Geometry in Partial Differential Equations

Geometry in Partial Differential Equations
Title Geometry in Partial Differential Equations PDF eBook
Author Agostino Prastaro
Publisher World Scientific
Pages 482
Release 1994
Genre Mathematics
ISBN 9789810214074

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This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Geometric Analysis and Nonlinear Partial Differential Equations

Geometric Analysis and Nonlinear Partial Differential Equations
Title Geometric Analysis and Nonlinear Partial Differential Equations PDF eBook
Author Stefan Hildebrandt
Publisher Springer Science & Business Media
Pages 663
Release 2012-12-06
Genre Mathematics
ISBN 3642556272

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This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Geometric Partial Differential Equations and Image Analysis

Geometric Partial Differential Equations and Image Analysis
Title Geometric Partial Differential Equations and Image Analysis PDF eBook
Author Guillermo Sapiro
Publisher Cambridge University Press
Pages 415
Release 2001-01-08
Genre Computers
ISBN 0521790751

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This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practioners. It is intened to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Partial Differential Equations

Partial Differential Equations
Title Partial Differential Equations PDF eBook
Author Walter A. Strauss
Publisher John Wiley & Sons
Pages 467
Release 2007-12-21
Genre Mathematics
ISBN 0470054565

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Partial Differential Equations arising from Physics and Geometry

Partial Differential Equations arising from Physics and Geometry
Title Partial Differential Equations arising from Physics and Geometry PDF eBook
Author Mohamed Ben Ayed
Publisher Cambridge University Press
Pages 471
Release 2019-05-02
Genre Mathematics
ISBN 1108431631

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Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.

Partial Differential Equations and Geometric Measure Theory

Partial Differential Equations and Geometric Measure Theory
Title Partial Differential Equations and Geometric Measure Theory PDF eBook
Author Alessio Figalli
Publisher Springer
Pages 224
Release 2018-05-23
Genre Mathematics
ISBN 3319740423

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This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

Partial Differential Equations for Geometric Design

Partial Differential Equations for Geometric Design
Title Partial Differential Equations for Geometric Design PDF eBook
Author Hassan Ugail
Publisher Springer Science & Business Media
Pages 110
Release 2011-08-24
Genre Computers
ISBN 0857297848

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The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in Applied Mathematics such as Euler, Legendre, Laplace and Fourier and has applications to each and every physical phenomenon known to us e.g. fluid flow, elasticity, electricity and magnetism, weather forecasting and financial modelling. This book introduces the recent developments of PDEs in the field of Geometric Design particularly for computer based design and analysis involving the geometry of physical objects. Starting from the basic theory through to the discussion of practical applications the book describes how PDEs can be used in the area of Computer Aided Design and Simulation Based Design. Extensive examples with real life applications of PDEs in the area of Geometric Design are discussed in the book.