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Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)

J.F. Pommaret
4.9/5 (10507 ratings)
Read Now Download Now ⏭ listen AudioBook
Description:Ordinary differential control thPory (the classical theory) studies input/output re­ lations defined by systems of ordinary differential equations (ODE). The various con­ cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re­ cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con­ cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ­ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the­ ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications). To get started finding Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
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PDF, EPUB & Kindle Edition
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9048144329

Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications)

J.F. Pommaret
4.4/5 (1290744 ratings)
Read Now Download now ⏭ listen AudioBook
Description: Ordinary differential control thPory (the classical theory) studies input/output re­ lations defined by systems of ordinary differential equations (ODE). The various con­ cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re­ cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con­ cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ­ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the­ ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications). To get started finding Partial Differential Equations and Group Theory: New Perspectives for Applications (Mathematics and Its Applications), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
—
Format
PDF, EPUB & Kindle Edition
Publisher
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Release
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ISBN
9048144329

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