Calculus (Classic Reprint)

Excerpt from Calculus

One of the purposes of the elementary working courses in mathematics of the freshman and sophomore years is to exhibit the bond that unites the experimental sciences. "The bond of union among the physical sciences is the mathematical spirit and the mathematical method which pervade them." For this reason, the applications of mathematics, not to artificial problems, but to the more elementary of the classical problems of natural science, find a place in every working course in mathematics. This presents probably the most difficult task of the text-book writer,- namely, to make clear to the student that mathematics has to do with the laws of actual phenomena, without at the same time undertaking to teach technology, or attempting to build upon ideas which the student does not possess. It is easy enough to give examples of the application of the processes of mathematics to scientific problems; it is more difficult to exhibit by these problems, how, in mathematics, the very language and methods of thought fit naturally into the expression and derivation of scientific laws and of natural concepts.

It is in this spirit that the authors have endeavored to develop the fundamental processes of the calculus which play so important a part in the physical sciences; namely, to place the emphasis upon the mode of thought in the hope that, even though the student may forget the details of the subject, he will continue to apply these fundamental modes of thinking in his later scientific or technical career. It is with this purpose in mind that problems in geometry, physics, and mechanics have been freely used. The problems chosen will be readily comprehended by students ordinarily taking the first course in the calculus.

A second purpose in an elementary working course in mathematics is to secure facility in using the rules of operation which must be applied in calculations.