W.F. Shadwick's Books

Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

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Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

Dedicated to the late Juan Carlos Simo, this volume contains the proceedings of a workshop held at the Fields Institute in October 1993. The articles focus on current algorithms for the integration of mechanical systems, from systems in celestial mechanics to coupled rigid bodies to fluid mechanics. The scope of the articles ranges from symplectic integration methods to energy-momentum methods and related themes.

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258

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821802593

ISBN 13

9780821802595

Local Jet Bundle Formulation of Bäckland Transformations

With Applications to Non-Linear Evolution Equations

By: F.A.E. Pirani,D.C. Robinson,W.F. Shadwick

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Local Jet Bundle Formulation of Bäckland Transformations

With Applications to Non-Linear Evolution Equations

By: F.A.E. Pirani,D.C. Robinson,W.F. Shadwick

The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans formations. These transformations are used to solve certain partial differential equations, particularly non-linear evolution equations. Of course jets have been employed for some time in the theory of partial differential equations, but so far little use has been made of them in applications. In the meanwhile, substantial progress has been made in the study of non-linear evolution equations. This work has been encouraged by the dis covery of remarkable properties of some such equations, for example the existence of soliton solutions and of infinite se quences of conservation laws. Among the techniques devised to deal with these equations are the inverse scattering method and the Backlund transformation. In our opinion the jet bundle formulation offers a unifying geometrical framework for under standing the properties of non-linear evolution equations and the techniques used to deal with them, although we do not consider all of these properties and techniques here. The relevance of the theory of jet bundles lS that it legitimates the practice of regarding the partial derivatives of field variables as independent quantities. Since Backlund trans formations require from the outset manipulation of these partial derivatives, and repeated shifts of point of view about which variables are dependent on which, this geometrical setting clari fies and simplifies the concepts involved, and offers the prospect of bringing coherence to a variety of disparate results.

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Page Count

138

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400995113

ISBN 13

9789400995116

Local Jet Bundle Formulation of Bäckland Transformations

With Applications to Non-Linear Evolution Equations

By: F.A.E. Pirani,D.C. Robinson,W.F. Shadwick

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Local Jet Bundle Formulation of Bäckland Transformations

With Applications to Non-Linear Evolution Equations

By: F.A.E. Pirani,D.C. Robinson,W.F. Shadwick

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138

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Springer Science & Business Media

Published Date

ISBN 10

9400995113

ISBN 13

9789400995116

Mechanics Day

By: W. F. Shadwick,Perinkulam Sambamurthy Krishnaprasad,Tudor S. Rațiu

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Mechanics Day

By: W. F. Shadwick,Perinkulam Sambamurthy Krishnaprasad,Tudor S. Rațiu

This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial diffe.

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271

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821802615

ISBN 13

9780821802618

Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

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Integration Algorithms and Classical Mechanics

By: Jerrold E. Marsden,George William Patrick,W. F. Shadwick

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258

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821802593

ISBN 13

9780821802595

Differential Geometry

The Interface Between Pure and Applied Mathematics : Proceedings of a Conference Held April 23-25, 1986 with Support from the National Science Foundation

By: Mladen Luksic,Clyde Martin,W. F. Shadwick

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Differential Geometry

The Interface Between Pure and Applied Mathematics : Proceedings of a Conference Held April 23-25, 1986 with Support from the National Science Foundation

By: Mladen Luksic,Clyde Martin,W. F. Shadwick

Normally, mathematical research has been divided into ``pure'' and ``applied,'' and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled ``Differential Geometry: The Interface Between Pure and Applied Mathematics,'' which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis, and control theory.

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Page Count

288

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821854070

ISBN 13

9780821854075

Differential Geometry: The Interface between Pure and Applied Mathematics

The Interface Between Pure and Applied Mathematics : Proceedings of a Conference Held April 23-25, 1986 with Support from the National Science Foundation

By: Mladen Luksic

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Differential Geometry: The Interface between Pure and Applied Mathematics

The Interface Between Pure and Applied Mathematics : Proceedings of a Conference Held April 23-25, 1986 with Support from the National Science Foundation

By: Mladen Luksic

Contains papers that represent the proceedings of a conference entitled 'Differential Geometry: The Interface Between Pure and Applied Mathematics', which was held in San Antonio, Texas, in April 1986. This work covers a range of applications and techniques in such areas as ordinary differential equations, Lie groups, algebra and control theory.

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Page Count

286

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082185075X

ISBN 13

9780821850756

Differential Geometry, Global Analysis, and Topology

Proceedings of a Special Session of the Canadian Mathematical Society Summer Meeting Held June 1-3, 1990

By: Canadian Mathematical Society. Summer Meeting

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Differential Geometry, Global Analysis, and Topology

Proceedings of a Special Session of the Canadian Mathematical Society Summer Meeting Held June 1-3, 1990

By: Canadian Mathematical Society. Summer Meeting

This book contains the proceedings of a special session held during the Summer Meeting of the Canadian Mathematical Society in 1990. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. The topics covered include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry and provide an insight into some recent trends in these areas.

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Page Count

198

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821860178

ISBN 13

9780821860175

Nonlinear Boundary Value Problems in Science and Engineering

By: C. Rogers,W. F. Ames

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Nonlinear Boundary Value Problems in Science and Engineering

By: C. Rogers,W. F. Ames

Overall, our object has been to provide an applications-oriented text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.

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Page Count

433

Publisher

Academic Press

Published Date

ISBN 10

0080958702

ISBN 13

9780080958705

Book's by W.F. Shadwick

Integration Algorithms and Classical Mechanics

Integration Algorithms and Classical Mechanics

Local Jet Bundle Formulation of Bäckland Transformations

Local Jet Bundle Formulation of Bäckland Transformations

Local Jet Bundle Formulation of Bäckland Transformations

Local Jet Bundle Formulation of Bäckland Transformations

Mechanics Day

Mechanics Day

Integration Algorithms and Classical Mechanics

Integration Algorithms and Classical Mechanics

Differential Geometry

Differential Geometry

Differential Geometry: The Interface between Pure and Applied Mathematics

Differential Geometry: The Interface between Pure and Applied Mathematics

Differential Geometry, Global Analysis, and Topology

Differential Geometry, Global Analysis, and Topology

Nonlinear Boundary Value Problems in Science and Engineering

Nonlinear Boundary Value Problems in Science and Engineering

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