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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)
Resource Information
The item Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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)
 Language

 eng
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (672 p.)
 Note
 Description based upon print version of record
 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 Constantcoefficient linear systems; exponentiation of matrices; 5 Variablecoefficient 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 Firstorder, 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 stressenergy tensors; 8 More general hyperbolic equations; energy estimates; 9 The symbol of a differential operator and a general GreenStokes formula; 10 The Hodge Laplacian on kforms; 11 Maxwell's equations; References; 3 Fourier Analysis, Distributions,and ConstantCoefficient 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 constantcoefficient 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
 Isbn
 9781441970558
 Label
 Partial Differential Equations I : Basic Theory
 Title
 Partial Differential Equations I
 Title remainder
 Basic Theory
 Statement of responsibility
 by Michael E. Taylor
 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)
 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
 QA370380
 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)
 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 Constantcoefficient linear systems; exponentiation of matrices; 5 Variablecoefficient 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 Firstorder, 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 stressenergy tensors; 8 More general hyperbolic equations; energy estimates; 9 The symbol of a differential operator and a general GreenStokes formula; 10 The Hodge Laplacian on kforms; 11 Maxwell's equations; References; 3 Fourier Analysis, Distributions,and ConstantCoefficient 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 constantcoefficient 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
 10.1007/9781441970558
 Specific material designation
 remote
 System control number

 (CKB)2550000000020021
 (EBL)993880
 (OCoLC)768729279
 (SSID)ssj0000450056
 (PQKBManifestationID)11316373
 (PQKBTitleCode)TC0000450056
 (PQKBWorkID)10444764
 (PQKB)10707670
 (DEHe213)9781441970558
 (MiAaPQ)EBC993880
 (EXLCZ)992550000000020021
 Label
 Partial Differential Equations I : Basic Theory, by Michael E. Taylor, (electronic resource)
 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 Constantcoefficient linear systems; exponentiation of matrices; 5 Variablecoefficient 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 Firstorder, 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 stressenergy tensors; 8 More general hyperbolic equations; energy estimates; 9 The symbol of a differential operator and a general GreenStokes formula; 10 The Hodge Laplacian on kforms; 11 Maxwell's equations; References; 3 Fourier Analysis, Distributions,and ConstantCoefficient 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 constantcoefficient 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
 10.1007/9781441970558
 Specific material designation
 remote
 System control number

 (CKB)2550000000020021
 (EBL)993880
 (OCoLC)768729279
 (SSID)ssj0000450056
 (PQKBManifestationID)11316373
 (PQKBTitleCode)TC0000450056
 (PQKBWorkID)10444764
 (PQKB)10707670
 (DEHe213)9781441970558
 (MiAaPQ)EBC993880
 (EXLCZ)992550000000020021
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