The Resource Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource)

Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource)

Label
Partial Differential Equations I : Basic Theory
Title
Partial Differential Equations I
Title remainder
Basic Theory
Statement of responsibility
by Michael E. Taylor
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (SIAM Review, June 1998)
Member of
Is Subseries of
http://library.link/vocab/creatorName
Taylor, Michael E
Dewey number
  • 515.3
  • 515.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
I2wHxIaqqw8
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Applied Mathematical Sciences,
Series volume
115
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Cell aggregation
  • Partial Differential Equations
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Partial Differential Equations I; Contents; Contents of Volumes II and III; Preface; 1 Basic Theory of ODE and Vector Fields; 1 The derivative; 2 Fundamental local existence theorem for ODE; 3 Inverse function and implicit function theorems; 4 Constant-coefficient linear systems; exponentiation of matrices; 5 Variable-coefficient linear systems of ODE: Duhamel's principle; 6 Dependence of solutions on initial data and on other parameters; 7 Flows and vector fields; 8 Lie brackets; 9 Commuting flows; Frobenius's theorem; 10 Hamiltonian systems; 11 Geodesics
  • 12 Variational problems and the stationary action principle13 Differential forms; 14 The symplectic form and canonical transformations; 15 First-order, scalar, nonlinear PDE; 16 Completely integrable hamiltonian systems; 17 Examples of integrable systems; central force problems; 18 Relativistic motion; 19 Topological applications of differential forms; 20 Critical points and index of a vector field; A Nonsmooth vector fields; References; 2 The Laplace Equation and Wave Equation; 1 Vibrating strings and membranes; 2 The divergence of a vector field
  • 3 The covariant derivative and divergence of tensor fields4 The Laplace operator on a Riemannian manifold; 5 The wave equation on a product manifold and energy conservation; 6 Uniqueness and finite propagation speed; 7 Lorentz manifolds and stress-energy tensors; 8 More general hyperbolic equations; energy estimates; 9 The symbol of a differential operator and a general Green-Stokes formula; 10 The Hodge Laplacian on k-forms; 11 Maxwell's equations; References; 3 Fourier Analysis, Distributions,and Constant-Coefficient Linear PDE; 1 Fourier series
  • 2 Harmonic functions and holomorphic functions in the plane3 The Fourier transform; 4 Distributions and tempered distributions; 5 The classical evolution equations; 6 Radial distributions, polar coordinates, and Bessel functions; 7 The method of images and Poisson's summation formula; 8 Homogeneous distributions and principal value distributions; 9 Elliptic operators; 10 Local solvability of constant-coefficient PDE; 11 The discrete Fourier transform; 12 The fast Fourier transform; A The mighty Gaussian and the sublime gamma function; References; 4 Sobolev Spaces; 1 Sobolev spaces on Rn
  • 2 The complex interpolation method3 Sobolev spaces on compact manifolds; 4 Sobolev spaces on bounded domains; 5 The Sobolev spaces Hs0(); 6 The Schwartz kernel theorem; 7 Sobolev spaces on rough domains; References; 5 Linear Elliptic Equations; 1 Existence and regularity of solutions to the Dirichlet problem; 2 The weak and strong maximum principles; 3 The Dirichlet problem on the ball in Rn; 4 The Riemann mapping theorem (smooth boundary); 5 The Dirichlet problem on a domain with a rough boundary; 6 The Riemann mapping theorem (rough boundary); 7 The Neumann boundary problem
  • 8 The Hodge decomposition and harmonic forms
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (672 p.)
Form of item
online
Isbn
9781441970558
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-7055-8
Specific material designation
remote
System control number
  • (CKB)2550000000020021
  • (EBL)993880
  • (OCoLC)768729279
  • (SSID)ssj0000450056
  • (PQKBManifestationID)11316373
  • (PQKBTitleCode)TC0000450056
  • (PQKBWorkID)10444764
  • (PQKB)10707670
  • (DE-He213)978-1-4419-7055-8
  • (MiAaPQ)EBC993880
  • (EXLCZ)992550000000020021
Label
Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Partial Differential Equations I; Contents; Contents of Volumes II and III; Preface; 1 Basic Theory of ODE and Vector Fields; 1 The derivative; 2 Fundamental local existence theorem for ODE; 3 Inverse function and implicit function theorems; 4 Constant-coefficient linear systems; exponentiation of matrices; 5 Variable-coefficient linear systems of ODE: Duhamel's principle; 6 Dependence of solutions on initial data and on other parameters; 7 Flows and vector fields; 8 Lie brackets; 9 Commuting flows; Frobenius's theorem; 10 Hamiltonian systems; 11 Geodesics
  • 12 Variational problems and the stationary action principle13 Differential forms; 14 The symplectic form and canonical transformations; 15 First-order, scalar, nonlinear PDE; 16 Completely integrable hamiltonian systems; 17 Examples of integrable systems; central force problems; 18 Relativistic motion; 19 Topological applications of differential forms; 20 Critical points and index of a vector field; A Nonsmooth vector fields; References; 2 The Laplace Equation and Wave Equation; 1 Vibrating strings and membranes; 2 The divergence of a vector field
  • 3 The covariant derivative and divergence of tensor fields4 The Laplace operator on a Riemannian manifold; 5 The wave equation on a product manifold and energy conservation; 6 Uniqueness and finite propagation speed; 7 Lorentz manifolds and stress-energy tensors; 8 More general hyperbolic equations; energy estimates; 9 The symbol of a differential operator and a general Green-Stokes formula; 10 The Hodge Laplacian on k-forms; 11 Maxwell's equations; References; 3 Fourier Analysis, Distributions,and Constant-Coefficient Linear PDE; 1 Fourier series
  • 2 Harmonic functions and holomorphic functions in the plane3 The Fourier transform; 4 Distributions and tempered distributions; 5 The classical evolution equations; 6 Radial distributions, polar coordinates, and Bessel functions; 7 The method of images and Poisson's summation formula; 8 Homogeneous distributions and principal value distributions; 9 Elliptic operators; 10 Local solvability of constant-coefficient PDE; 11 The discrete Fourier transform; 12 The fast Fourier transform; A The mighty Gaussian and the sublime gamma function; References; 4 Sobolev Spaces; 1 Sobolev spaces on Rn
  • 2 The complex interpolation method3 Sobolev spaces on compact manifolds; 4 Sobolev spaces on bounded domains; 5 The Sobolev spaces Hs0(); 6 The Schwartz kernel theorem; 7 Sobolev spaces on rough domains; References; 5 Linear Elliptic Equations; 1 Existence and regularity of solutions to the Dirichlet problem; 2 The weak and strong maximum principles; 3 The Dirichlet problem on the ball in Rn; 4 The Riemann mapping theorem (smooth boundary); 5 The Dirichlet problem on a domain with a rough boundary; 6 The Riemann mapping theorem (rough boundary); 7 The Neumann boundary problem
  • 8 The Hodge decomposition and harmonic forms
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (672 p.)
Form of item
online
Isbn
9781441970558
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4419-7055-8
Specific material designation
remote
System control number
  • (CKB)2550000000020021
  • (EBL)993880
  • (OCoLC)768729279
  • (SSID)ssj0000450056
  • (PQKBManifestationID)11316373
  • (PQKBTitleCode)TC0000450056
  • (PQKBWorkID)10444764
  • (PQKB)10707670
  • (DE-He213)978-1-4419-7055-8
  • (MiAaPQ)EBC993880
  • (EXLCZ)992550000000020021

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