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Preface; Contents; 1 Introduction; 1.1 Linear Ordinary Differential Equations; 1.2 Simple Linear Delay Differential Equations; 1.3 An Example from Population Dynamics; 1.4 An Example from Mechanical Engineering; 1.5 Scopes and Synopsis; Part ITheory; 2 Notation and Basics; 2.1 Notation; 2.2 The Cauchy Problem; 2.3 Stability of Solutions; 3 Stability of Linear Autonomous Equations; 3.1 The Solution Operator Semigroup and the Infinitesimal Generator; 3.2 Spectral Properties and the Characteristic Equation; 3.3 Linearization and Equilibria; 4 Stability of Linear Periodic Equations
4.1 The Evolution Operator and the Monodromy Operator4.2 Linearization and Periodic Solutions; Part IINumerical Analysis; 5 The Infinitesimal Generator Approach; 5.1 The Pseudospectral Differentiation Method; 5.2 The Piecewise Pseudospectral Differentiation Method; 5.3 Convergence Analysis; 5.3.1 A Related Collocation Problem; 5.3.2 Convergence of the Eigenvalues; 5.3.3 Quadrature for Distributed Delays; 5.4 Convergence of the Piecewise Method; 5.5 Other Methods; 6 The Solution Operator Approach; 6.1 The Pseudospectral Collocation Method; 6.1.1 Discretization of X; 6.1.2 Discretization of X+
6.1.3 Discretization of T6.2 The Collocation Equation; 6.3 Convergence Analysis; 6.3.1 Convergence of the Eigenvalues of T""0362TN; 6.3.2 Convergence of the Eigenvalues of T""0362TM,N; 6.3.3 Quadrature for Distributed Delays; 6.4 Other Methods; Part IIIImplementation and Applications; 7 MATLAB Implementation; 7.1 Introducing the Model in MATLAB; 7.2 The Infinitesimal Generator Approach; 7.2.1 A Single Discrete Delay; 7.2.2 A Single Distributed Delay; 7.2.3 The Piecewise Method; 7.3 The Solution Operator Approach; 7.3.1 The Meshes; 7.3.2 The Matrix TM(1); 7.3.3 The Matrix TM,N(2)
7.3.4 The Matrix UM,N(1)7.3.5 The Matrix UN(2); 8 Applications; 8.1 Test Cases; 8.1.1 Test 1: Linear Autonomous Equations with a Discrete Delay; 8.1.2 Test 2: Linear Autonomous Equations with Multiple Discrete Delays; 8.1.3 Test 3: Linear Autonomous Equations with a Distributed Delay; 8.1.4 Test 4: Linear Autonomous Systems; 8.1.5 Test 5: Linear Periodic Equations; 8.1.6 Test 6: Linearized Periodic Equations; 8.2 Equilibria in Population Dynamics; 8.3 Periodic Problems in Engineering; References; Series Editors' Biographies
4.1 The Evolution Operator and the Monodromy Operator4.2 Linearization and Periodic Solutions; Part IINumerical Analysis; 5 The Infinitesimal Generator Approach; 5.1 The Pseudospectral Differentiation Method; 5.2 The Piecewise Pseudospectral Differentiation Method; 5.3 Convergence Analysis; 5.3.1 A Related Collocation Problem; 5.3.2 Convergence of the Eigenvalues; 5.3.3 Quadrature for Distributed Delays; 5.4 Convergence of the Piecewise Method; 5.5 Other Methods; 6 The Solution Operator Approach; 6.1 The Pseudospectral Collocation Method; 6.1.1 Discretization of X; 6.1.2 Discretization of X+
6.1.3 Discretization of T6.2 The Collocation Equation; 6.3 Convergence Analysis; 6.3.1 Convergence of the Eigenvalues of T""0362TN; 6.3.2 Convergence of the Eigenvalues of T""0362TM,N; 6.3.3 Quadrature for Distributed Delays; 6.4 Other Methods; Part IIIImplementation and Applications; 7 MATLAB Implementation; 7.1 Introducing the Model in MATLAB; 7.2 The Infinitesimal Generator Approach; 7.2.1 A Single Discrete Delay; 7.2.2 A Single Distributed Delay; 7.2.3 The Piecewise Method; 7.3 The Solution Operator Approach; 7.3.1 The Meshes; 7.3.2 The Matrix TM(1); 7.3.3 The Matrix TM,N(2)
7.3.4 The Matrix UM,N(1)7.3.5 The Matrix UN(2); 8 Applications; 8.1 Test Cases; 8.1.1 Test 1: Linear Autonomous Equations with a Discrete Delay; 8.1.2 Test 2: Linear Autonomous Equations with Multiple Discrete Delays; 8.1.3 Test 3: Linear Autonomous Equations with a Distributed Delay; 8.1.4 Test 4: Linear Autonomous Systems; 8.1.5 Test 5: Linear Periodic Equations; 8.1.6 Test 6: Linearized Periodic Equations; 8.2 Equilibria in Population Dynamics; 8.3 Periodic Problems in Engineering; References; Series Editors' Biographies