|
Showing 1 - 8 of
8 matches in All Departments
The fourth of a five-volume exposition of the main principles of
nonlinear functional analysis and its applications to the natural
sciences, economics, and numerical analysis. The presentation is
self-contained and accessible to the non-specialist, and topics
covered include applications to mechanics, elasticity, plasticity,
hydrodynamics, thermodynamics, statistical physics, and special and
general relativity including cosmology. The book contains a
detailed physical motivation of the relevant basic equations and a
discussion of particular problems which have played a significant
role in the development of physics and through which important
mathematical and physical insight may be gained. It combines
classical and modern ideas to build a bridge between the language
and thoughts of physicists and mathematicians. Many exercises and a
comprehensive bibliography complement the text.
This is the second of a five-volume exposition of the main
principles of nonlinear functional analysis and its applications to
the natural sciences, economics, and numerical analysis. The
presentation is self -contained and accessible to the
nonspecialist. Part II concerns the theory of monotone operators.
It is divided into two subvolumes, II/A and II/B, which form a
unit. The present Part II/A is devoted to linear monotone
operators. It serves as an elementary introduction to the modern
functional analytic treatment of variational problems, integral
equations, and partial differential equations of elliptic,
parabolic and hyperbolic type. This book also represents an
introduction to numerical functional analysis with applications to
the Ritz method along with the method of finite elements, the
Galerkin methods, and the difference method. Many exercises
complement the text. The theory of monotone operators is closely
related to Hilbert's rigorous justification of the Dirichlet
principle, and to the 19th and 20th problems of Hilbert which he
formulated in his famous Paris lecture in 1900, and which strongly
influenced the development of analysis in the twentieth century.
As long as a branch of knowledge offers an abundance of problems,
it is full of vitality. David Hilbert Over the last 15 years I have
given lectures on a variety of problems in nonlinear functional
analysis and its applications. In doing this, I have recommended to
my students a number of excellent monographs devoted to specialized
topics, but there was no complete survey-type exposition of
nonlinear functional analysis making available a quick survey to
the wide range of readers including mathematicians, natural
scientists, and engineers who have only an elementary knowledge of
linear functional analysis. I have tried to close this gap with my
five-part lecture notes, the first three parts of which have been
published in the Teubner-Texte series by Teubner-Verlag, Leipzig,
1976, 1977, and 1978. The present English edition was translated
from a completely rewritten manuscript which is significantly
longer than the original version in the Teubner-Texte series. The
material is organized in the following way: Part I: Fixed Point
Theorems. Part II: Monotone Operators. Part III: Variational
Methods and Optimization. Parts IV jV: Applications to Mathematical
Physics. The exposition is guided by the following considerations:
(a) What are the supporting basic ideas and what intrinsic
interrelations exist between them? (/3) In what relation do the
basic ideas stand to the known propositions of classical analysis
and linear functional analysis? ( y) What typical applications are
there? Vll Preface viii Special emphasis is placed on motivation.
This is the second of a five-volume exposition of the main
principles of nonlinear functional analysis and its applications to
the natural sciences, economics, and numerical analysis. The
presentation is self -contained and accessible to the
nonspecialist. Part II concerns the theory of monotone operators.
It is divided into two subvolumes, II/A and II/B, which form a
unit. The present Part II/A is devoted to linear monotone
operators. It serves as an elementary introduction to the modern
functional analytic treatment of variational problems, integral
equations, and partial differential equations of elliptic,
parabolic and hyperbolic type. This book also represents an
introduction to numerical functional analysis with applications to
the Ritz method along with the method of finite elements, the
Galerkin methods, and the difference method. Many exercises
complement the text. The theory of monotone operators is closely
related to Hilbert's rigorous justification of the Dirichlet
principle, and to the 19th and 20th problems of Hilbert which he
formulated in his famous Paris lecture in 1900, and which strongly
influenced the development of analysis in the twentieth century.
