An introduction to difference equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 389 S. graph. Darst. |
| ISBN: | 0387945822 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | SABER N. ELAYDI
AN INTRODUCTION TO
DIFFERENCE EQUATIONS
WITH 64 ILLUSTRATIONS
SPRINGER
CONTENTS
PREFACE VII
1 DYNAMICS OF FIRST ORDER DIFFERENCE EQUATIONS 1
1.1 INTRODUCTION 1
1.2 LINEAR FIRST ORDER DIFFERENCE EQUATIONS 2
1.2.1 IMPORTANT SPECIAL CASES 4
1.3 EQUILIBRIUM POINTS 8
1.3.1 THE STAIR STEP (COBWEB) DIAGRAMS 15
1.3.2 THE COBWEB THEOREM OF ECONOMICS 20
1.4 CRITERIA FOR ASYMPTOTIC STABILITY OF EQUILIBRIUM POINTS 24
1.5 PERIODIC POINTS AND CYCLES 31
1.6 THE LOGISTIC EQUATION AND BIFURCATION 38
1.6.1 EQUILIBRIUM POINTS (FIXED POINTS OF F/U,) 38
1.6.2 2 CYCLES 38
1.6.3 2
2
CYCLES 42
1.6.4 THE BIFURCATION DIAGRAM 42
2 LINEAR DIFFERENCE EQUATIONS OF HIGHER ORDER 49
2.1 DIFFERENCE CALCULUS 49
2.1.1 THE POWER SHIFT . . 51
2.1.2 FACTORIAL POLYNOMIALS 52
2.1.3 THE ANTIDIFFERENCE OPERATOR 53
2.2 GENERAL THEORY OF LINEAR DIFFERENCE EQUATIONS 56
2.3 LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS ..
. 67
XII CONTENTS
2.4 LINEAR NONHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED
COEFFICIENTS . . . 75
2.4.1 THE METHOD OF VARIATION OF CONSTANTS (PARAMETERS) ..
. 81
2.5 LIMITING BEHAVIOR OF SOLUTIONS 83
2.6 NONLINEAR EQUATIONS TRANSFORMABLE TO LINEAR EQUATIONS 91
2.7 APPLICATIONS 97
2.7.1 PROPAGATION OF ANNUAL PLANTS [1] 97
2.7.2 GAMBLER S RUIN 100
2.7.3 NATIONAL INCOME [2, 3] 101
2.7.4 THE TRANSMISSION OF INFORMATION [4] 103
3 SYSTEMS OF DIFFERENCE EQUATIONS 113
3.1 AUTONOMOUS (TIME-INVARIANT) SYSTEMS 113
3.1.1 THE DISCRETE ANALOGUE OF THE PUTZER ALGORITHM 114
3.1.2 THE DEVELOPMENT OF THE ALGORITHM FOR
A
115
3.2 THE BASIC THEORY 120
3.3 THE JORDAN FORM: AUTONOMOUS (TIME-INVARIANT) SYSTEMS REVISITED 129
3.4 LINEAR PERIODIC SYSTEMS 144
3.5 APPLICATIONS 149
3.5.1 MARKOV CHAINS 149
3.5.2 REGULAR MARKOV CHAINS 151
3.5.3 ABSORBING MARKOV CHAINS 153
3.5.4 A TRADE MODEL [4] 155
3.5.5 THE HEAT EQUATION 157
4 STABILITY THEORY 163
4.1 PRELIMINARIES 163
4.2 STABILITY OF LINEAR SYSTEMS 172
4.3 SCALAR EQUATIONS 180
4.4 PHASE SPACE ANALYSIS 185
4.5 STABILITY BY LINEAR APPROXIMATION 196
4.6 LIAPUNOV S DIRECT OR SECOND METHOD 204
5 THE Z-TRANSFORM METHOD 221
5.1 DEFINITIONS AND EXAMPLES 221
5.1.1 PROPERTIES OF THE Z TRANSFORM 225
5.2 THE INVERSE Z TRANSFORM AND SOLUTIONS OF DIFFERENCE EQUATIONS 230
5.2.1 THE POWER SERIES METHOD 230
5.2.2 THE PARTIAL FRACTION METHOD 231
5.2.3 THE INVERSION INTEGRAL METHOD
1
234
5.3 VOLTERRA DIFFERENCE EQUATIONS OF CONVOLUTION TYPE: THE SCALAR
CASE239
5.4 EXPLICIT CRITERIA FOR STABILITY OF VOLTERRA EQUATIONS 243
5.5 VOLTERRA SYSTEMS 247
5.6 A VARIATION OF CONSTANTS FORMULA 250
5.7 THE Z TRANSFORM VERSUS LAPLACE TRANSFORM 254
CONTENTS XIII
CONTROL THEORY 259
6.1 INTRODUCTION 259
6.1.1 DISCRETE EQUIVALENTS FOR CONTINUOUS SYSTEMS 261
