'Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering.' London Mathematical Society We introduce interdisciplinary research and get students and the audience familiarized with the difference equations; solving them explicitly, determining the long-term behavior of solutions (convergence, boundedness and periodicity). We help to develop intuition in analyzing convergence of solutions in terms of subsequences and analyzing patterns of periodic cycles. Our book helps you learn applications in biology, economics and business, computer science and engineering

lgrsnf/Difference Equations For Scientists And Engineering - Interdisciplinary Difference Equations.pdf

nexusstc/Difference Equations for Scientists and Engineering: Interdisciplinary Difference Equations/8c957ecb1a02893167d2a567bdd9784f.pdf

Radin, Michael A

World Scientific Publishing Company Pvt. Ltd.

Singapore [etc.], Singapore, 2019

2019-09-18

lg2894469

producers:
Acrobat Distiller 10.0.0 (Windows); modified using iText 4.2.0 by 1T3XT

{"edition":"1","isbns":["9789811202964","9789811202971","9789811203855","9811202966","9811202974","9811203857"],"last_page":330,"publisher":"WORLD SCIENTIFIC"}

Contains references.

Указ.: с. 315-317
Библиогр.: с. 309-313

РГБ

Russian State Library [rgb] MARC:
=001 010374487
=005 20200907153642.0
=008 200805s2019\\\\si\||||\\\\\\\0||\|\eng|d
=017 \\ $a И3283-20 $b RuMoRGB
=020 \\ $a 978-981-120-296-4 (pbk)
=040 \\ $a RuMoRGB $b rus $e rcr
=041 0\ $a eng
=044 \\ $a si
=084 \\ $a В161.614,0 $2 rubbk
=100 1\ $a Radin, Michael A.
=245 00 $a Difference equations for scientists and engineering : $b interdisciplinary difference equations $c Michael A. Radin
=260 \\ $a Singapore [etc.] $b World scientific $c cop. 2019
=300 \\ $a XII, 317 с. $b ил. $c 25 см
=336 \\ $a Текст (визуальный)
=337 \\ $a непосредственный
=500 \\ $a Указ.: с. 315-317
=504 \\ $a Библиогр.: с. 309-313
=650 \7 $a Физико-математические науки -- Математика -- Математический анализ -- Дифференциальные уравнения -- Обыкновенные дифференциальные уравнения -- Дифференциально-разностные уравнения $2 rubbk
=852 \\ $a РГБ $b FB $j 5 20-4/67 $x 90

