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I am wondering if it is a bad idea to use an old textbook, such as
Differential and integral calculus, with examples and applications by George A. Osborne. This book was published in 1906 and there are no known copy right restrictions, which means students may use a free e-version if they would like to save money. On the other hand, hard copies are still available for sale.

To me, this book is very well written and contains all the basic materials that need to be covered in a traditional calculus course. Furthermore, it also contains a large number of examples, which is very helpful to the students. On the other hand, I am wondering if there is any issue with using an old textbook like this. For example,

1. Are there any terminologies and notations that are considered outdated?


2. Are there any new discoveries in the past 110 years or so that need to be included into the calculus course which were not found in an old book?


3. What will my students and peers think about the idea of using an old textbook?

I personally do not know any teacher who uses such an old book as the textbook; but is it really a bad idea to do so?

I'm all for using old editions and/or free e-texts. But, this is a bit too outdated in my opinion. I could have missed it, but I did not spot a clear section on:

• related rates


• mean value theorem


• L'hopital's Rule


• surface integration


• Green's, or Divergence or Stokes' Theorems


• modern vector notation

Yes, there is a preponderance of examples on basic calculational techniques, quite impressive. But, I do think the application of calculus to curve sketching and applications to say circuits, biology, finance are missing.

More to the point, the organization is very nonstandard when framed against the usual USA-based sequence. In summary, calculus II and III are mixed together in a rather strange way. Also, missing as far as I remember:

• introduction to differential equations


• second order constant coefficient ODEs

We can agree or disagree about whether or not these belong, but some schools need these covered early to help engineering keep their students up to speed with engineering curriculum which needs this basic ODE stuff.

Probably the worst thing, the lack of nice diagrams and organizing boxes. All Calculus texts for about the last 5 decades have pretty nice pictures and a lot of organizational aids for studying. I think some of these are worth it. Of course, you could use this book as a backdrop for adding all that nice stuff if you want to work on it, but it seems like a lot of work when you could just as reasonably say use the 4th edition of Thomas or some such thing which is widely available for 10's of dollars.

The text is fine (even good), but I would opt for Granville instead. Granville: Very clear by using simple vocabulary (low grade level English). Brief but not in a Rudin manner...more in a Schaum's manner. Excellent exercises. Most answers provided. Granville was the standard text from ~1910-1960. Also uses American English, which will serve you better unless you are in the Commonwealth. (minor point).

While the Granville Sage example is clearly a labor of love and well done, I would avoid that and just use the actual Granville text. Learning calculus is hard enough. When you add in some programming, it makes it harder. (Even easy stuff...it just does.) Also, the drill exercises are much more numerous in Granville and more helpful in terms of drill (which beginners need) as opposed to "cool project" type problems that professors like.