Differential and Difference Equations: A Comparison of Methods of Solution
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Cham]
Springer
[2016]
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| Subjects: | |
| Online Access: | TUM01 UBT01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (XV, 162 p) |
| ISBN: | 9783319297361 |
| DOI: | 10.1007/978-3-319-29736-1 |
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| 650 | 4 | |a Functional equations | |
| 650 | 4 | |a Differential equations | |
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| 650 | 4 | |a Applied mathematics | |
| 650 | 4 | |a Engineering mathematics | |
| 650 | 4 | |a Mathematical Methods in Physics | |
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| 650 | 4 | |a Mathematische Physik | |
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Record in the Search Index
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| adam_text | DIFFERENTIAL AND DIFFERENCE EQUATIONS
/ MAXIMON, LEONARD C.
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
DIFFERENTIAL AND DIFFERENCE EQUATIONS
/ MAXIMON, LEONARD C.
: 2016
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| indexdate | 2024-07-10T07:28:31Z |
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| isbn | 9783319297361 |
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| spelling | Maximon, Leonard C. Verfasser aut Differential and Difference Equations A Comparison of Methods of Solution Leonard C. Maximon [Cham] Springer [2016] © 2016 1 Online-Ressource (XV, 162 p) txt rdacontent c rdamedia cr rdacarrier Physics Difference equations Functional equations Differential equations Mathematical physics Applied mathematics Engineering mathematics Mathematical Methods in Physics Appl.Mathematics/Computational Methods of Engineering Difference and Functional Equations Mathematical Applications in the Physical Sciences Ordinary Differential Equations Mathematische Physik Erscheint auch als Druckausgabe 978-3-319-29735-4 https://doi.org/10.1007/978-3-319-29736-1 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961870&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Maximon, Leonard C. Differential and Difference Equations A Comparison of Methods of Solution Physics Difference equations Functional equations Differential equations Mathematical physics Applied mathematics Engineering mathematics Mathematical Methods in Physics Appl.Mathematics/Computational Methods of Engineering Difference and Functional Equations Mathematical Applications in the Physical Sciences Ordinary Differential Equations Mathematische Physik |
| title | Differential and Difference Equations A Comparison of Methods of Solution |
| title_auth | Differential and Difference Equations A Comparison of Methods of Solution |
| title_exact_search | Differential and Difference Equations A Comparison of Methods of Solution |
| title_full | Differential and Difference Equations A Comparison of Methods of Solution Leonard C. Maximon |
| title_fullStr | Differential and Difference Equations A Comparison of Methods of Solution Leonard C. Maximon |
| title_full_unstemmed | Differential and Difference Equations A Comparison of Methods of Solution Leonard C. Maximon |
| title_short | Differential and Difference Equations |
| title_sort | differential and difference equations a comparison of methods of solution |
| title_sub | A Comparison of Methods of Solution |
| topic | Physics Difference equations Functional equations Differential equations Mathematical physics Applied mathematics Engineering mathematics Mathematical Methods in Physics Appl.Mathematics/Computational Methods of Engineering Difference and Functional Equations Mathematical Applications in the Physical Sciences Ordinary Differential Equations Mathematische Physik |
| topic_facet | Physics Difference equations Functional equations Differential equations Mathematical physics Applied mathematics Engineering mathematics Mathematical Methods in Physics Appl.Mathematics/Computational Methods of Engineering Difference and Functional Equations Mathematical Applications in the Physical Sciences Ordinary Differential Equations Mathematische Physik |
| url | https://doi.org/10.1007/978-3-319-29736-1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961870&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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