CONTENTS 10
Preface 6
Author Introduction 8
1. Introduction 14
1.1. Recursive Sequences 16
1.2. Order of a Difference Equation and Explicit Solution 19
1.2.1. Non-autonomous difference equations 22
1.2.2. Convolution 23
1.3. Equilibrium Points 25
1.4. Convergent Sequences (Solutions) 28
1.5. Periodic Sequences (Solutions) 32
1.6. Complex Numbers and Periodic Cycles 35
1.7. Specific Patterns of Periodic Cycles 37
1.8. Eventually Constant Sequences (Solutions) 39
1.9. Eventually Periodic Sequences (Solutions) 40
1.10. Additional Examples of Periodic and Eventually Periodic Solutions 42
1.11. Divergent (Unbounded) Sequences (Solutions) 44
1.12. Chapter 1 Exercises 46
2. First Order Linear Difference Equations 54
2.1. Homogeneous First Order Linear Difference Equations 55
2.1.1. Applications of first order linear difference equations in biology 60
2.1.2. Applications of first order linear difference equations in finance 61
2.2. Nonhomogeneous First Order Linear Difference Equations 62
2.3. Non-autonomous First Order Linear Difference Equations 66
2.3.1. Applications of non-autonomous first order linear difference equations in signal processing 74
2.4. Periodic Traits of Non-autonomous First Order Linear Difference Equations 75
2.5. Chapter 2 Exercises 82
3. First Order Nonlinear Difference Equations 90
3.1. Local Stability Character of Equilibrium Points 93
3.1.1. The Beverton–Holt Model 102
3.1.2. The Logistic Models 102
3.1.3. The Ricker Model 103
3.1.4. The Ricker Stock Recruitment Model 103
3.1.5. The Hassell Model 104
3.2. The Cobweb Method 104
3.3. Global Asymptotic Stability (Convergence) 107
3.4. Periodic Traits of Solutions 113
3.4.1. Periodic solutions of the Riccati Difference Equation 114
3.4.2. Periodic solutions of Non-autonomous Riccati Difference Equations 118
3.4.3. The periodic solutions of the Logistic Difference Equation 123
3.4.4. Chaos and Chaotic orbits 130
3.4.5. The Tent-Map 131
3.4.6. The 3X+1 Conjecture 139
3.4.7. Autonomous Piecewise difference equation as a Neuron model 140
3.4.8. Autonomous Piecewise difference equation as a Neuron model when β = 1 150
3.4.9. The Williamson’s Model 153
3.4.10. The West Nile Epidemics Model 153
3.5. Chapter 3 Exercises 153
4. Second Order Linear Difference Equations 160
4.1. Homogeneous Second Order Linear Difference Equations 161
4.1.1. The Fibonacci Sequence 167
4.1.2. The Riccati Difference Equation as a second order linear difference equation 169
4.1.3. The Gambler’s Ruin Problem 171
4.2. Asymptotic Behavior of Second Order Linear Difference Equations 172
4.3. Nonhomogeneous Second Order Linear Difference Equations with a Constant Coefficient 176
4.3.1. The National Income 181
4.4. Nonhomogeneous Second Order Linear Difference Equations with a Variable Geometric Coefficient 182
4.5. Nonhomogeneous Second Order Linear Difference with a Variable Coefficient nk 186
4.5.1. Applications of non-autonomous second order linear difference equations in signal processing 188
4.6. Linear Independence of Solutions 190
4.7. Periodic Solutions of Second Order Homogeneous Linear Difference Equations 191
4.8. Periodic Traits of Non-autonomous Second Order Linear Difference Equations 195
4.9. Third and Higher Order Linear Difference Equations 207
4.10. Chapter 4 Exercises 207
5. Second Order Nonlinear Difference Equations 216
5.1. Local Stability Character of Equilibrium Points 219
5.1.1. Pielou’s Δ.E. (Model) 227
5.1.2. Delayed Ricker Model 228
5.1.3. Harvard School of Public Health population model 228
5.1.4. Perennial Grass Model 229
5.2. Global Asymptotic Stability (Convergence) 230
5.3. Patterns of Periodic Solutions of Second Order Rational Difference Equations 235
5.4. Periodic Patterns of Second Order Non-autonomous Rational Difference Equations 242
5.5. Periodic and Eventually Periodic Solutions of Max-Type Difference Equations 255
5.6. Chapter 5 Exercises 264
6. Advanced Characteristics and New Research Questions 270
6.1. Higher Order Linear Difference Equations 270
6.2. Periodic Traits of Third and Higher Order Linear Difference Equations 273
6.3. Applications of Higher Order Linear Difference Equations in Signal Processing 276
6.4. Systems of Linear Difference Equations 278
6.5. Periodic Traits of Systems of Linear Difference Equations 279
6.6. Applications of Systems of Linear Difference Equations in Signal Processing 284
6.7. Systems of Nonlinear Difference Equations 285
6.7.1. The Host Parasitoid Model 287
6.7.2. May’s Host Parasitoid Model 287
6.7.3. System of Beverton−Holt Equations 288
6.7.4. System of Ricker Equations 288
6.7.5. Predator-Prey Model 288
6.7.6. Applications of systems of difference equations in synchronization 289
6.8. Advanced Periodic Characteristics of Higher Order Nonlinear Difference Equations 289
6.9. Third and Higher Order Rational Difference Equations 290
6.10. Third and Higher Order Non-autonomous Rational Difference Equations 291
6.11. More on Max-Type Difference Equations 293
6.12. Non-autonomous Piecewise Difference Equations and Systems of Piecewise Difference Equations 293
6.12.1. Applications of systems of piecewise difference equations in neural networking 295
6.13. Additional Examples of Periodicity Graphs 298
6.14. Chapter 6 Exercises 299
7. Answers to Selected Odd-Numbered Problems 304
7.1. Answers to Chapter 1 Exercises 304
7.2. Answers to Chapter 2 Exercises 306
7.3. Answers to Chapter 3 Exercises 307
7.4. Answers to Chapter 4 Exercises 312
7.5. Answers to Chapter 5 Exercises 313
7.6. Answers to Chapter 6 Exercises 315
Appendices 318
A.1. Patterns of Sequences 318
A.2. Alternating Patterns of Sequences 318
A.3. Finite Series 319
A.4. Convergent Infinite Series 319
A.5. Periodic Sequences and Modulo Arithmetic 320
A.6. Alternating Periodic Sequences and ModuloArithmetic 320
Bibliography 322
Index 328

2020-12-28