Certain Partial Differential Equations Connected With the Theory of Surfaces (Classic Reprint) - Couverture souple

Pattillo, Nathan Allen

9781333622664: Certain Partial Differential Equations Connected With the Theory of Surfaces (Classic Reprint)

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ISBN 10 : 133362266X ISBN 13 : 9781333622664

Editeur : Forgotten Books, 2018

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Explore the mathematics behind surfaces and curves through a rigorous treatment of partial differential equations. This scholarly work investigates how certain linear PDEs connect to the geometry of surfaces, using invariants, isothermal systems, and Laplace’s methods to unlock new relationships between curvature, geodesics, and the coordinates of a surface.

This edition presents a structured analysis: starting from a linear PDE and moving through invariants, substitutions, and reductions to reveal how curvature, lines of curvature, and principal radii interact with differential equations. It combines classical techniques with precise derivations, offering a deep look at how the theory of surfaces informs and is informed by partial differential equations.

Derivations of invariants and their role in simplifying complex PDEs tied to surface geometry

Connections between curvature, geodesic curvature, and lines of curvature through Laplace’s methods

Isothermal systems and conditions under which curvature lines form special coordinate nets

Step-by-step transformations and substitutions that illuminate the interplay between analysis and geometry

Ideal for readers with a background in differential geometry and PDEs who seek a thorough, methodical exploration of how these topics converge in the study of surfaces.

Les informations fournies dans la section � Synopsis � peuvent faire r�f�rence � une autre �dition de ce titre.

�diteur: Forgotten Books
Date d'�dition: 2018
Langue: anglais
ISBN 10: 133362266X
ISBN 13: 9781333622664
Reliure: Broch�
Nombre de pages: 39
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Certain Partial Differential Equations Connected With the Theory of Surfaces

Nathan Allen Pattillo

Edit� par Forgotten Books, 2018

ISBN 10 : 133362266X ISBN 13 : 9781333622664

Neuf Paperback

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Vendeur : Forgotten Books, London, Royaume-Uni

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Paperback. Etat : New. Print on Demand. This book delves into partial differential equations, with a specific focus on those related to surfaces. The author builds upon the work of Professor Craig, examining equations connected to the theory of surfaces. By considering linear partial differential equations of the second order, the book provides a thorough understanding of Laplace's method for integration. It explores the concept of invariants, which enjoy a significant role in the study of the proposed equations, and demonstrates how these functions can be used to derive general formulas for calculating invariants. The author also investigates the relationship between the equations and the curvature of surfaces, showing that under certain conditions, the lines of curvature form an isothermal system. The book's insights on partial differential equations connected to surfaces offer valuable knowledge for mathematicians and researchers working in differential geometry and related fields. 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. N� de r�f. du vendeur 9781333622664_0

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