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Excerpt from The Integration of Functions of a Single Variable, Vol. 2
The reader who is familiar with the theory of algebraical functions and algebraical plane curves will no doubt find the treatment in Section V. Of the integrals of algebraical functions sketchy and inadequate. I hope, however, that he will bear in mind the great difficulty of presenting even an outline of the elements of so vast a subject in a short space and without presupposing a wider range of mathematical knowledge than I am at liberty to assume.
I have naturally not said much about particular devices which are only useful in special cases, but I have tried to show, where it is possible, how such devices find their place in the general theory. And I would strongly recommend any reader who is not already familiar with the general processes here explained to work through a number of examples (those for instance which have been set in the Mathe matical Tripos in recent years) using in each case both the general method and any special method which he may find better adapted to the particular case.
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Paperback. Zustand: New. Print on Demand. This book is a comprehensive guide to integrating functions of a single variable. It is written with the student in mind and aims to provide a systematic and straightforward approach to this fundamental area of the Calculus. The author begins by introducing the basic concepts of the Integral Calculus and then proceeds to discuss the integration of rational functions, showing how to express them as sums of partial fractions. The book explores various methods of integration, including integration by substitution and by parts, and explains how to integrate transcendental functions such as trigonometric and exponential functions. The author also examines the integration of functions that cannot be expressed in elementary terms and introduces the concept of elliptic integrals, which are used to solve problems in areas such as astronomy and physics. Throughout the book, the author provides numerous solved examples and exercises to help the reader master the techniques of integration. This book is essential reading for students of mathematics, engineering, and physics who wish to deepen their understanding of the Integral Calculus. It is also a valuable resource for professionals who use integration in their work. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781330308271_0
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