Excerpt from An Elementary Treatise on Calculus: A Text Book for Colleges and Technical Schools

1. We believe that the most important thing in the teaching oft calculus is to lead the student to a clear understanding of principles. Therefore our chief endeavor has been to develop the subject as simply and as directly as possible.

2. We fully appreciate the importance of extensive practice in the handling of algebraic transformations. Therefore we have given an adequate collection of formal problems in differentiation and integration.

3. We are convinced, however, that it is a pedagogical mistake, in a text book on calculus for young men, to break the thread of the textual discussion by unnecessary algebraic developments and by large and frequent groups of purely formal problems. We believe indeed that the proverbial unintelligibility of calculus is to a very great extent a psychological consequence of this almost universal and really hideous feature. Therefore we have arranged the greater portion of our formal problems in an appendix.

4. Nearly every elementary science text in existence carries a false suggestion of completeness and finality, and there are two things which young men should understand in connection with their study of the mathematical sciences. The first is that such study is exacting beyond all compromise, involving as it does a degree of constraint which it is beyond the power of any teacher greatly to mitigate. And the second is that the completest science stands abashed before the infinitely complicated and fluid array of phenomena of the material world, except only in the assurance which method gives. We hope that this elementary treatise on calculus may prove to be sufficiently definite and exacting to be useful, next to this there is nothing we could wish to have more in evidence from beginning to end than its incompleteness.

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