Excerpt from The Calculus

The significance of the Calculus, the possibility of applying it in other fields, its usefulness, ought to be kept constantly and vividly before the student during his study of the subject, rather than be deferred to an uncertain future.

Not only for students who intend to become engineers, but also for those planning a profound study of other sciences, the usefulness of the Calculus is universally recognized by teachers; it should be consciously realized by the student himself. It is obvious that students interested primarily in mathematics, particularly if they expect to instruct others, should recognize the same fact.

To all these, and even to the student who expects only general culture, the use of certain types of applications tends to make the subject more real and tangible, and offers a basis for an interest that is not artificial. Such an interest is necessary to secure proper attention and to insure any real grasp of the essential ideas.

For this reason, the attempt is made in this book to present as many and as varied applications of the Calculus as it is possible to do without venturing into technical fields whose subject matter is itself unknown and incomprehensible to the student, and without abandoning an orderly presentation of fundamental principles.

The same general tendency has led to the treatment of topics with a view toward bringing out their essential usefulness.

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