Recommended Books © 1999,2002 by Karl Hahn

Karl's Calculus Tutor is completely nonprofit. Commissions from book sales are the sole source of funding with which to offset the expenses of keeping Karl's Calculus Tutor on line.

The difference between a clear and lucid math book and one that is, to coin a politically correct phrase, organizationally challenged, can be the difference between success and failure for the math student. I can't tell you that I have read through even a sizeable fraction of the calculus texts and study guides that are on the market, but I have looked at a bunch of them. If you are taking a college calculus course, you probably have already been assigned a required text. You will, of course, have to buy that text, whether it is any good or not, just so that you can do the homework assignments. But it doesn't hurt anything besides your pocket book to have other references at your fingertips. So here I shall make my recommendations from among the books I am familiar with that are still in print. If you click on a book, it will take you to the page of where you can order that title. The prices listed here are those posted by Amazon.com at the time I prepared this page.

Study Guides

Here is a book I highly recommend for anybody who tends to fall asleep while reading math books. The style in How to Ace Calculus: The Streetwise Guide by Joel Hass, Abigail Thompson, Colin Conrad Adams is so lively that I had to put it down in order avoid succumbing to the urge to plagiarize it. In the actual calculus material, you don't have to wade through a lot of stuff to get to the critical points. This book specializes in critical points -- that is the stuff you must know to pull down a good grade. And it describes them language so plain it will have you chuckling from time to time. It also has some great practical advice on how to select a good teacher, how to ask questions, how to study, etc. The examples worked in the text are not the really difficult ones that sometimes might show up on an exam, but you have to learn the not-so-hard ones before you can do the hard ones. To those of you who thought you could never understand math, this book is worth many times its price.

• How to Ace Calculus: The Streetwise Guide by Hass, Thompson, and Adams, Paperback: $11.96

• How to Ace Calculus the Rest of Calculus by Hass, Thompson, and Adams, Paperback: $10.47

An outfit called Schaum's Outline Series has been publishing study aids in a wide variety of subjects for decades now. I once had a coworker who was fond of saying that he got his degree from Schaum's Institute of Technology. There are several calculus volumes that they publish. One of them I am quite familiar with, and that is the one by Frank Ayres and Elliot Mendelson. There are brief, clear explanations of the concepts and methods. But the emphasis is upon worked examples. There are over 1000 of them. For what it's worth, this book has sold over a million copies in the 30 years it's been in print.

• Theory and Problems of Differential and Integral Calculus by Ayres and Mendelson, 3rd ed., Paperback: $11.96

Here's another from the Schaum's series. It has fewer worked problems, covers fewer topics, but has much more explanatory text. And the explanations are organized in a consistent way. Each section is divided into the concepts of Approximation, Refinement, and Limit. The author, Eli Passow, shows how these three stages are effective at attacking a wide variety of problems.

• Understanding Calculus Concepts by Eli Passow, Paperback: $11.16

Improving Your Understanding

The study guides listed above are the equivalent to books that teach artists how to hold the brush, mix the paint, and techniques for applying it to canvas -- all very practical stuff. But just as an art student must also learn how to see the world he or she is trying to render, so too must a calculus student learn to see the world that calculus renders. And there is nothing impractical about that. That is what the books that follow teach.

Having a different viewpoint of a topic always helps. Silvanus P. Thompson believed that calculus did not have to be difficult. In the first decade of the 20th century, he wrote a little book called Calculus Made Easy in which he appealed to concepts that most of us already have to explain how calculus works. His approach is different from the one commonly used in college calculus courses today (no epsilons and no deltas). He uses a concept he calls "orders of smallness." But when married to elementary algebra it leads to the very same conclusions you would learn in any calculus course. More recently Martin Gardner (author of Scientific American's Mathematical Games column) has annotated Thompson's work, and this edition is now available from St. Martin's Press. Some of Gardner's comments explain how Thompson's approach to a topic differs from the approaches that are popular today. The important point, though, is that Thompson's methods and his elegantly simple explanations lead you to an understanding that is every bit as useful and valid as the one you will get in class. And once you have traveled Thompson's road, your instructor's road won't seem nearly as rocky.

