A Course in Mathematics, Vol. 1

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Excerpt from A Course in Mathematics, Vol. 1: For Students of Engineering and Applied ScienceAs compared with the usual first course in analytic geometry, there will be found in this volume fewer of the properties of the conic sections, except as they appear in problems set for the student. On the other hand, a greater variety of curves are given, and it is believed that greater emphasis is placed on the essential principles. All work in three dimensions is postponed to the second year, and is to be taken up in the second volume in connection with functions of two or more variables, partial differentiation, and double and triple integration.This volume contains the matter usually given in a first course in differential calculus, with the exception of differentials, series, indeterminate forms, partial differentiation, envelopes, and some advanced applications to curves. These subjects will find their appropriate place in the further development of the course in the second volume. Integration has been sparingly used as the inverse operation of differentiation. And without employing the integral Sign. Simple applications to areas and velocities are given. To do more would require the expenditure of too much time on the Operation of integration, and the introduction of too many new ideas into one year's work. The integral, as a limit of a sum, with its many applications, will form an important part of the second year's work.In the preparation of the text the needs of a student who desires to use mathematics as a tool in engineering and scientific work have been primarily considered, but it is believed that the course is also adapted to the student who studies mathematics for its own sake. Abstract discussions are avoided and frequent applications and illustrations are given. Illustrations, however, which are beyond the range of a first-year student's knowledge of physical science are omitted. The proofs are made as rigorous as the maturity of the student will admit. It is to be remembered in this connection that the earlier chapters are to be studied by students who have just entered college.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.