Functions of Three Real Variables (Reprint from American Journal of Mathematics): Thesis for the Degree of Doctor of Philosophy in the Graduate School ... of Illinois, 1903 (Classic Reprint) - Softcover
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Excerpt from Functions of Three Real Variables (Reprint From American Journal of Mathematics): Thesis for the Degree of Doctor of Philosophy in the Graduate School in the University of Illinois, 1903
We must now define limiting values and limits. We say that we is a limiting value of the variable as, if there exist values of a: in every neighborhood of 900. This may also be expressed by saying that the values of a: are dense at £00. Similarly, if no, y, and z are dense, respectively, at yo, and ac, then (1130, is a limiting value of (x, y, z). In this case (x, y, 2) may approach (mo, yo, zo) in any one of three different ways, or, to use the language of geometry, the point (x, y, z) may approach the point (mo, yo, 20) in any one of three different ways.
Wirst, we may let each of the variables vary by itself, that is, we may regard any two of the variables as constant and let the third vary. Secondly, we may let two of the variables vary simultaneously while we regard the third variable as constant. Lastly, we may let all three variables vary simultaneously. These three different kinds of variation of the variables give rise to three different kinds of limits.
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Paperback. Condition: New. Print on Demand. This book elegantly explores the theoretical foundations of functions of three real variables, presenting crucial concepts with clarity and rigor. The author meticulously examines simultaneous limits, discontinuity, and continuity in three variables, providing a comprehensive framework for understanding these intricate mathematical objects. The book deftly situates its subject within the broader context of real analysis, tracing its historical development while highlighting its ongoing significance. The author's insightful discussions illuminate the interplay between continuity and discontinuity, offering a nuanced perspective on the nature of functions in higher dimensions. Throughout the book, the author emphasizes the importance of simultaneous limits in understanding the behavior of functions in three variables. Through detailed proofs and examples, the author demonstrates the conditions under which these limits exist and how they can be used to characterize the regularity and discontinuity of functions. This book is an invaluable resource for students, researchers, and anyone seeking a deeper understanding of the foundations of real analysis. Its clear exposition and comprehensive coverage make it an essential addition to any library on the subject. 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. Seller Inventory # 9781527740105_0
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