Geometric Partial Differential Equations
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Geometry in Partial Differential Equations
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.
Partial Differential Equations for Geometric Design
Author: Hassan Ugail
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-08-24
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.
Lecture Notes on Geometrical Aspects of Partial Differential Equations
Author: Viktor Viktorovich Zharinov
language: en
Publisher: World Scientific
Release Date: 1992
This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.