The Calculus Lifesaver by Adrian Banner Review

Taking a very causal and easy to understand approach, Banner has created a complete guide for any introductory calculus student.  This book really does have all the tools you need to excel at calculus.  It is titled appropriately I would say. 

More important than that though, is that this book is put into simple terms making it easy to understand.  It is common to see calculus textbooks that use technical mathematical language to explain complicated concepts.  The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides) by Adrian Banner is not one of those books.  Adrian Banner uses casual language that is easy to understand.  I think this is important because anyone that is trying to learn calculus topics for the first time would not be an expert on the technical jargon in order to make sense of the concepts as they are described in some other textbooks.

How much does The Calculus Lifesaver cost?

The Calculus Lifesaver is priced very reasonable.  Below is the pricing available at the time of this writing, but you can confirm the updated cost on Amazon by clicking here. 

You can purchase both the e-book and paperback version of this book on Amazon for under $20.  The price for ebook and paperback tend to stay fairly consistent, whereas the hardback price really ranges. If you prefer hardback instead, it will cost you a little bit more, coming in between $20 – $80.  If you want to get access to this book for even less, Amazon does offer it used and to rent if you only need it for the term you are taking a calculus class.

Who is this book not helpful for?

Although this casual approach can be great for someone learning the basic concepts on which calculus is built, this could be a negative for a math major who will need to go more in depth or someone trying to develop a deeper understanding of the theory or thought behind the math.  If you are interested in proofs and understanding how calculus was derived, this probably is not the book for you.

Another downside of this book is that it does not contain collections of problems at the end of each chapter.  It is not packed full of practice problems for you to practice the concepts discussed in the chapters.  There are certainly problems that are solved by Banner throughout the book, but there is not a ton of problems that you would be able to do on your own.  It is more of an explanation of the concepts you need to know as well as an explanation of how to apply them.  Then you would be left on your own to find problems that you can get some practice with.  It does fantastic job at breaking down all the tools you need to know to excel at calculus and how to apply them, then sends you on your way to go get the repletion you need elsewhere.

Fortunately, there are other options out there to get the list of practice problems.  One option could be to look in the required textbook for your course if you are enrolled in one.  If you are not taking a calculus class though, there are other books that you can get that are just books of practice problems.  If you pair one of those with The Calculus Lifesaver, you should be set to make sure you know the concepts you need and get the practice to really get it down solid.

Who is this book perfect for?

Like I mentioned before, Banner takes a very casual approach in this text.  He does not focus on the technical mathematical terminology that most textbooks focus on much more.  This fact is certainly a positive for someone learning calculus for the first time.  If math is not your major and you are taking a calculus class for general requirements this could be the perfect book for you.  It’s the perfect bridge to get you from being new to calculus to understanding the complex explanations in the textbook you may have already had to buy.

For example, at one point in this book, Banner writes, “perhaps you’d like to say that f(2)=1, but that would be a load of bull since 2 isn’t even in the domain of f.”  This is just one example that illustrates the casual approach Banner takes in The Calculus Lifesaver.  And there are many more.

And I am not trying to say that the technical terminology in math is not important.  I think it certainly is.  But it is usually helpful to understand the concepts before trying to build on that with a more in depth understanding of the language and terminology.  When you are learning about a brand-new topic in math, it can be easy to get distracted with the terms.  And this can prevent you from putting more focus on the general concepts that you are trying to understand.  This may make you feel like you don’t understand the concepts you are trying to learn, when in reality you would understand the concepts it they were explained in terms you already understand.

This pickle is completely avoided thanks to the casual approach in The Calculus Lifesaver.  Banner ensures that the language is simple and straight forward so you can easily understand the thinking behind the actual math.  It is done brilliantly.

What topics are covered in The Calculus Lifesaver by Adrian Banner?

The Calculus Lifesaver covers topics that you need to know in calculus 1, 2, and 3.  You know you will really be able to get some longevity out of this book if you need to take multiple calculus classes.  It’s always great when you can buy one book that can be used to help you through multiple courses.  This is not a comprehensive list, but some of the main important topics covered by Banner in this book are:

  • Functions and review of prerequisite material
  • Limits and techniques for evaluating them
  • Continuity
  • Derivatives and different methods to find them
  • Optimization and linear approximation
  • Implicit differentiation and related rates problems
  • Definite and indefinite integrals and how to find them
  • The Fundamental Theorem of Calculus (FTC)
  • Improper integrals
  • Basic concepts of sequences and series
  • Taylor Polynomials, Taylor Series, and Power Series
  • Polar coordinates and how they relate to topics of calculus
  • Volumes, arc length, and surface area
  • Differential equations

Final Recommendations

I strongly recommend this book for anyone that is a non-math major taking calculus classes because they need to for their major.  I would also recommend this book for any high school students taking AP Calculus AB or BC or taking IB Math SL or HL.  It may be more applicable for an IB Math HL student than SL, but it would certainly be helpful for both.  I think this book would also be immensely helpful for someone who is trying to learn calculus without having enrolled in a high school or college calculus class.  The casual approach is perfect for anyone that is trying to get a grip on the basic concepts taught in calculus and how to apply them.  Click here to go get yourself a copy of The Calculus Lifesaver.

However, if you are a math major or are interested in learning more about the ideas behind calculus or proving the concepts that make up calculus, this may not be the book for you.  This is certainly not a proof-based resource and does not contain a ton of practice problems.  So if you are looking to really dive deep into calculus, you may want to consider Calculus by Michael Spivak, which would be my personal recommendation for a proof-based approach to calculus.

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