[Math] Is reading old calculus books still beneficial for undergraduate students today

calculusreference-request

this is really a question about math and not books. I am mainly wondering if reading really old calculus books is still beneficial for undrgraduate students today. I was told that the material covered won't be of much benefit, things like curves, various mechanical integration methods, etc., and that I would be better off studying a 'calculus with an intro to analysis' type book like Apostol or Spivak's calculus. Is this true? Some specific examples of old books I have in mind are:

Edwards: https://archive.org/details/anelementarytre01edwagoog

Todhunter: https://archive.org/details/atreatiseondiff06todhgoog

Williamson: https://archive.org/details/anelementarytre20willgoog

One thing's for sure: The problems in these books are much harder than in modern books, which is very appealing to me coming from an olympiad background.

So they aren't as far back as say Cauchy, but still are fairly old. I would still be interested however in knowing if something like Cauchy's Calcul Differentiel et Integral (I can read french!) is worth studying today; I know that Clerk Maxwell studied it at Edinburgh University for instance (before "going up" to Cambridge): https://archive.org/details/leonsdecalculdi02goog

Thanks

Best Answer

To answer your question: yes, it still can be beneficial to read old textbooks or publications, especially from a history of math point of view it is even necessary to read the original works. You get an idea on how the original ideas have been developed. Very interesting - no question about it.

However, you have to take into account that these old books most likely:

  • lack of course on modern references
  • are not aligned with the modern curriculum
  • use often a different notation
  • are often hard to come by

Maybe a good compromise would be to read a history of math book, for example History of Topology and parallel a modern book to compare the ideas and get appropriate modern references.

EDIT (due to a comment of Andrew D. Hwang)

Andrew mentioned the Gutenberg project with a big collection of old and mildly adapted math publications, I find this reference needs definitely to be in this answer, great reference!

Related Question