The Resource Partial differential equations : mathematical techniques for engineers, Marcelo Epstein
Partial differential equations : mathematical techniques for engineers, Marcelo Epstein
Resource Information
The item Partial differential equations : mathematical techniques for engineers, Marcelo Epstein represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Partial differential equations : mathematical techniques for engineers, Marcelo Epstein represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This monograph presents a graduatelevel treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single firstorder PDE, including shock waves and genuinely nonlinear models, with applications to traffic design and gas dynamics. The rest of the book deals with secondorder equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry
 Language
 eng
 Extent
 1 online resource (xiii, 255 pages)
 Contents

 Preface; Contents; Part I Background; 1 Vector Fields and Ordinary Differential Equations; 1.1 Introduction; 1.2 Curves and Surfaces in mathbbRn; 1.2.1 Cartesian Products, Affine Spaces; 1.2.2 Curves in mathbbRn; 1.2.3 Surfaces in mathbbR3; 1.3 The Divergence Theorem; 1.3.1 The Divergence of a Vector Field; 1.3.2 The Flux of a Vector Field over an Orientable Surface; 1.3.3 Statement of the Theorem; 1.3.4 A Particular Case; 1.4 Ordinary Differential Equations; 1.4.1 Vector Fields as Differential Equations; 1.4.2 Geometry Versus Analysis; 1.4.3 An Example
 1.4.4 Autonomous and Nonautonomous Systems1.4.5 HigherOrder Equations; 1.4.6 First Integrals and Conserved Quantities; 1.4.7 Existence and Uniqueness; 1.4.8 Food for Thought; References; 2 Partial Differential Equations in Engineering; 2.1 Introduction; 2.2 What is a Partial Differential Equation?; 2.3 Balance Laws; 2.3.1 The Generic Balance Equation; 2.3.2 The Case of Only One Spatial Dimension; 2.3.3 The Need for Constitutive Laws; 2.4 Examples of PDEs in Engineering; 2.4.1 Traffic Flow; 2.4.2 Diffusion; 2.4.3 Longitudinal Waves in an Elastic Bar; 2.4.4 Solitons
 2.4.5 TimeIndependent Phenomena2.4.6 Continuum Mechanics; References; Part II The FirstOrder Equation; 3 The Single FirstOrder Quasilinear PDE; 3.1 Introduction; 3.2 Quasilinear Equation in Two Independent Variables; 3.3 Building Solutions from Characteristics; 3.3.1 A Fundamental Lemma; 3.3.2 Corollaries of the Fundamental Lemma; 3.3.3 The Cauchy Problem; 3.3.4 What Else Can Go Wrong?; 3.4 Particular Cases and Examples; 3.4.1 Homogeneous Linear Equation; 3.4.2 Nonhomogeneous Linear Equation; 3.4.3 Quasilinear Equation; 3.5 A Computer Program; References; 4 Shock Waves; 4.1 The Way Out
 4.2 Generalized Solutions4.3 A Detailed Example; 4.4 Discontinuous Initial Conditions; 4.4.1 Shock Waves; 4.4.2 Rarefaction Waves; References; 5 The Genuinely Nonlinear FirstOrder Equation; 5.1 Introduction; 5.2 The Monge Cone Field; 5.3 The Characteristic Directions; 5.4 Recapitulation; 5.5 The Cauchy Problem; 5.6 An Example; 5.7 More Than Two Independent Variables; 5.7.1 Quasilinear Equations; 5.7.2 Nonlinear Equations; 5.8 Application to Hamiltonian Systems; 5.8.1 Hamiltonian Systems; 5.8.2 Reduced Form of a FirstOrder PDE; 5.8.3 The Hamilton  Jacobi Equation; 5.8.4 An Example
 Isbn
 9783319552118
 Label
 Partial differential equations : mathematical techniques for engineers
 Title
 Partial differential equations
 Title remainder
 mathematical techniques for engineers
 Statement of responsibility
 Marcelo Epstein
 Language
 eng
 Summary
 This monograph presents a graduatelevel treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single firstorder PDE, including shock waves and genuinely nonlinear models, with applications to traffic design and gas dynamics. The rest of the book deals with secondorder equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Epstein, M.
