Preface |
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v | |
Author Introduction |
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vii | |
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1 | (40) |
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3 | (3) |
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1.2 Order of a Difference Equation and Explicit Solution |
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6 | (6) |
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12 | (3) |
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1.4 Convergent Sequences (Solutions) |
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15 | (4) |
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1.5 Periodic Sequences (Solutions) |
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19 | (3) |
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1.6 Complex Numbers and Periodic Cycles |
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22 | (2) |
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1.7 Specific Patterns of Periodic Cycles |
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24 | (2) |
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1.8 Eventually Constant Sequences (Solutions) |
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26 | (1) |
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1.9 Eventually Periodic Sequences (Solutions) |
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27 | (2) |
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1.10 Additional Examples of Periodic and Eventually Periodic Solutions |
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29 | (2) |
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1.11 Divergent (Unbounded) Sequences (Solutions) |
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31 | (2) |
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33 | (8) |
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2 First Order Linear Difference Equations |
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41 | (36) |
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2.1 Homogeneous First Order Linear Difference Equations |
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42 | (7) |
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2.2 Nonhomogeneous First Order Linear Difference Equations |
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49 | (4) |
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2.3 Non-autonomous First Order Linear Difference Equations |
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53 | (9) |
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2.4 Periodic Traits of Non-autonomous First Order Linear Difference Equations |
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62 | (7) |
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69 | (8) |
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3 First Order Nonlinear Difference Equations |
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77 | (70) |
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3.1 Local Stability Character of Equilibrium Points |
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80 | (11) |
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91 | (3) |
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3.3 Global Asymptotic Stability (Convergence) |
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94 | (6) |
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3.4 Periodic Traits of Solutions |
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100 | (40) |
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140 | (7) |
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4 Second Order Linear Difference Equations |
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147 | (56) |
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4.1 Homogeneous Second Order Linear Difference Equations |
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148 | (11) |
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4.2 Asymptotic Behavior of Second Order Linear Difference Equations |
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159 | (4) |
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4.3 Nonhomogeneous Second Order Linear Difference Equations with a Constant Coefficient |
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163 | (6) |
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4.4 Nonhomogeneous Second Order Linear Difference Equations with a Variable Geometric Coefficient |
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169 | (4) |
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4.5 Nonhomogeneous Second Order Linear Difference with a Variable Coefficient nk |
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173 | (4) |
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4.6 Linear Independence of Solutions |
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177 | (1) |
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4.7 Periodic Solutions of Second Order Homogeneous Linear Difference Equations |
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178 | (4) |
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4.8 Periodic Traits of Non-autonomous Second Order Linear Difference Equations |
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182 | (12) |
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4.9 Third and Higher Order Linear Difference Equations |
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194 | (1) |
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194 | (9) |
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5 Second Order Nonlinear Difference Equations |
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203 | (54) |
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5.1 Local Stability Character of Equilibrium Points |
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206 | (11) |
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5.2 Global Asymptotic Stability (Convergence) |
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217 | (5) |
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5.3 Patterns of Periodic Solutions of Second Order Rational Difference Equations |
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222 | (7) |
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5.4 Periodic Patterns of Second Order Non-autonomous Rational Difference Equations |
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229 | (13) |
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5.5 Periodic and Eventually Periodic Solutions of Max-Type Difference Equations |
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242 | (9) |
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251 | (6) |
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6 Advanced Characteristics and New Research Questions |
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257 | (34) |
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6.1 Higher Order Linear Difference Equations |
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257 | (3) |
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6.2 Periodic Traits of Third and Higher Order Linear Difference Equations |
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260 | (3) |
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6.3 Applications of Higher Order Linear Difference Equations in Signal Processing |
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263 | (2) |
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6.4 Systems of Linear Difference Equations |
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265 | (1) |
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6.5 Periodic Traits of Systems of Linear Difference Equations |
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266 | (5) |
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6.6 Applications of Systems of Linear Difference Equations in Signal Processing |
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271 | (1) |
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6.7 Systems of Nonlinear Difference Equations |
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272 | (4) |
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6.8 Advanced Periodic Characteristics of Higher Order Nonlinear Difference Equations |
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276 | (1) |
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6.9 Third and Higher Order Rational Difference Equations |
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277 | (1) |
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6.10 Third and Higher Order Non-autonomous Rational Difference Equations |
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278 | (2) |
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6.11 More on Max-Type Difference Equations |
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280 | (1) |
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6.12 Non-autonomous Piecewise Difference Equations and Systems of Piecewise Difference Equations |
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280 | (5) |
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6.13 Additional Examples of Periodicity Graphs |
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285 | (1) |
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286 | (5) |
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7 Answers to Selected Odd-Numbered Problems |
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291 | (14) |
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7.1 Answers to Chapter 1 Exercises |
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291 | (2) |
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7.2 Answers to Chapter 2 Exercises |
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293 | (1) |
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7.3 Answers to Chapter 3 Exercises |
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294 | (5) |
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7.4 Answers to Chapter 4 Exercises |
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299 | (1) |
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7.5 Answers to Chapter 5 Exercises |
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300 | (2) |
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7.6 Answers to Chapter 6 Exercises |
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302 | (3) |
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305 | (4) |
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A.1 Patterns of Sequences |
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305 | (1) |
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A.2 Alternating Patterns of Sequences |
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305 | (1) |
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306 | (1) |
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A.4 Convergent Infinite Series |
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306 | (1) |
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A.5 Periodic Sequences and Modulo Arithmetic |
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307 | (1) |
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A.6 Alternating Periodic Sequences and Modulo Arithmetic |
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307 | (2) |
Bibliography |
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309 | (6) |
Index |
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315 | |