Difference equations: an introduction with applications
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego [u.a.]
Acad. Press
2001
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 403 S. graph. Darst. |
| ISBN: | 012403330X |
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MARC
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| adam_text | Titel: Difference equations
Autor: Kelley, Walter G
Jahr: 2001
Difference Equations
An Introduction with Applications
Second Edition
WALTER G. KELLEY
University of Oklahoma
ALLAN C. PETERSON
University of Nebraska
San Diego San Francisco New York Boston
London Toronto Sydney Tokyo
Contents
Preface vü
Chapter 1 Introduction l
Chapter2 The Difference Calculus 13
Section 2.1 The Difference Operator 13
Section 2.2 Summation 20
Section 2.3 Generating Functions and Approximate Summation 29
Chapter 3 Linear Difference Equations 43
Section 3.1 First Order Equations 43
Section 3.2 General Results for Linear Equations 50
Section 3.3 Solving Linear Equations 54
Section 3.4 Applications 63
Section 3.5 Equations with Variable Coefficients 75
Section 3.6 Nonlinear Equations That Can Be Linearized 82
Section 3.7 The z-Transform 86
Chapter 4 Stability Theory 125
Section 4.1 Initial Value Problems for Linear Systems 125
Section 4.2 Stability of Linear Systems 133
Section 4.3 Phase Plane Analysis for Linear Systems 141
Section 4.4 Fundamental Matrices and Floquet Theory 150
Section 4.5 Stability of Nonlinear Systems 159
Section 4.6 Chaotic Behavior 173
Chapter 5 Asymptotic Methods 195
Section 5.1 Introduction 195
Section 5.2 Asymptotic Analysis of Sums 199
Section 5.3 Linear Equations 205
Section 5.4 Nonlinear Equations 215
Chapter 6 The Self-Adjoint Second Order
Linear Equation 229
Section 6.1 Introduction 229
Section 6.2 Sturmian Theory 239
v
vi CONTENTS
Section 6.3 Green s Functions 243
Section 6.4 Disconjugacy 250
Section 6.5 The Riccati Equation 258
Section 6.6 Oscillation 265
Chapter 7 The Sturm-LiouviUe Problem 279
Section 7.1 Introduction 279
Section 7.2 Finite Fourier Analysis 282
Section 7.3 Nonhomogeneous Problem 289
Chapter 8 Discrete Calculus of Variations 301
Section 8.1 Introduction 301
Section 8.2 Necessary Conditions 302
Section 8.3 Sufficient Conditions and Disconjugacy 312
Chapter 9 Boundary Value Problems for
Nonlinear Equations 327
Section 9.1 Introduction 327
Section 9.2 The Lipschitz Case 329
Section 9.3 Existence of Solutions 335
Section 9.4 Boundary Value Problems for Differential Equations 341
Chapter 10 Partial Difference Equations 349
Section 10.1 Discretization of Partial Differential Equations 349
Section 10.2 Solutions of Partial Difference Equations 356
Appendix 367
Answers to Selected Problems 373
References 383
Index 401
|
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| isbn | 012403330X |
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| spelling | Kelley, Walter G. Verfasser aut Difference equations an introduction with applications Walter G. Kelley ; Allan C. Peterson 2. ed. San Diego [u.a.] Acad. Press 2001 IX, 403 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Differentialgleichung (DE-588)4012249-9 s DE-604 Differenzengleichung (DE-588)4012264-5 s Peterson, Allan C. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009081640&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kelley, Walter G. Peterson, Allan C. Difference equations an introduction with applications Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4012264-5 (DE-588)4012249-9 (DE-588)4151278-9 |
| title | Difference equations an introduction with applications |
| title_auth | Difference equations an introduction with applications |
| title_exact_search | Difference equations an introduction with applications |
| title_full | Difference equations an introduction with applications Walter G. Kelley ; Allan C. Peterson |
| title_fullStr | Difference equations an introduction with applications Walter G. Kelley ; Allan C. Peterson |
| title_full_unstemmed | Difference equations an introduction with applications Walter G. Kelley ; Allan C. Peterson |
| title_short | Difference equations |
| title_sort | difference equations an introduction with applications |
| title_sub | an introduction with applications |
| topic | Differenzengleichung (DE-588)4012264-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Differenzengleichung Differentialgleichung Einführung |
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