 Dewey number
 515/.353
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA377
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Mathematical engineering,
 http://library.link/vocab/subjectName

 Differential equations, Partial
 Engineering
 Theoretical and Applied Mechanics
 Partial Differential Equations
 Mathematical Modeling and Industrial Mathematics
 Label
 Partial differential equations : mathematical techniques for engineers, Marcelo Epstein
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; Part I Background; 1 Vector Fields and Ordinary Differential Equations; 1.1 Introduction; 1.2 Curves and Surfaces in mathbbRn; 1.2.1 Cartesian Products, Affine Spaces; 1.2.2 Curves in mathbbRn; 1.2.3 Surfaces in mathbbR3; 1.3 The Divergence Theorem; 1.3.1 The Divergence of a Vector Field; 1.3.2 The Flux of a Vector Field over an Orientable Surface; 1.3.3 Statement of the Theorem; 1.3.4 A Particular Case; 1.4 Ordinary Differential Equations; 1.4.1 Vector Fields as Differential Equations; 1.4.2 Geometry Versus Analysis; 1.4.3 An Example
 1.4.4 Autonomous and Nonautonomous Systems1.4.5 HigherOrder Equations; 1.4.6 First Integrals and Conserved Quantities; 1.4.7 Existence and Uniqueness; 1.4.8 Food for Thought; References; 2 Partial Differential Equations in Engineering; 2.1 Introduction; 2.2 What is a Partial Differential Equation?; 2.3 Balance Laws; 2.3.1 The Generic Balance Equation; 2.3.2 The Case of Only One Spatial Dimension; 2.3.3 The Need for Constitutive Laws; 2.4 Examples of PDEs in Engineering; 2.4.1 Traffic Flow; 2.4.2 Diffusion; 2.4.3 Longitudinal Waves in an Elastic Bar; 2.4.4 Solitons
 2.4.5 TimeIndependent Phenomena2.4.6 Continuum Mechanics; References; Part II The FirstOrder Equation; 3 The Single FirstOrder Quasilinear PDE; 3.1 Introduction; 3.2 Quasilinear Equation in Two Independent Variables; 3.3 Building Solutions from Characteristics; 3.3.1 A Fundamental Lemma; 3.3.2 Corollaries of the Fundamental Lemma; 3.3.3 The Cauchy Problem; 3.3.4 What Else Can Go Wrong?; 3.4 Particular Cases and Examples; 3.4.1 Homogeneous Linear Equation; 3.4.2 Nonhomogeneous Linear Equation; 3.4.3 Quasilinear Equation; 3.5 A Computer Program; References; 4 Shock Waves; 4.1 The Way Out
 4.2 Generalized Solutions4.3 A Detailed Example; 4.4 Discontinuous Initial Conditions; 4.4.1 Shock Waves; 4.4.2 Rarefaction Waves; References; 5 The Genuinely Nonlinear FirstOrder Equation; 5.1 Introduction; 5.2 The Monge Cone Field; 5.3 The Characteristic Directions; 5.4 Recapitulation; 5.5 The Cauchy Problem; 5.6 An Example; 5.7 More Than Two Independent Variables; 5.7.1 Quasilinear Equations; 5.7.2 Nonlinear Equations; 5.8 Application to Hamiltonian Systems; 5.8.1 Hamiltonian Systems; 5.8.2 Reduced Form of a FirstOrder PDE; 5.8.3 The Hamilton  Jacobi Equation; 5.8.4 An Example
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 255 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319552118
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319552125
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 ocn985105723
 Label
 Partial differential equations : mathematical techniques for engineers, Marcelo Epstein
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; Part I Background; 1 Vector Fields and Ordinary Differential Equations; 1.1 Introduction; 1.2 Curves and Surfaces in mathbbRn; 1.2.1 Cartesian Products, Affine Spaces; 1.2.2 Curves in mathbbRn; 1.2.3 Surfaces in mathbbR3; 1.3 The Divergence Theorem; 1.3.1 The Divergence of a Vector Field; 1.3.2 The Flux of a Vector Field over an Orientable Surface; 1.3.3 Statement of the Theorem; 1.3.4 A Particular Case; 1.4 Ordinary Differential Equations; 1.4.1 Vector Fields as Differential Equations; 1.4.2 Geometry Versus Analysis; 1.4.3 An Example
 1.4.4 Autonomous and Nonautonomous Systems1.4.5 HigherOrder Equations; 1.4.6 First Integrals and Conserved Quantities; 1.4.7 Existence and Uniqueness; 1.4.8 Food for Thought; References; 2 Partial Differential Equations in Engineering; 2.1 Introduction; 2.2 What is a Partial Differential Equation?; 2.3 Balance Laws; 2.3.1 The Generic Balance Equation; 2.3.2 The Case of Only One Spatial Dimension; 2.3.3 The Need for Constitutive Laws; 2.4 Examples of PDEs in Engineering; 2.4.1 Traffic Flow; 2.4.2 Diffusion; 2.4.3 Longitudinal Waves in an Elastic Bar; 2.4.4 Solitons
 2.4.5 TimeIndependent Phenomena2.4.6 Continuum Mechanics; References; Part II The FirstOrder Equation; 3 The Single FirstOrder Quasilinear PDE; 3.1 Introduction; 3.2 Quasilinear Equation in Two Independent Variables; 3.3 Building Solutions from Characteristics; 3.3.1 A Fundamental Lemma; 3.3.2 Corollaries of the Fundamental Lemma; 3.3.3 The Cauchy Problem; 3.3.4 What Else Can Go Wrong?; 3.4 Particular Cases and Examples; 3.4.1 Homogeneous Linear Equation; 3.4.2 Nonhomogeneous Linear Equation; 3.4.3 Quasilinear Equation; 3.5 A Computer Program; References; 4 Shock Waves; 4.1 The Way Out
 4.2 Generalized Solutions4.3 A Detailed Example; 4.4 Discontinuous Initial Conditions; 4.4.1 Shock Waves; 4.4.2 Rarefaction Waves; References; 5 The Genuinely Nonlinear FirstOrder Equation; 5.1 Introduction; 5.2 The Monge Cone Field; 5.3 The Characteristic Directions; 5.4 Recapitulation; 5.5 The Cauchy Problem; 5.6 An Example; 5.7 More Than Two Independent Variables; 5.7.1 Quasilinear Equations; 5.7.2 Nonlinear Equations; 5.8 Application to Hamiltonian Systems; 5.8.1 Hamiltonian Systems; 5.8.2 Reduced Form of a FirstOrder PDE; 5.8.3 The Hamilton  Jacobi Equation; 5.8.4 An Example
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 255 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319552118
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319552125
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 ocn985105723
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