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)

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
Creator
Author
Author
Subject
Language
  • eng
  • 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
Dewey number
530
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
WP4VzsvKEvw
Language note
English
LC call number
QC5.53
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Mathematical physics
  • Engineering mathematics
  • Functional equations
  • Differential Equations
  • Mathematical Methods in Physics
  • Mathematical and Computational 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)
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
Preface -- Introduction -- 1 Operators -- 2 Solution of homogeneous and inhomogeneous linear equations -- 3 First order homogeneous and inhomogeneous linear equations -- 4 Second-order homogeneous and inhomogeneous equations -- 5 Self-adjoint linear equations -- 6 Green’s function -- 7 Generating function, z-transforms, 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
Edition
1st ed. 2016.
Extent
1 online resource (166 p.)
Form of item
online
Isbn
9783319297361
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-319-29736-1
Specific material designation
remote
System control number
  • (CKB)3710000000649180
  • (EBL)4508874
  • (SSID)ssj0001665944
  • (PQKBManifestationID)16454866
  • (PQKBTitleCode)TC0001665944
  • (PQKBWorkID)14999715
  • (PQKB)10136427
  • (DE-He213)978-3-319-29736-1
  • (MiAaPQ)EBC4508874
  • (EXLCZ)993710000000649180
Label
Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (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
Preface -- Introduction -- 1 Operators -- 2 Solution of homogeneous and inhomogeneous linear equations -- 3 First order homogeneous and inhomogeneous linear equations -- 4 Second-order homogeneous and inhomogeneous equations -- 5 Self-adjoint linear equations -- 6 Green’s function -- 7 Generating function, z-transforms, 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
Edition
1st ed. 2016.
Extent
1 online resource (166 p.)
Form of item
online
Isbn
9783319297361
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-319-29736-1
Specific material designation
remote
System control number
  • (CKB)3710000000649180
  • (EBL)4508874
  • (SSID)ssj0001665944
  • (PQKBManifestationID)16454866
  • (PQKBTitleCode)TC0001665944
  • (PQKBWorkID)14999715
  • (PQKB)10136427
  • (DE-He213)978-3-319-29736-1
  • (MiAaPQ)EBC4508874
  • (EXLCZ)993710000000649180

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