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Author: Celso Melchiades Doria
Publisher: Springer Nature
ISBN: 3030778347
Category : Mathematics
Languages : en
Pages : 362
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Book Description
This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Author: Celso Melchiades Doria
Publisher: Springer Nature
ISBN: 3030778347
Category : Mathematics
Languages : en
Pages : 362
Get Book Here
Book Description
This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Author: Yves Talpaert
Publisher: CRC Press
ISBN: 9780824703851
Category : Mathematics
Languages : en
Pages : 480
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Book Description
An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780817637071
Category : Education
Languages : en
Pages : 532
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Book Description
This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.
Author: Kondagunta Sundaresan
Publisher: Springer
ISBN: 354039415X
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Author: S. G. Kreui
Publisher: American Mathematical Soc.
ISBN: 0821869035
Category : Mathematics
Languages : en
Pages : 398
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Book Description
Author: Haim Brezis
Publisher: Springer Science & Business Media
ISBN: 0387709142
Category : Mathematics
Languages : en
Pages : 600
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Book Description
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461205417
Category : Mathematics
Languages : en
Pages : 553
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Book Description
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author:
Publisher: Elsevier
ISBN: 0080875246
Category : Mathematics
Languages : en
Pages : 504
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Book Description
Differential Forms in Mathematical Physics
Author:
Publisher: Cambridge University Press
ISBN: 0521408504
Category : Banach spaces
Languages : en
Pages : 288
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Book Description
Author: I. Cioranescu
Publisher: Springer Science & Business Media
ISBN: 9400921217
Category : Mathematics
Languages : en
Pages : 274
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Book Description
One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