6.2 CONTROLLABILITY 262
6.2.1 CONTROLLABILITY CANONICAL FORMS 268
6.3 OBSERVABILITY 274
6.3.1 OBSERVABILITY CANONICAL FORMS 281
6.4 STABILIZATION BY STATE FEEDBACK (DESIGN VIA POLE PLACEMENT) . . 284
6.4.1 STABILIZATION OF NONLINEAR SYSTEMS BY FEEDBACK 291
6.5 OBSERVERS 294
6.5.1 EIGENVALUE SEPARATION THEOREM 295
ASYMPTOTIC BEHAVIOR OF DIFFERENCE EQUATIONS 303
7.1 TOOLS OF APPROXIMATION 303
7.2 POINCARE S THEOREM 309
7.3 SECOND ORDER DIFFERENCE EQUATIONS 318
7.4 ASYMPTOTICALLY DIAGONAL SYSTEMS 326
7.5 HIGH ORDER DIFFERENCE EQUATIONS 335
7.6 NONLINEAR DIFFERENCE EQUATIONS 343
OSCILLATION THEORY 351
8.1 THREE-TERM DIFFERENCE EQUATIONS 351
8.2 NONLINEAR DIFFERENCE EQUATIONS 357
8.3 SELF-ADJOINT SECOND ORDER EQUATIONS 361
ANSWERS TO SELECTED PROBLEMS 371
INDEX 383
|
| any_adam_object | 1 |
| author | Elaydi, Saber N. 1943- |
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| callnumber-raw | QA431.E43 1996 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre_facet | Lehrbuch - Differenzengleichung |
| id | DE-604.BV010756124 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:22Z |
| institution | BVB |
| isbn | 0387945822 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007183863 |
| oclc_num | 246853217 |
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| physical | XIII, 389 S. graph. Darst. |
| publishDate | 1996 |
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| series2 | Undergraduate texts in mathematics |
| spelling | Elaydi, Saber N. 1943- Verfasser (DE-588)121601455 aut An introduction to difference equations Saber N. Elaydi New York [u.a.] Springer 1996 XIII, 389 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Difference equations Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Lehrbuch - Differenzengleichung Differenzengleichung (DE-588)4012264-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007183863&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elaydi, Saber N. 1943- An introduction to difference equations Difference equations Differenzengleichung (DE-588)4012264-5 gnd |
| subject_GND | (DE-588)4012264-5 |
| title | An introduction to difference equations |
| title_auth | An introduction to difference equations |
| title_exact_search | An introduction to difference equations |
| title_full | An introduction to difference equations Saber N. Elaydi |
| title_fullStr | An introduction to difference equations Saber N. Elaydi |
| title_full_unstemmed | An introduction to difference equations Saber N. Elaydi |
| title_short | An introduction to difference equations |
| title_sort | an introduction to difference equations |
| topic | Difference equations Differenzengleichung (DE-588)4012264-5 gnd |
| topic_facet | Difference equations Differenzengleichung Lehrbuch - Differenzengleichung |
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