. In that case it will make for terrific review and a great reference. This book will best benefit those who are already enrolled in a calculus course, and are having trouble with their text or teacher. For those going solo, it’s still a good book, but it doesn’t quite stand on its own.

5. I have a wide array of calculus self-help books riddling my book shelf — half of them have not been opened. Luckily, this book is not so heavy to weigh down my bookshelf more than any other book.

   “The Calculus Lifesaver” was one of the few calculus books that I opened and began to peruse. As a self-learner who has never taken a course in calculus (my previous experience was trigonometry), I found the book to be somewhat daunting.

   The explanations are rather inconsistent: they tend to be concise and easy to understand at times; they can also be long, tedious, and circumlocutive, making them difficult to follow for the lay. Even though there are a handful of examples, they don’t show up until the middle chapters of the book, after derivatives and differentiation. It would be better if the book had more examples and illustrations early on during the two crux of calculus in order to familiarize the reader before moving onto more advanced topics. Because of this, I am struggling to get past chapter 9.

   There are some good points about this textbook. First of all, this book will appeal to people who are already in or trying to rekindle a relationship with calculus. The explanations are explained in such a way that the reader should have a loose grasp of the concepts of calculus. Also, the author tries to make the text entertaining by injecting a dose of humor every now and then. The symbols let readers know what to expect from the text, so if they see an example, they won’t confuse it with a principle.

   Right now, I am reading “Calculus Made Easy” by Silvanus Thompson and “The Humongous Book of Calculus Problems” by Mike Kelly, hoping to get more confident in calculus before coming back to this book.