Exterior Differential Systems and Euler-Lagrange Partial Differential Equations: Chicago Lectures in Mathematics
Autor Robert Bryant, Phillip Griffiths, Daniel Grossmanen Limba Engleză Hardback – 30 iun 2003
InExterior
Differential
Systems,
the
authors
present
the
results
of
their
ongoing
development
of
a
theory
of
the
geometry
of
differential
equations,
focusing
especially
on
Lagrangians
and
Poincaré-Cartan
forms.
They
also
cover
certain
aspects
of
the
theory
of
exterior
differential
systems,
which
provides
the
language
and
techniques
for
the
entire
study.
Because
it
plays
a
central
role
in
uncovering
geometric
properties
of
differential
equations,
the
method
of
equivalence
is
particularly
emphasized.
In
addition,
the
authors
discuss
conformally
invariant
systems
at
length,
including
results
on
the
classification
and
application
of
symmetries
and
conservation
laws.
The
book
also
covers
the
Second
Variation,
Euler-Lagrange
PDE
systems,
and
higher-order
conservation
laws.
This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
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Specificații
ISBN-13: 9780226077932
ISBN-10: 0226077934
Pagini: 216
Dimensiuni: 152 x 229 x 18 mm
Greutate: 0.42 kg
Ediția:1
Editura: University of Chicago Press
Colecția University of Chicago Press
Seria Chicago Lectures in Mathematics
ISBN-10: 0226077934
Pagini: 216
Dimensiuni: 152 x 229 x 18 mm
Greutate: 0.42 kg
Ediția:1
Editura: University of Chicago Press
Colecția University of Chicago Press
Seria Chicago Lectures in Mathematics
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Notă biografică
Robert
Bryantis
the
J.
M.
Kreps
Professor
in
the
Department
of
Mathematics
at
Duke
University.
Phillip Griffithsis the director of the Institute for Advanced Study and professor in the Department of Mathematics at Duke University.
Daniel Grossmanwas an L. E. Dickson Instructor in the Department of Mathematics at the University of Chicago at the time of writing, and is now a consultant at the Chicago office of the Boston Consulting Group.
Phillip Griffithsis the director of the Institute for Advanced Study and professor in the Department of Mathematics at Duke University.
Daniel Grossmanwas an L. E. Dickson Instructor in the Department of Mathematics at the University of Chicago at the time of writing, and is now a consultant at the Chicago office of the Boston Consulting Group.
Cuprins
Preface
Introduction
1. Lagrangians and Poincaré-Cartan Forms
1.1 Lagrangians and Contact Geometry
1.2 The Euler-Lagrange System
1.3 Noether's Theorem
1.4 Hypersurfaces in Euclidean Space
2. The Geometry of Poincaré-Cartan Forms
2.1 The Equivalence Problem forn= 2
2.2 Neo-Classical Poincaré-Cartan Forms
2.3 Digression on Affine Geometry for Hypersurfaces
2.4 The Equivalence Problem forn>3
2.5 The Prescribed Mean Curvature System
3. Conformally Invariant Euler-Lagrange Systems
3.1 Background Material on Conformal Geometry
3.2 Confromally Invariant Poincaré-Cartan Forms
3.3 The Conformal Branch of the Equivalence Problem
3.4 Conservation Laws for Du = Cu n+2/n-2
3.5 Conservation Laws for Wave Equations
4. Additional Topics
4.1 The Second Variation
4.2 Euler-Lagrange PDE Systems
4.3 Higher-Order Conservation Laws
Introduction
1. Lagrangians and Poincaré-Cartan Forms
1.1 Lagrangians and Contact Geometry
1.2 The Euler-Lagrange System
1.3 Noether's Theorem
1.4 Hypersurfaces in Euclidean Space
2. The Geometry of Poincaré-Cartan Forms
2.1 The Equivalence Problem forn= 2
2.2 Neo-Classical Poincaré-Cartan Forms
2.3 Digression on Affine Geometry for Hypersurfaces
2.4 The Equivalence Problem forn>3
2.5 The Prescribed Mean Curvature System
3. Conformally Invariant Euler-Lagrange Systems
3.1 Background Material on Conformal Geometry
3.2 Confromally Invariant Poincaré-Cartan Forms
3.3 The Conformal Branch of the Equivalence Problem
3.4 Conservation Laws for Du = Cu n+2/n-2
3.5 Conservation Laws for Wave Equations
4. Additional Topics
4.1 The Second Variation
4.2 Euler-Lagrange PDE Systems
4.3 Higher-Order Conservation Laws