Recommended Calculus Books

Updating my "Recommended Books" web page

Last week I reorganized my “Recommended Books” web page, now including seven calculus titles. Three of these books I have come across through my students: Stewart’s Calculus; Larson/Hostetler/Edwards Calculus: Early Transcendental Functions; and Frank Blume’s Applied Calculus for Scientists and Engineers.
Stewart’s Calculus book is popular among college professors; many students have it as their textbook. Of course it is a very good book but personally I prefer the way the topics are organized in the Larson/Hostetler/Edwards textbook.
Then there are a few books I was familiar with since I was in college myself. Spivak’s Calculus is an excellent book with superb explanations of the concepts and the proofs. This is a classic book for mathematicians. The vector calculus books: “Vector Calculus” by Marsden & Tromba; and “Div, Grad, Curl and All That” by Schey are also very good, with very clear explanations and examples.
Among these calculus books I listed a book that is not a calculus book per se: “e: The Story of a Number” by Eli Maor. Here there are many illuminating stories about the number e, the base of the natural logarithms. The number e is customarily defined as a limit in calculus and it is used extensively in exponential functions and hyperbolic functions, as well as in many types of differential equations. Many students are often mystified by the number e and its strange looking definition, because e is a transcendental number, as pi is but e does not have an obvious geometrical point of reference like the circle to understand its meaning. Eli Maor in its book does an outstanding job of illuminating many of the relationships the number e has with the real world and with other parts of math.

Buy the right math prep book

Pay attention and read the book’s preface, not only the title.

One of my students was going to take a standardized test specific to some job he wanted to apply for. The test includes a math section, and this is the only part of the test where this student felt he needed tutoring. My student has a friend who already took the same test, successfully. This friend told my student that, if he prepared well for the GRE, he would sure pass this other test, because it is an easier test than the GRE.
So my student went to the bookstore and bought a book he saw there titled “Cracking the GRE* Math Subject Test.” He did this a few weeks before we started our tutoring sessions. He brought this book to our second session for us to work on its problems.
When we started going through the book I was amazed to see double integrals, differential equations, matrices, power series, three-dimensional surfaces, polar coordinates, and almost any calculus topic covered in college, not to mention Abelian groups and topological spaces.
We found only three problems that could actually be in the general GRE test.
I suggested for my student to go back to the bookstore and get the normal Kaplan GRE prep book.
When my student realized he had no use for the book he had bought, he gave it to me.
I was puzzled by this “GRE” prep book because it obviously has nothing to do with the general GRE test. So when I got home I started reading the preface. I found a paragraph with the heading “What is the GRE Math Subject test?” explaining that this test is taken by students who are applying for admission to study math at the graduate level. Now it all made sense!
So, the moral of the story is: be careful when buying a math test prep book. Before paying for it you want to make sure it’s going to help you, and that you are not buying something that has nothing to do with the actual test you are preparing for.