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
Contributor
Author
Provider
Subject
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)
Instantiates
Publication
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 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
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
10.1007/978-3-319-29736-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-29736-1
Label
Differential and Difference Equations : A Comparison of Methods of Solution, by Leonard C. Maximon, (electronic resource)
Publication
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 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
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
10.1007/978-3-319-29736-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-29736-1

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