The Topology Of Function Spaces And The Calculus Of Variations In The Large

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The Topology Of Function Spaces And The Calculus Of Variations In The Large

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Author : L. A. Ljusternik
language : en
Publisher: American Mathematical Soc.
Release Date : 1967-12-31

The Topology Of Function Spaces And The Calculus Of Variations In The Large written by L. A. Ljusternik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-12-31 with Mathematics categories.

The Topology Of Function Spaces And The Calculus Of Variations In The Large

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Author : L. A. Ljusternik
language : en
Publisher:
Release Date : 1989

The Topology Of Function Spaces And The Calculus Of Variations In The Large written by L. A. Ljusternik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

The Calculus Of Variations In The Large

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Author : Marston Morse
language : en
Publisher: American Mathematical Soc.
Release Date : 1934-12-31

The Calculus Of Variations In The Large written by Marston Morse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934-12-31 with Mathematics categories.

Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Unbounded Functionals In The Calculus Of Variations

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Author : Luciano Carbone
language : en
Publisher: CRC Press
Release Date : 2019-06-13

Unbounded Functionals In The Calculus Of Variations written by Luciano Carbone and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener

The Calculus Of Variations In The Large

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Author : Marston Morse
language : en
Publisher: American Mathematical Soc.
Release Date : 1934-12-31

The Calculus Of Variations In The Large written by Marston Morse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934-12-31 with Mathematics categories.

Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Real Analysis

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Author : Emmanuele DiBenedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Real Analysis written by Emmanuele DiBenedetto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This graduate text in real analysis is a solid building block for research in analysis, PDEs, the calculus of variations, probability, and approximation theory. It covers all the core topics, such as a basic introduction to functional analysis, and it discusses other topics often not addressed including Radon measures, the Besicovitch covering Theorem, the Rademacher theorem, and a constructive presentation of the Stone-Weierstrass Theoroem.

Six Themes On Variation

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Author : Steven James Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Six Themes On Variation written by Steven James Cox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

Selected Papers Of Wilhelm P A Klingenberg

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Author : Wilhelm P A Klingenberg
language : en
Publisher: World Scientific
Release Date : 1991-11-18

Selected Papers Of Wilhelm P A Klingenberg written by Wilhelm P A Klingenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-18 with Mathematics categories.

This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geometric Algebra, Classical Differential Geometry and Foundations of Geometry of Klingenberg. Of significance were his contributions to Riemannian Geometry in the Large which opened a new area in Global Riemannian Geometry. He also introduced the Hilbert manifold of closed curves of class H1 on a Riemannian manifold. In connection with his work in closed geodesics, he became interested in the properties of the geodesic flow. Classical results from dynamical systems became useful tools for the study of closed geodesics. He was also credited for drawing closer together Riemannian Geometry and Hamiltonian systems, which had developed separately since the time of H Poincaré.Besides publishing research papers, Klingenberg also wrote a dozen books and lecture notes, among which is the important reference work “Riemannsche Geometrie im Groβen”.

Mathematical Essays

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Author : Chuan-Chih Hsiung
language : en
Publisher: World Scientific
Release Date : 1983

Mathematical Essays written by Chuan-Chih Hsiung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

This is a collection of research papers published in various mathematical journals by friends, colleagues and former students of Professor Buchin Su in honor ofhis 80th birthday and 50th year of educational work.Professor Su was born in 1902 in Pingyang County, Zhejiang Province, People's Republic of China. He received the degree of Bachelor of Science inmathematics from Tohoku University, Sendai, Japan in 1927, and the degree ofDoctor of Science from the same university in 1931. After returning to Chinain 1931, he first taught at Zhejiang University in Hangzhou until 1952 when thewhole College of Science of Zhejiang University was merged into Fudan Universityin Shanghai. During his 50 years of educational work besides teaching, he alsohas taken up various administrative positions serving as Chairman, Dean, VicePresident and finally the President of Fudan University in 1978

Lectures On Closed Geodesics

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Author : W. Klingenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Lectures On Closed Geodesics written by W. Klingenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the object of intensive investigations since the beginning of global differential geo metry during the last century. The simplest case occurs for c10sed surfaces of negative curvature. Here, the fundamental group is very large and, as shown by Hadamard [Had] in 1898, every non-null homotopic c10sed curve can be deformed into a c10sed curve having minimallength in its free homotopy c1ass. This minimal curve is, up to the parameterization, uniquely determined and represents a c10sed geodesic. The question of existence of a c10sed geodesic on a simply connected c10sed surface is much more difficult. As pointed out by Poincare [po 1] in 1905, this problem has much in common with the problem ofthe existence of periodic orbits in the restricted three body problem. Poincare [l.c.] outlined a proof that on an analytic convex surface which does not differ too much from the standard sphere there always exists at least one c10sed geodesic of elliptic type, i. e., the corres ponding periodic orbit in the geodesic flow is infinitesimally stable.