Preface to the Second Edition |
Preface to the First Edition |
Preliminaries / Chapter 1: |
Notations / 1.1.: |
Difference Equations / 1.2.: |
Initial Value Problems / 1.3.: |
Some Examples: Initial Value Problems / 1.4.: |
Boundary Value Problems / 1.5.: |
Some Examples: Boundary Value Problems / 1.6.: |
Some Examples: Real World Phenomena / 1.7.: |
Finite Difference Calculus / 1.8.: |
Problems / 1.9.: |
Notes / 1.10.: |
References / 1.11.: |
Linear Initial Value Problems / Chapter 2: |
Introduction / 2.1.: |
Preliminary Results from Algebra / 2.2.: |
Linear Dependence and Independence / 2.3.: |
Matrix Linear Systems / 2.4.: |
Variation of Constants Formula / 2.5.: |
Green's Matrix / 2.6.: |
Adjoint Systems / 2.7.: |
Systems with Constant Coefficients / 2.8.: |
Periodic Linear Systems / 2.9.: |
Almost Periodic Linear Systems / 2.10.: |
Higher Order Linear Equations / 2.11.: |
Method of Generating Functions / 2.12.: |
Bernoulli's Method / 2.13.: |
Poincare's and Perron's Theorems / 2.14.: |
Regular and Singular Perturbations / 2.15.: |
Miscellaneous Difference Equations / 2.16.: |
Clairaut's Equation / 3.1.: |
Euler's Equation / 3.2.: |
Riccati's Equation / 3.3.: |
Bernoulli's Equation / 3.4.: |
Verhulst's Equation / 3.5.: |
Best Discrete Approximations: Harmonic Oscillator Equation / 3.6.: |
Duffing's Equation / 3.7.: |
van der Pol's Equation / 3.8.: |
Hill's Equation / 3.9.: |
Mathieu's Equation / 3.10.: |
Weierstrass' Elliptic Equations / 3.11.: |
Volterra's Equations / 3.12.: |
Elementary Partial Difference Equations: Riccati's Extended Form / 3.13.: |
Wave Equation / 3.14.: |
FitzHugh-Nagumo's Equation / 3.15.: |
Korteweg-de Vries' Equation / 3.16.: |
Modified KdV Equation / 3.17.: |
Lagrange's Equations / 3.18.: |
Difference Inequalities / 3.19.: |
Gronwall Inequalities / 4.1.: |
Nonlinear Inequalities / 4.2.: |
Inequalities Involving Differences / 4.3.: |
Finite Systems of Inequalities / 4.4.: |
Opial Type Inequalities / 4.5.: |
Wirtinger Type Inequalities / 4.6.: |
Qualitative Properties of Solutions of Difference Systems / 4.7.: |
Dependence on Initial Conditions and Parameters / 5.1.: |
Asymptotic Behavior of Linear Systems / 5.2.: |
Asymptotic Behavior of Nonlinear Systems / 5.3.: |
Concepts of Stability / 5.4.: |
Stability of Linear Systems / 5.5.: |
Stability of Nonlinear Systems / 5.6.: |
Nonlinear Variation of Constants / 5.7.: |
Dichotomies / 5.8.: |
Lyapunov's Direct Method for Autonomous Systems / 5.9.: |
Lyapunov's Direct Method for Non-Autonomous Systems / 5.10.: |
Stability of Discrete Models in Population Dynamics / 5.11.: |
Converse Theorems / 5.12.: |
Total Stability / 5.13.: |
Practical Stability / 5.14.: |
Mutual Stability / 5.15.: |
Qualitative Properties of Solutions of Higher Order Difference Equations / 5.16.: |
Qualitative Properties of Solutions of Neutral Difference Equations / Chapter 7: |
Boundary Value Problems for Linear Systems / Chapter 8: |
Existence and Uniqueness / 8.1.: |
Method of Complementary Functions / 8.2.: |
Method of Particular Solutions / 8.3.: |
Method of Adjoints / 8.4.: |
Method of Chasing / 8.5.: |
Method of Imbedding: First Formulation / 8.6.: |
Method of Imbedding: Second Formulation / 8.7.: |
Method of Sweep / 8.8.: |
Miller's and Olver's Algorithms / 8.9.: |
Boundary Value Problems for Nonlinear Systems / 8.10.: |
Preliminary Results from Analysis / 9.1.: |
Approximate Picard's Iterates / 9.2.: |
Oscillatory State / 9.4.: |
Stopping Criterion / 9.5.: |
Application to the Perturbation Method / 9.6.: |
Monotone Convergence / 9.7.: |
Periodic Boundary Value Problems / 9.8.: |
Newton's Method / 9.9.: |
Approximate Newton's Method / 9.10.: |
Initial-Value Methods / 9.11.: |
Invariant Imbedding Method / 9.12.: |
Miscellaneous Properties of Solutions of Higher Order Linear Difference Equations / 9.13.: |
Disconjugacy / 10.1.: |
Right and Left Disconjugacy / 10.2.: |
Adjoint Equations / 10.3.: |
Right and Left Disconjugacy for the Adjoint Equation / 10.4.: |
Right Disfocality / 10.5.: |
Eventual Disconjugacy and Right Disfocality / 10.6.: |
A Classification of Solutions / 10.7.: |
Interpolating Polynomials / 10.8.: |
Green's Functions / 10.9.: |
Inequalities and Equalities for Green's Functions / 10.10.: |
Maximum Principles / 10.11.: |
Error Estimates in Polynomial Interpolation / 10.12.: |
Boundary Value Problems for Higher Order Difference Equations / 10.13.: |
Picard's and Approximate Picard's Methods / 11.1.: |
Quasilinearization and Approximate Quasilinearization / 11.3.: |
Uniqueness Implies Existence / 11.4.: |
Sturm-Liouville Problems and Related Inequalities / 11.7.: |
Sturm-Liouville Problems / 12.1.: |
Eigenvalue Problems for Symmetric Matrices / 12.2.: |
Matrix Formulation of Sturm-Liouville Problems / 12.3.: |
Symmetric, Antisymmetric and Periodic Boundary Conditions / 12.4.: |
Discrete Fourier Series / 12.5.: |
Generalized Wirtinger Type Inequalities / 12.6.: |
Generalized Opial Type Inequalities / 12.8.: |
Comparison Theorems for Eigenvalues / 12.9.: |
Positive Solutions of (12.10.1) [Delta][superscript 3]u(k) + [lambda]a(k)f(u(k)) = 0, k [set membership] N(2, K + 2) (12.10.2) u(0) = u(1) = u(K + 3) = 0 / 12.10.: |
Difference Inequalities in Several Independent Variables / 12.11.: |
Discrete Riemann's Function / 13.1.: |
Linear Inequalities / 13.2.: |
Wendroff Type Inequalities / 13.3.: |
Inequalities Involving Partial Differences / 13.4.: |
Multidimensional Linear Inequalities / 13.6.: |
Multidimensional Nonlinear Inequalities / 13.7.: |
Convolution Type Inequalities / 13.8.: |
Opial and Wirtinger Type Inequalities in Two Variables / 13.9.: |
Author Index / 13.10.: |
Subject Index |
Preface to the Second Edition |
Preface to the First Edition |
Preliminaries / Chapter 1: |