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 Are there any terminologies and notations that are considered outdated?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

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  • $\begingroup$ Once upon a time, I spent a dozen hours perusing older calculus texts. We've come a long way. $\endgroup$ – James S. Cook Dec 11 '18 at 0:28
  • $\begingroup$ Ask the members of your department who have taught this course before. Are there engineering students in the course? If so, ask engineering faculty about your proposed book. Same for biology students, physics students, economics students, etc. See mathoverflow.net/questions/13089 despite being "no longer relevant" $\endgroup$ – Gerald Edgar Dec 11 '18 at 1:11
  • $\begingroup$ This is certainly possible: William Joyner did this with Granville's calculus, adding SageMath exercises - currently still available at wdjoyner.files.wordpress.com/2015/04/… $\endgroup$ – kcrisman Dec 11 '18 at 4:01
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    $\begingroup$ (comment, because I don't have time for a more careful answer now) I'm familiar with this book, having had a copy since 1972 or 1973 (around age 14-15; got it at a Goodwill store, back in the days when these places sometimes had very old textbooks like this). I've used exercises and ideas from the book in teaching, but I would advise against using it as a text --- there are just too many notational and other matters that you probably "read past" because of your background, but which will affect your students now and in later courses. There are plenty of 1960s books that would be better. $\endgroup$ – Dave L Renfro Dec 11 '18 at 12:09
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    $\begingroup$ Regarding your questions #1 and #2, my feeling is that if you have to ask these two questions, then you should not be attempting this. $\endgroup$ – Dave L Renfro Dec 11 '18 at 12:10
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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.

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  • $\begingroup$ Thank you your detailed analysis on this book! Am just curious, do you use any old book as your textbook for Calculus? I am using Serge Lang's A First Course in Calculus as the textbook for Calculus I and II; Lang's Calculus of Several Variables for Calculus III. They are old (but not antique) and nice and I am wondering if there are even older ones that will be suitable, such as the one I was asking about. There was also a calculus book by Grigorii Fichtenholz but I failed to find the book. $\endgroup$ – Zuriel Dec 11 '18 at 3:23
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    $\begingroup$ I try to follow my course notes which are almost a complete calculus book. I lack exercises and a proper write up of a chunk of calculus II (to my standards anyway). My notes are born of Stewart, Thomas, Anton and where it gets deeper Apostol. My usual approach is to recommend or require the text my institution uses in case I need to cite more practice problems etc. The openstax text by Strang may be pretty great by now. My notes: supermath.info/OldschoolCalculusII.pdf and supermath.info/CalculusIIIf2014.pdf $\endgroup$ – James S. Cook Dec 11 '18 at 3:29
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    $\begingroup$ Thanks for sharing! Do you happen to know any book that is around 100 years old but is still worth to be used as a textbook of calculus today? $\endgroup$ – Zuriel Dec 11 '18 at 3:37
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    $\begingroup$ @YetAnotherUser, I'm using the OpenStax Calculus 1 book right now, and it has many typographical errors. (You get what you pay for.) $\endgroup$ – Joel Reyes Noche Dec 11 '18 at 4:35
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    $\begingroup$ I hope the Openstax book works out the typos soon. I would point out, we had the same problem with a much more expensive first edition a few years back. I think about 10% of the answers in the back of the text were incorrect. I'm not sure it's money. I think students and actual professors are better at finding errors than reviewers or editors. $\endgroup$ – James S. Cook Dec 11 '18 at 13:58
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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.

Here is a link: https://archive.org/details/elementsdiffere02goog/page/n18 (may need a slightly earlier edition for copyright, but I don't know...1941 could have lapsed also.)

It has a very nice set of chapters on series. Also the diffyQ survey is good. There are a few chapters at the end that verge towards calc 3, but don't cover it all. You can skip those. Also a few special topics (e.g. Mercator projection) that may be of less interest in this day.

I don't think the absence of EE problems is a flaw since many calc students are still weak on behavior of inductors, capacitors, etc. Would leave that for physics or perhaps ODE course applications. Problems with motion or with fluids are more easy to visualize.

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  • $\begingroup$ Thank you for your detailed answer! Since you said " There are a few chapters at the end that verge towards calc 3, but don't cover it all." Should I aim at using this book for Calculus I and II but use a different one for Calculus III? Does Granville also have a book for calculus III? $\endgroup$ – Zuriel Dec 11 '18 at 13:03
  • $\begingroup$ Zuriel: You would need another book for what is normally considered calc 3. Granville has partial differentials and multiple integration (usually considered calc 3), but is missing divgradcurl and Stokes/Green's. The text has enough for a stereotipical American first year of calculus (calc 1 and calc 2, each a semester and covering single variable differentiation, methods of integration as well as series and basic ODEs.) It has about half of calc 3. $\endgroup$ – guest Dec 11 '18 at 17:35
  • $\begingroup$ Note that in the US, there is a market for books that are 2 or 3 semester calc books. My high school experience was a book that covered 2 semesters (AP). But colleges often have a 3 semester book. $\endgroup$ – guest Dec 11 '18 at 17:38
  • $\begingroup$ Bottom line is I agree with Dave, that if you have to ask these questions with lack of perspective, to date, you are better off using a standard recent textbook. Once you have more perspective on all the different ways to teach calculus, you can be more iconoclastic. $\endgroup$ – guest Dec 11 '18 at 17:47
  • $\begingroup$ If you want a more traditional text with medium difficulty (not Harvard reform craziness, not Spivak baby real analysis), I would look at Thomas Finney. If you can select a text with ALL the answers, I would opt for that...drillbooks rock. What I liked about 1980 TF and still like about Schaum's. $\endgroup$ – guest Dec 11 '18 at 17:50
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While the style of writing is quite readable, many theorems are given without a proof. That is a severe deficiency. I find this text by E. Goursat (1902) much superior: https://archive.org/details/mathematicalanal021323mbp/page/n1

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  • $\begingroup$ Much better written than most current textbooks. If you like it, use it. Question about notation: on page 7, question 11: what is the meaning of the right angle surrounding from below and left symbols m, n, m+n? $\endgroup$ – qed Dec 11 '18 at 9:16
  • $\begingroup$ Ok sorry - this angle surrounding a symbol is a notation for a factorial, as evident from page 10. $\endgroup$ – qed Dec 11 '18 at 9:20
  • $\begingroup$ That said, the scan of Goursat 1902 posted above cuts off upper and lower margins. $\endgroup$ – qed Dec 11 '18 at 9:32
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    $\begingroup$ Welcome to Stack Exchange! Please edit your answer instead of posting new answers, and delete the newer ones. $\endgroup$ – Glorfindel Dec 11 '18 at 9:49

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