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Sobolev Gradients and Differential Equations (Record no. 29353)

000 -LEADER
fixed length control field 04070nam a22004335i 4500
003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310154226.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 100301s2010 gw | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783642040412
978-3-642-04041-2
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA370-380
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.353
Edition number 23
264 #1 -
-- Berlin, Heidelberg :
-- Springer Berlin Heidelberg,
-- 2010.
912 ## -
-- ZDB-2-SMA
-- ZDB-2-LNM
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Neuberger, J.W.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
Title Sobolev Gradients and Differential Equations
Medium [electronic resource] /
Statement of responsibility, etc by J.W. Neuberger.
300 ## - PHYSICAL DESCRIPTION
Extent XIII, 289p.
Other physical details online resource.
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Lecture Notes in Mathematics,
International Standard Serial Number 0075-8434 ;
Volume number/sequential designation 1670
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Several Gradients -- Comparison of Two Gradients -- Continuous Steepest Descent in Hilbert Space: Linear Case -- Continuous Steepest Descent in Hilbert Space: Nonlinear Case -- Orthogonal Projections, Adjoints and Laplacians -- Ordinary Differential Equations and Sobolev Gradients -- Convexity and Gradient Inequalities -- Boundary and Supplementary Conditions -- Continuous Newton’s Method -- More About Finite Differences -- Sobolev Gradients for Variational Problems -- An Introduction to Sobolev Gradients in Non-Inner Product Spaces -- Singularities and a Simple Ginzburg-Landau Functional -- The Superconductivity Equations of Ginzburg-Landau -- Tricomi Equation: A Case Study -- Minimal Surfaces -- Flow Problems and Non-Inner Product Sobolev Spaces -- An Alternate Approach to Time-dependent PDEs -- Foliations and Supplementary Conditions I -- Foliations and Supplementary Conditions II -- Some Related Iterative Methods for Differential Equations -- An Analytic Iteration Method -- Steepest Descent for Conservation Equations -- Code for an Ordinary Differential Equation -- Geometric Curve Modeling with Sobolev Gradients -- Numerical Differentiation, Sobolev Gradients -- Steepest Descent and Newton’s Method and Elliptic PDE -- Ginzburg-Landau Separation Problems -- Numerical Preconditioning Methods for Elliptic PDEs -- More Results on Sobolev Gradient Problems -- Notes and Suggestions for Future Work.
520 ## - SUMMARY, ETC.
Summary, etc A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Differential equations, partial.
Topical term or geographic name as entry element Numerical analysis.
Topical term or geographic name as entry element Mathematics.
Topical term or geographic name as entry element Partial Differential Equations.
Topical term or geographic name as entry element Numerical Analysis.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783642040405
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-642-04041-2
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-03-27AUM Main Library2014-03-27 2014-03-27 E-Book   AUM Main Library515.353
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