As long as a branch of knowledge offers an abundance of problems,
it is full of vitality. David Hilbert Over the last 15 years I have
given lectures on a variety of problems in nonlinear functional
analysis and its applications. In doing this, I have recommended to
my students a number of excellent monographs devoted to specialized
topics, but there was no complete survey-type exposition of
nonlinear functional analysis making available a quick survey to
the wide range of readers including mathematicians, natural
scientists, and engineers who have only an elementary knowledge of
linear functional analysis. I have tried to close this gap with my
five-part lecture notes, the first three parts of which have been
published in the Teubner-Texte series by Teubner-Verlag, Leipzig,
1976, 1977, and 1978. The present English edition was translated
from a completely rewritten manuscript which is significantly
longer than the original version in the Teubner-Texte series. The
material is organized in the following way: Part I: Fixed Point
Theorems. Part II: Monotone Operators. Part III: Variational
Methods and Optimization. Parts IV jV: Applications to Mathematical
Physics. The exposition is guided by the following considerations:
(a) What are the supporting basic ideas and what intrinsic
interrelations exist between them? (/3) In what relation do the
basic ideas stand to the known propositions of classical analysis
and linear functional analysis? ( y) What typical applications are
there? Vll Preface viii Special emphasis is placed on motivation.
The main concern in all scientific work must be the human being
himsel[ This, one should never forget among all those diagrams and
equations. Albert Einstein This volume is part of a comprehensive
presentation of nonlinear functional analysis, the basic content of
which has been outlined in the Preface of Part I. A Table of
Contents for all five volumes may also be found in Part I. The Part
IV and the following Part V contain applications to mathematical
present physics. Our goals are the following: (i) A detailed
motivation of the basic equations in important disciplines of
theoretical physics. (ii) A discussion of particular problems which
have played a significant role in the development of physics, and
through which important mathe matical and physical insight may be
gained. (iii) A combination of classical and modern ideas. (iv) An
attempt to build a bridge between the language and thoughts of
physicists and mathematicians. Weshall always try to advance as
soon as possible to the heart ofthe problern under consideration
and to concentrate on the basic ideas.
This is the second of a five-volume exposition of the main
principles of nonlinear functional analysis and its applications to
the natural sciences, economics, and numerical analysis. The
presentation is self -contained and accessible to the
nonspecialist. Part II concerns the theory of monotone operators.
It is divided into two subvolumes, II/A and II/B, which form a
unit. The present Part II/A is devoted to linear monotone
operators. It serves as an elementary introduction to the modern
functional analytic treatment of variational problems, integral
equations, and partial differential equations of elliptic,
parabolic and hyperbolic type. This book also represents an
introduction to numerical functional analysis with applications to
the Ritz method along with the method of finite elements, the
Galerkin methods, and the difference method. Many exercises
complement the text. The theory of monotone operators is closely
related to Hilbert's rigorous justification of the Dirichlet
principle, and to the 19th and 20th problems of Hilbert which he
formulated in his famous Paris lecture in 1900, and which strongly
influenced the development of analysis in the twentieth century.
The fourth of a five-volume exposition of the main principles of
nonlinear functional analysis and its applications to the natural
sciences, economics, and numerical analysis. The presentation is
self-contained and accessible to the non-specialist, and topics
covered include applications to mechanics, elasticity, plasticity,
hydrodynamics, thermodynamics, statistical physics, and special and
general relativity including cosmology. The book contains a
detailed physical motivation of the relevant basic equations and a
discussion of particular problems which have played a significant
role in the development of physics and through which important
mathematical and physical insight may be gained. It combines
classical and modern ideas to build a bridge between the language
and thoughts of physicists and mathematicians. Many exercises and a
comprehensive bibliography complement the text.
|
You may like...
Bad Luck Penny
Amy Heydenrych
Paperback
(1)
R350
R255
Discovery Miles 2 550
Only The Brave
Danielle Steel
Paperback
R365
R260
Discovery Miles 2 600
Book Lovers
Emily Henry
Paperback
(4)
R245
R192
Discovery Miles 1 920
Lost Property
Megan Choritz
Paperback
R310
R266
Discovery Miles 2 660
|