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Excerpt from The Elements of the Integral Calculus: With Its Applications to Geometry The work here submitted to the notice of the public form the third volume of a course intended to famish to the mathematical student a pretty comprehensive view of the principles of modern analytical science. To complete this design will require a fourth volume, in some measure plementary to the three now completed, and to contain tlie subject of Finite Differences, a fuller inquiry into the theory of Partial Differential Equations, and a chapter on Definite Integrals. This final volume 1 hope hereafter to be able to prepare, although I do not propose to enter immediately upon the undertaking. With respect to this third volume, I ought to observe that, in Common with all modern elementary writers, I have availed myself pretty freely of the writings of the French mathematicians. In stating this, I am aware that I am not offering any apology for my book; but am, on the contrary, setting forth its principal claim to the notice of the English student; for the superiority of the French in every department of abstract science, is now pretty generally acknowledged in this country. Notwithstanding this admission, however, I have long been persuaded that many of the French processes, now universally adopted in English Books, are very deficient in mathematical rigour, and in not a few cases fail altogether to establish the conclusions aimed at. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.
Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Excerpt from The Elements of the Integral Calculus: With Its Applications to Geometry The third section contains the elements Of a theory of almost boundless extent, the theory Of Differential Equations. As far as equations Of two variables and Of the first order are. Concerned, and beyond which the powers Of the calculus are at present but very limited, the information conveyed in this section will, it is thought, be found to be sufficiently copious. I have endeavoured to render this part of the subject clear and intelligible, and have, in some cases, preferred appearing lengthy where brevity might involve any Obscurity, as in the article on Riccati's equation, for instance In the latter part Of this section I have compressed into small compass several topics Of a nature too difficult and too extensive to be completely discussed in a work Of this kind; but I have taken care to direct the inquiring student to the sources where more satisfactory information may be Obtained I hope, also, to touch again upon these matters at a more convenient opportunity; in the mean time, I trust that the three volumes now finished may contribute something towards improving the taste and exciting the inquiries Of the young analyst. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.