• Calculus Made Easy by Sylvanus P. Thompson and Martin Gardner, Hardcover: $15.37

Only someone who has fallen in love with calculus can know its poetry. Just as any musician can tell you how music is far deeper than mere spots on a score sheet, John C. Sparks leads you to understand how calculus is far deeper than mere cryptic symbols on a blackboard.

The sad truth is that too many calculus classes and texts teach students only the rules by which you manipulate the cryptic symbols. But those cryptic symbols, like all symbols, stand for something greater. Spots on a score sheet stand for melodic sounds, and mathematical symbols stand for beautiful ideas. It is these ideas that Calculus Without Limits teaches.

Without grasping the ideas and concepts of calculus, a student is left only with the grind of applying pencil lead to paper in this or that prescribed manner and has thoroughly missed the point. So it's hardly a surprise that so many calculus students are frustrated. But for a student who reads John C. Sparks' explanations of how the symbols assemble themselves into something meaningful, the symbology becomes just a tool -- as it should have been all along. The real knowledge and beauty behind the symbols glimmer through. And for a student who makes the special effort (and all mathematics learning requires special effort, even from those who love it) to follow that light where it leads -- that student too might very well fall in love and know the poetry.

• Calculus Without Limits: Almost by John C. Sparks, Paperback: $22.95

Here's another book that has emphasis on readability and an exposition style that effectively glues the concepts to your memory.

• Calculus (College Review Series) by Elliot Gootman $10.47

Textbooks

Of all the beginning calculus texts that have been foist onto students, there is one that, in my opinion, stands head and shoulders above the rest. Apparently I am not the only one to think so. Enough others feel this way to have kept this book in print for nearly 40 years. This is Calculus and Analytic Geometry by George B. Thomas Jr. at M.I.T. It is now in its 9th edition. Later editions have some contributions from Thomas' associate, Ross L. Finney. The development is logical, there are loads of worked examples, the explanations are clear, and the authors have had 9 editions and several decades to bring this work very near perfection.

Note: Titles shown in box ads are Amazon.com's recommendations based upon topic.

• Calculus and Analytic Geometry by Thomas & Finney, 9th ed., Hardcover: $102.67

• Calculus and Analytic Geometry Study Guide by Thomas & Finney, Paperback Vol 1: $30.40

• Calculus and Analytic Geometry Study Guide by Thomas & Finney, Paperback Vol 2: $30.40

For anyone planning a career in science or engineering, I recommend that you eventually get Mathematical Methods in the Physical Sciences by Mary Boas. It is a broad survey of theory and methods that you will be using to solve problems that involve physics or engineering. It is quite accessible to anybody who has had two semesters of calculus, and the explanations of the methods are clear and concise. When you take your advanced undergrad courses, this book may prove to be invaluable.

• Mathematical Methods in the Physical Sciences by Mary L. Boas, 2nd ed. $106.50

If your second or third semester calculus course covers differential equations, you will want this book. It begins by explaining concepts in linear algebra, which is a skill you will need if you plan to continue your math education. It then goes on to the basics of differential equations, with emphasis on linear differential equations. There is plenty of explanatory text and worked examples.

• Introduction to Linear Algebra and Differential Equations by John W. Dettman, Paperback: $10.36

Reference books

Here are two very useful reference books for those of you who will be using math in your future studies or careers:

• CRC Standard Math Tables and Formulae 30th ed. Hardcover $59.95

• Handbook of Mathematical Functions by Milton Abramowitz and Irene Stegun Paperback: $23.07

Recreational Math Books

• 1 2 3 Infinity by George Gamow, Paperback: $8.76

• The Mathematical Tourist by Ivars Peterson, Paperback: $11.96

• Math Trek: Adventures in the Mathzone by Ivars Peterson (for younger readers), Paperback: $10.36

• Math Trek 2: A Mathematical Space Odyssey by Ivars Peterson (for younger readers), Paperback: $11.80

• The Language of Mathematics: Making the Invisible Visible by Keith J. Devlin, Paperback: $12.00

More books will be appearing on this page soon, as I get a chance to review them.

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