The Principles Of Elliptic And Hyperbolic Analysis (1894) - Softcover

Macfarlane, Alexander

Softcover

ISBN 10: 1437162010 ISBN 13: 9781437162011

Verlag: Kessinger Publishing, LLC, 2008

Inhaltsangabe

""The Principles of Elliptic and Hyperbolic Analysis"" is a comprehensive guide to the mathematical principles and techniques of elliptic and hyperbolic analysis. Written by Alexander Macfarlane and first published in 1894, this book provides an in-depth exploration of the mathematical concepts and theories that underpin these two branches of analysis.The book begins with an introduction to the basic principles of elliptic and hyperbolic analysis, including an overview of the fundamental equations and definitions. From there, Macfarlane delves into more advanced topics, such as the theory of functions of a complex variable, integral equations, and the calculus of variations.Throughout the book, Macfarlane provides numerous examples and exercises to help readers better understand the material. He also includes a detailed bibliography for further reading and research.Overall, ""The Principles of Elliptic and Hyperbolic Analysis"" is an essential resource for anyone interested in the theory and applications of elliptic and hyperbolic analysis. Whether you are a student, researcher, or practitioner in the field of mathematics, this book offers a comprehensive and accessible introduction to these important mathematical concepts.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Über diesen Titel

Reseña del editor

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Reseña del editor

which we denote by Let OPA (Fig. 1) represent aA and OAQ represent B; then OPQ, the third side of the spherical triangle, represents the product aAB. To prove that aAB = cos A cos B - sin A sin B cos a + {cos B sin A a+cos A sin B - sin A sin B sin a}. The first part of this proposition, namely, that cos aAB = cos A cos B - sin A sin B cos a, is equivalent to the well-known fundamental theorem of Spherical Trigonometry; the only difference is, that a denotes, not the angle included by the sides, but the angle between the planes; or, to speak more accurately, the angle between the axes a and. It is more difficult to prove the complementary proposition, namely, that Sin aAB = cos B sin A a + cos A sin B - sin A sin B sina a, for it is necessary to prove, not only that the magnitude of the right-hand member is equal to - cos2aAB, but also that its direction coincides with the axis normal to the plane of OPQ At page 7 of Fundamental Theorems, I have proved the above statement as regards the magnitude, but I was then unable to give a general proof as regards the axis. Now, however, I am able to supply a general proof, and it will be found of the highest importance in the further development of the analysis. In Fig. 1, OP is the initial line of aA, and OQ the terminal line of B; let OR be drawn equal to cos B sin A a + cos A sin B - sin A sin B sina a; it is required to prove that OR is perpendicular to OP and to OQ. Now, OP = a-A = (cos A - sin A). About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology. Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text.

Details zur Ausgabe

• Verlag: Kessinger Publishing, LLC
• Erscheinungsdatum: 2008
• ISBN 10: 1437162010
• ISBN 13: 9781437162011
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 56
• Kontakt zum Hersteller: Nicht verfügbar