Linear difference equations with discrete transform methods:
This book covers the basic elements of difference equations and the tools of difference and the sum calculus necessary for studying and solving, primarily, ordinary linear difference equations. It is lucidly written and carefully motivated with examples from various fields of applications. These exa...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1996
|
| Schriftenreihe: | Mathematics and its applications
363 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book covers the basic elements of difference equations and the tools of difference and the sum calculus necessary for studying and solving, primarily, ordinary linear difference equations. It is lucidly written and carefully motivated with examples from various fields of applications. These examples are presented in the first chapter and then discussed with their detailed solutions in Chapter 2. A particular feature is the use of the discrete Fourier transforms for solving difference equations associated with, generally nonhomogeneous, boundary conditions. Emphasis is placed on illustrating this new method by means of applications. The primary goal of the book is to serve as a primer for a first course in linear difference equations but, with the addition of more theory and applications, the book is suitable for more advanced courses. |
| Beschreibung: | XXI, 439 S. graph. Darst. |
| ISBN: | 0792339401 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear difference equations with discrete transform methods |c by Abdul J. Jerri |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1996 | |
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 363 | |
| 520 | 3 | |a This book covers the basic elements of difference equations and the tools of difference and the sum calculus necessary for studying and solving, primarily, ordinary linear difference equations. It is lucidly written and carefully motivated with examples from various fields of applications. These examples are presented in the first chapter and then discussed with their detailed solutions in Chapter 2. A particular feature is the use of the discrete Fourier transforms for solving difference equations associated with, generally nonhomogeneous, boundary conditions. Emphasis is placed on illustrating this new method by means of applications. The primary goal of the book is to serve as a primer for a first course in linear difference equations but, with the addition of more theory and applications, the book is suitable for more advanced courses. | |
| 650 | 4 | |a Difference equations | |
| 650 | 4 | |a Transformations (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804125269574811648 |
|---|---|
| adam_text | Contents
PREFACE xv
Acknowledgements xix
COURSE ADOPTION xxi
1 SEQUENCES AND DIFFERENCE OPERATORS 1
1.1 Sequences 1
1.2 Difference Operators 13
1.3 The Inverse Difference Operator as a Sum Operator . 33
2 SUM CALCULUS AND THE DISCRETE TRANS¬
FORMS METHODS 41
2.1 Difference Equations 41
2.2 Summation by Parts and The Fundamental Theorem
of Sum Calculus 57
2.3 Discrete Transforms and Review of Integral and Finite
Transforms 65
2.4 The Discrete Fourier Transforms and
Their Sum Calculus Method 95
3 BASIC METHODS OF SOLVING LINEAR DIFFER¬
ENCE EQUATIONS 139
3.1 Fvindamentals of Linear Difference Equations 139
3.2 Solutions of Homogeneous Difference Equations with
Constant Coefficients 157
vii
viii
3.3 Nonhomogeneous Difference Equations with Constant
Coefficients 171
3.4 Linear System of Difference Equations with Constant
Coefficients 197
3.5 Linear Partial Difference Equations with Constant Co¬
efficients 204
3.6 First Order Difference Equations with Variable Coef¬
ficients 225
3.7 Linear Second Order Difference Equations with Vari¬
able Coefficients 240
3.8 Convergence, Equilibrium, and Stability of Linear Equa¬
tions 270
4 DISCRETE FOURIER TRANSFORMS 281
4.1 Continuous to Discrete 281
4.2 Properties of the Discrete Fourier Transform (DFT) . 285
4.3 Sine Cosine (DST DCT) Form of the DFT .... 297
4.4 Solution of a Difference Equation by the DFT Traffic
Network 303
4.5 Further Properties of the DFT for its Operational Sum
Calculus Method 313
4.6 The Fast Fourier Transform 321
5 THE DISCRETE SINE (DST) AND COSINE (DCT)
TRANSFORMS FOR BOUNDARY VALUE PROB¬
LEMS 329
5.1 Establishing the Discrete Sine and Cosine Transforms 330
5.2 Solution of Difference Equations with Boundary Con¬
ditions by DST and DCT 340
6 THE z TRANSFORM FOR INITIAL VALUE PROB¬
LEMS 355
6.1 Discrete Initial Value Problems for the ^ Transform . 355
6.2 The z Transform 359
6.3 The Operational Sum Calculus Method of the z
Transform for Solving Initial Value Problems 375
ix
7 MODELING WITH DIFFERENCE EQUATIONS 385
7.1 Various Discrete Problems Modeled as Difference Equa¬
tions 386
7.2 Solution of the Altruistic Neighborhood Modeled by
DCT 398
REFERENCES 405
ANSWERS TO EXERCISES 409
INDEX OF NOTATIONS 425
SUBJECT INDEX 431
|
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| discipline | Mathematik |
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| id | DE-604.BV010786626 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:53Z |
| institution | BVB |
| isbn | 0792339401 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007205170 |
| oclc_num | 34115211 |
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| physical | XXI, 439 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Jerri, Abdul J. Verfasser aut Linear difference equations with discrete transform methods by Abdul J. Jerri Dordrecht [u.a.] Kluwer Acad. Publ. 1996 XXI, 439 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 363 This book covers the basic elements of difference equations and the tools of difference and the sum calculus necessary for studying and solving, primarily, ordinary linear difference equations. It is lucidly written and carefully motivated with examples from various fields of applications. These examples are presented in the first chapter and then discussed with their detailed solutions in Chapter 2. A particular feature is the use of the discrete Fourier transforms for solving difference equations associated with, generally nonhomogeneous, boundary conditions. Emphasis is placed on illustrating this new method by means of applications. The primary goal of the book is to serve as a primer for a first course in linear difference equations but, with the addition of more theory and applications, the book is suitable for more advanced courses. Difference equations Transformations (Mathematics) Lineare Differenzengleichung (DE-588)4203414-0 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Lineare Differenzengleichung (DE-588)4203414-0 s Transformation Mathematik (DE-588)4060637-5 s DE-604 Mathematics and its applications 363 (DE-604)BV008163334 363 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007205170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jerri, Abdul J. Linear difference equations with discrete transform methods Mathematics and its applications Difference equations Transformations (Mathematics) Lineare Differenzengleichung (DE-588)4203414-0 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| subject_GND | (DE-588)4203414-0 (DE-588)4060637-5 |
| title | Linear difference equations with discrete transform methods |
| title_auth | Linear difference equations with discrete transform methods |
| title_exact_search | Linear difference equations with discrete transform methods |
| title_full | Linear difference equations with discrete transform methods by Abdul J. Jerri |
| title_fullStr | Linear difference equations with discrete transform methods by Abdul J. Jerri |
| title_full_unstemmed | Linear difference equations with discrete transform methods by Abdul J. Jerri |
| title_short | Linear difference equations with discrete transform methods |
| title_sort | linear difference equations with discrete transform methods |
| topic | Difference equations Transformations (Mathematics) Lineare Differenzengleichung (DE-588)4203414-0 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| topic_facet | Difference equations Transformations (Mathematics) Lineare Differenzengleichung Transformation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007205170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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