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The Resource Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource)
Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource)
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The item Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations  variation of constants, reduction of order, Laplace transforms and generating functions  bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer’s rule, a detailed consideration of the role of the superposition principal in the Green’s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients
 Language
 eng
 Extent
 XV, 162 p.
 Contents

 Preface
 Introduction
 1 Operators
 2 Solution of homogeneous and inhomogeneous linear equations
 3 First order homogeneous and inhomogeneous linear equations
 4 Secondorder homogeneous and inhomogeneous equations
 5 Selfadjoint linear equations
 6 Green’s function
 7 Generating function, ztransforms, Laplace transforms and the solution of linear differential and difference equations
 8 Dictionary of difference equations with polynomial coefficients
 Appendix A: Difference operator
 Appendix B: Notation
 Appendix C: Wronskian Determinant
 Appendix D: Casoratian Determinant
 Appendix E: Cramer’s Rule
 Appendix F: Green’s function and the Superposition principle
 Appendix G: Inverse Laplace transforms and Inverse Generating functions
 Appendix H: Hypergeometric function
 Appendix I: Confluent Hypergeometric function
 Appendix J. Solutions of the second kind
 Bibliography
 Isbn
 9783319297361
 Label
 Differential and Difference Equations : A Comparison of Methods of Solution
 Title
 Differential and Difference Equations
 Title remainder
 A Comparison of Methods of Solution
 Statement of responsibility
 by Leonard C. Maximon
 Subject

 Differential equations
 Differential equations
 Physics
 Mathematical physics
 Ordinary Differential Equations
 Functional equations
 Mathematical physics
 Appl.Mathematics/Computational Methods of Engineering
 Engineering mathematics
 Functional equations
 Electronic resources
 Physics
 Engineering mathematics
 Difference equations
 Physics
 Mathematical Applications in the Physical Sciences
 Difference and Functional Equations
 Mathematical Methods in Physics
 Difference equations
 Applied mathematics
 Applied mathematics
 Language
 eng
 Summary
 This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations  variation of constants, reduction of order, Laplace transforms and generating functions  bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer’s rule, a detailed consideration of the role of the superposition principal in the Green’s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients
 http://library.link/vocab/creatorName
 Maximon, Leonard C
 Image bit depth
 0
 LC call number
 QC5.53
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Physics
 Difference equations
 Functional equations
 Differential equations
 Mathematical physics
 Applied mathematics
 Engineering mathematics
 Physics
 Mathematical Methods in Physics
 Appl.Mathematics/Computational Methods of Engineering
 Difference and Functional Equations
 Mathematical Applications in the Physical Sciences
 Ordinary Differential Equations
 Label
 Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Introduction  1 Operators  2 Solution of homogeneous and inhomogeneous linear equations  3 First order homogeneous and inhomogeneous linear equations  4 Secondorder homogeneous and inhomogeneous equations  5 Selfadjoint linear equations  6 Green’s function  7 Generating function, ztransforms, Laplace transforms and the solution of linear differential and difference equations  8 Dictionary of difference equations with polynomial coefficients  Appendix A: Difference operator  Appendix B: Notation  Appendix C: Wronskian Determinant  Appendix D: Casoratian Determinant  Appendix E: Cramer’s Rule  Appendix F: Green’s function and the Superposition principle  Appendix G: Inverse Laplace transforms and Inverse Generating functions  Appendix H: Hypergeometric function  Appendix I: Confluent Hypergeometric function  Appendix J. Solutions of the second kind  Bibliography
 Dimensions
 unknown
 Extent
 XV, 162 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319297361
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319297361
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319297361
 Label
 Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Introduction  1 Operators  2 Solution of homogeneous and inhomogeneous linear equations  3 First order homogeneous and inhomogeneous linear equations  4 Secondorder homogeneous and inhomogeneous equations  5 Selfadjoint linear equations  6 Green’s function  7 Generating function, ztransforms, Laplace transforms and the solution of linear differential and difference equations  8 Dictionary of difference equations with polynomial coefficients  Appendix A: Difference operator  Appendix B: Notation  Appendix C: Wronskian Determinant  Appendix D: Casoratian Determinant  Appendix E: Cramer’s Rule  Appendix F: Green’s function and the Superposition principle  Appendix G: Inverse Laplace transforms and Inverse Generating functions  Appendix H: Hypergeometric function  Appendix I: Confluent Hypergeometric function  Appendix J. Solutions of the second kind  Bibliography
 Dimensions
 unknown
 Extent
 XV, 162 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319297361
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319297361
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319297361
Subject
 Appl.Mathematics/Computational Methods of Engineering
 Applied mathematics
 Applied mathematics
 Difference and Functional Equations
 Difference equations
 Difference equations
 Differential equations
 Differential equations
 Electronic resources
 Engineering mathematics
 Engineering mathematics
 Functional equations
 Functional equations
 Mathematical Applications in the Physical Sciences
 Mathematical Methods in Physics
 Mathematical physics
 Mathematical physics
 Ordinary Differential Equations
 Physics
 Physics
 Physics
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