An introduction to difference equations差分方程概论
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作者： Saber Elaydi著
出 版 社：
出版时间： 2005-3-1字数：版次： 1页数： 539印刷时间： 2005/03/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387230597包装： 精装内容简介
This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, and also recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model.
目录
Preface to the First Edition
List of Symbols
1Dynamics of First-Order Difference Equations
1.1 Introduction
1.2 Linear First-Order Difference Equations
1.2.1 Important Special Cases
1.3 Equilibrium Points
1.3.1 The Stair Step (Cobweb) Diagrams
1.3.2 The Cobweb Theorem of Economics
1.4 Numerical Solutions of Differential Equations
1.4.1 Euler's Method
1.4.2 A Nonstandard Scheme
1.5 Criterion for the Asymptotic Stability of Equilibrium Points
1.6 Periodic Points and Cycles
1.7 The Logistic Equation and Bifurcation
1.7.1 Equilibrium Points
1.7.2 2-Cycles
1.7.3 22-Cycles
1.7.4 The Bifurcation Diagram
1.8 Basin of Attraction and Global Stability (Optional)
2 Linear Difference Equations of Higher Order
2.1 Difference Calculus
2.1.1 The Power Shift
2.1.2 Factorial Polynomials
2.1.3 The Antidifference Operator
2.2 General Theory of Linear Difference Equations
2.3 Linear Homogeneous Equations with Constant Coefficients
2.4 Nonhomogeneous Equations: Methods of Undetermind Coefficeints
2.4.1 The Method of Variation of Constants (Parameters)
2.5 Limiting Behavior of Solutions
2.6 Nonlinear Equations Transformable to Linear Equations
2.7 Applications
2.7.1 Propagation of Annual Plants
2.7.2 Gambler's Ruin
2.7.3 National Income
2.7.4 The Transmission of Information
3 Systems of Linear Difference Equations
3.1 Autonomous (Time-Invariant) Systems
3.1.1 The Discrete Analogue of the Putzer Algorithm
3.1.2 The Development of the Algorithm for An
3.2 The Basic Theory
3.3 The Jordan Form: Autonomous (Time-Invariant) Systems Revisited
3.3.1 Diagonalizable Matrices
3.3.2 The Jordan Form
3.3.3 Block-Diagonal Matrices
3.4 Linear Periodic Systems
3.5 Applications
3.5.1 Markov Chains
3.5.2 Regular Markov Chains
3.5.3 Absorbing Markov Chains
3.5.4 A Trade Model
3.5.5 The Heat Equation
4 Stability Theory
4.1 A Norm of a Matrix
4.2 Notions of Stability
……
5 Higher-Order Scalar Difference Eqations
6 The Z-Transform Method and volterra Difference Equations
7 Oscillation Theory
8 Asymptotic Behavior of Difference Equations
9 Applications to Contnued Fractions and Orthogonal Polynomials
10 Control Theory
A Stability of Nonhyperbolic Fixed Points of Maps on the Real Line
B The Vamdermonde Matrix
C Stability of Nomdifferentiable
D Stahble Manifold and the Hartman-Grobman-Cushing Theorems
E The Levin-May Theorem
F Classical Orthogonal Polynomials
G Identities and Formulas
Answers and Hints to Selected Problems
Maple Programs
References
Index