Monday, July 04, 2005

Self-Directed Learning of Calculus - Part 1

One of my current interests is to relearn calculus. One approach would be to take a first year university course on the topic, either as an audit or as a registered student. But my preference is to direct my own Learning. The road less travelled ...

My first step was to review a number of potential resources (both books and online). In the case of books I spent quite a few hours using both Google and to locate information and reviews of calculus textbooks and resources. I also visited the local bookstores and university library to examine the books on their shelves.

Once again, I was at a decision point. I could have opted for one good book and worked my way through it. This would have been very close to a course approach with one textbook. But I realized almost immediately that I wanted to use more than one book. They all have different approaches and emphasises. The real goal is not to Learn a book, but to Learn the topic (i.e. calculus) in a deep and substantive manner. Thus I wanted to see how the topic was presented by a number of different authorities.

I have ended up with 5 books. Two of the books are introductory books for the general public and are an excellent introduction to the topic.

- Calculus Made Easy (1998) by Silvanus P. Thompson & Martin Gardner. This is a modern revision of a 1910 classic.

- The Complete Idiot's Guide to Calculus (2002) by W. Michael Kelley. This is considered to be a useful supplement to a more rigorous textbook.

One of the advantages of the above two books is that they are relatively small and thus tend to focus on the important concepts and leave the details to other sources. They also have a friendly informal style.

The remaining three books are university level textbooks.

- Calculus: An Intuitive and Physical Approach (Second Edition)(1977) by Morris Kline. This is an oft-quoted classic that is still in print, an excellent indicator of its value.

- Calculus With Analytic Geometry. 6th ed. (1998) by Larson, R. E, Hostetler, R. P. & Edwards, B. H.. I bought this textbook in a used bookstore for a small fraction of the cost of a new edition. I had noticed many references to it on the Web and recognized the title when I was browsing the bookshelves. It is a thick and very heavy book. I feel confident that if I can handle this book I will be on top of the topic.

- Calculus. 3rd ed. (1994) by Michael Spivak. This received the highest comments on my Web searches, but the comments indicated that it was not for everyone. I located a copy of the original first edition (1967) in the university library and loved it. The emphasis is much more on the concepts and proofs than on applying algorithms to solve problems. Using the Web I was able to purchase a copy of the latest (1998) edition from the publisher.

I think that the combination of these 5 books should give me a good set of resources for my Learning activities.

Summarizing, I used the Web as well as bookstores and libraries to review a number of books on calculus, finally selecting 5 books for purchase. A promising start.


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