Quick Calculus

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I assume the reader knows calculus. Some readers, however, have weak or rusty math skills. Is there an easy way to learn what is needed?

Yes! Quick Calculus is a self-teaching guide written by Daniel Klepner and Norman Ramsey. Their preface states:

Before you plunge into Quick Calculus, perhaps we ought to tell you what it is supposed to do. Quick Calculus should teach you the elementary techniques of differential and integral calculus with a minimum of wasted effort on your part; it is designed for you to study by yourself. Since the best way for anyone to learn calculus is to work problems, we have included many problems in this book. You will always see the solution to your problem as soon as you have finished it, and what you do next will depend on your answer. A correct answer generally sends you to new material, while an incorrect answer sends you to further explanations and perhaps another problem.

The book covers nearly all the calculus needed in IPMB.

• Chapter One reviews functions and graphs, emphasizing trigonometry, exponentials, and logarithms.
• Chapter Two discusses differentiation—including the product rule and the chain rule—and maximum/minimum problems.
• Chapter Three analyzes integration, both definite and indefinite, and covers techniques such as change of variable, integration by parts, and multiple integrals.
• Chapter Four summarizes all the results in a few pages.

The only calculus in IPMB that Quick Calculus doesn’t teach is vector calculus; for that you should consult Div, Grad, Curl and All That. Used Math covers more ground than Quick Calculus, but it is a handbook rather than a self-teaching guide.

Quick Calculus has several virtues. It is clearly written, it emphasizes understanding math visually with lots of plots, and it focuses on utilitarian techniques without distracting rigor. If you want to understand math at a fundamental level, you should take a real calculus class. If you want to brush up on what’s needed to get through IPMB, use Quick Calculus.

One disadvantage is that Quick Calculus is old. The second edition—the most recent one I am aware of—was published in 1985. It might be difficult to purchase, although Amazon seems to have copies for sale. The authors make quaint comments about “readers who have an electronic calculator,” as opposed to slide rules I suppose. I also found several typos, which might frustrate readers using the book for self-study.

The format is unusual. The text is divided into approximately half-page “frames,” and the reader is guided from one frame to the next. Someone should put this book online, because it would lend itself to an interactive online format. Rather than explain how the book is organized, I’ve taken Section 1.17 of IPMB and rewritten it in the style of Quick Calculus (see below). In my opinion, if all of Intermediate Physics for Medicine and Biology were organized like this it would be tedious. What do you think?