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E-raamat: Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations

(Rochester Institute Of Technology, Usa)
  • Formaat: 332 pages
  • Ilmumisaeg: 24-Sep-2019
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811202988
  • Formaat - PDF+DRM
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  • Formaat: 332 pages
  • Ilmumisaeg: 24-Sep-2019
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811202988

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'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 SocietyWe 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.
Preface v
Author Introduction vii
1 Introduction
1(40)
1.1 Recursive Sequences
3(3)
1.2 Order of a Difference Equation and Explicit Solution
6(6)
1.3 Equilibrium Points
12(3)
1.4 Convergent Sequences (Solutions)
15(4)
1.5 Periodic Sequences (Solutions)
19(3)
1.6 Complex Numbers and Periodic Cycles
22(2)
1.7 Specific Patterns of Periodic Cycles
24(2)
1.8 Eventually Constant Sequences (Solutions)
26(1)
1.9 Eventually Periodic Sequences (Solutions)
27(2)
1.10 Additional Examples of Periodic and Eventually Periodic Solutions
29(2)
1.11 Divergent (Unbounded) Sequences (Solutions)
31(2)
1.12
Chapter 1 Exercises
33(8)
2 First Order Linear Difference Equations
41(36)
2.1 Homogeneous First Order Linear Difference Equations
42(7)
2.2 Nonhomogeneous First Order Linear Difference Equations
49(4)
2.3 Non-autonomous First Order Linear Difference Equations
53(9)
2.4 Periodic Traits of Non-autonomous First Order Linear Difference Equations
62(7)
2.5
Chapter 2 Exercises
69(8)
3 First Order Nonlinear Difference Equations
77(70)
3.1 Local Stability Character of Equilibrium Points
80(11)
3.2 The Cobweb Method
91(3)
3.3 Global Asymptotic Stability (Convergence)
94(6)
3.4 Periodic Traits of Solutions
100(40)
3.5
Chapter 3 Exercises
140(7)
4 Second Order Linear Difference Equations
147(56)
4.1 Homogeneous Second Order Linear Difference Equations
148(11)
4.2 Asymptotic Behavior of Second Order Linear Difference Equations
159(4)
4.3 Nonhomogeneous Second Order Linear Difference Equations with a Constant Coefficient
163(6)
4.4 Nonhomogeneous Second Order Linear Difference Equations with a Variable Geometric Coefficient
169(4)
4.5 Nonhomogeneous Second Order Linear Difference with a Variable Coefficient nk
173(4)
4.6 Linear Independence of Solutions
177(1)
4.7 Periodic Solutions of Second Order Homogeneous Linear Difference Equations
178(4)
4.8 Periodic Traits of Non-autonomous Second Order Linear Difference Equations
182(12)
4.9 Third and Higher Order Linear Difference Equations
194(1)
4.10
Chapter 4 Exercises
194(9)
5 Second Order Nonlinear Difference Equations
203(54)
5.1 Local Stability Character of Equilibrium Points
206(11)
5.2 Global Asymptotic Stability (Convergence)
217(5)
5.3 Patterns of Periodic Solutions of Second Order Rational Difference Equations
222(7)
5.4 Periodic Patterns of Second Order Non-autonomous Rational Difference Equations
229(13)
5.5 Periodic and Eventually Periodic Solutions of Max-Type Difference Equations
242(9)
5.6
Chapter 5 Exercises
251(6)
6 Advanced Characteristics and New Research Questions
257(34)
6.1 Higher Order Linear Difference Equations
257(3)
6.2 Periodic Traits of Third and Higher Order Linear Difference Equations
260(3)
6.3 Applications of Higher Order Linear Difference Equations in Signal Processing
263(2)
6.4 Systems of Linear Difference Equations
265(1)
6.5 Periodic Traits of Systems of Linear Difference Equations
266(5)
6.6 Applications of Systems of Linear Difference Equations in Signal Processing
271(1)
6.7 Systems of Nonlinear Difference Equations
272(4)
6.8 Advanced Periodic Characteristics of Higher Order Nonlinear Difference Equations
276(1)
6.9 Third and Higher Order Rational Difference Equations
277(1)
6.10 Third and Higher Order Non-autonomous Rational Difference Equations
278(2)
6.11 More on Max-Type Difference Equations
280(1)
6.12 Non-autonomous Piecewise Difference Equations and Systems of Piecewise Difference Equations
280(5)
6.13 Additional Examples of Periodicity Graphs
285(1)
6.14
Chapter 6 Exercises
286(5)
7 Answers to Selected Odd-Numbered Problems
291(14)
7.1 Answers to
Chapter 1 Exercises
291(2)
7.2 Answers to
Chapter 2 Exercises
293(1)
7.3 Answers to
Chapter 3 Exercises
294(5)
7.4 Answers to
Chapter 4 Exercises
299(1)
7.5 Answers to
Chapter 5 Exercises
300(2)
7.6 Answers to
Chapter 6 Exercises
302(3)
Appendices
305(4)
A.1 Patterns of Sequences
305(1)
A.2 Alternating Patterns of Sequences
305(1)
A.3 Finite Series
306(1)
A.4 Convergent Infinite Series
306(1)
A.5 Periodic Sequences and Modulo Arithmetic
307(1)
A.6 Alternating Periodic Sequences and Modulo Arithmetic
307(2)
Bibliography 309(6)
Index 315