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Field name	Details
Dewey Class	330.1
Title	Differential Equations, Discrete Systems and Control ([EBook] :) : Economic Models / / by Aristide Halanay, Judita Samuel.
Author	Halanay, Aristide
Added Personal Name	Samuel, Judita author.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 1997.
Physical Details	XVI, 360 p. : online resource.
Series	Mathematical modelling : theory and applications 1386-2960 ; ; 3
ISBN	9789401589154
Contents note	1 Linear and Affine Differential Equations. Equations with Separated Variables -- 1.1 Differential Equations Modelling Growth Processes -- 1.2 Linear Differential Equations -- 1.3 Linear Affine Differential Equations -- 1.4 Simplest Models of Price Evolution in a Market Economy -- 1.5 Discrete — Time Models for Price Evolution -- 1.6 Simplest Models for Economic Growth -- 1.7 Discrete — Time Models for Economic Growth -- 1.8 Production Functions -- 1.9 Equations with Separated Variables -- 1.10 Notes and References -- 2 Linear Differential Equations with Constant Coefficients -- 2.1 Second Order Differential Equations with Constant Coefficients -- 2.2 Discrete — Time Second Order Linear Equations -- 2.3 Price Evolution in the Presence of Inventories -- 2.4 Economic Growth Models -- 2.5 Second Order Linear Affine Equations -- 2.6 The Phillips Model with Several Types of Autonomous Investment -- 2.7 Higher Order Linear Differential Equations with Constant Coefficients -- 2.8 Discrete — Time Linear Affine Equations -- 2.9 The Samuelson — Hicks Model for Economic Growth -- 2.10 Notes and References -- 3 Linear Systems with Constant Coefficients -- 3.1 General Form of Solutions -- 3.2 Matrix Exponential -- 3.3 Linear Affine Systems -- 3.4 Economic Models -- 3.5 Leontieff — type Models -- 3.6 Phase — Portrait for Second Order Linear Systems with Constant Coefficients -- 3.7 Notes and References -- 4 General Theory of Nonlinear Systems. Stability -- 4.1 Existence and Uniqueness Theorem for the Initial Value Problem -- 4.2 Equilibria. Stability. Continuous Time -- 4.3 Stability. Discrete Time -- 4.4 Discrete—Time Logistic Equation -- 4.5 Stable Polynomials -- 4.6 Some Properties of Matrices that occur in Economic Models -- 4.7 Notes and References -- 5 Numerical Solution of Differential Equations -- 5.1 Euler Method -- 5.2 Richardson Extrapolation -- 5.3 Predictor — Corrector Methods -- 5.4 Numerical Quadrature -- 5.5 Adams Type Methods -- 5.6 Stiff Systems -- 5.7 Some Applications of Differential Equations in Numerical Analysis and Optimization -- 5.8 Notes and References -- 6 Control Systems. Stabilization of Linear Systems -- 6.1 Stabilization Problem. Stabilization by Linear State Feed-Back -- 6.2 Stabilization of Linear Systems by Using a Controller -- 6.3 Stabilization in an Economic Growth Model -- 6.4 A Monetary Policy Model -- 6.5 Stabilization of Discrete—Time Systems -- 6.6 A Discrete—Time Monetary Policy Model -- 6.7 Notes and References -- 7 Optimal Stabilization -- 7.1 Linear—Quadratic Optimization on Infinite Horizon. Continuous Time -- 7.2 Application to a Price Model -- 7.3 Optimal Stabilization in Discrete Time -- 7.4 Optimal Stabilization in a Discrete—Time Model of Price Evolution -- 7.5 Notes and References -- 8 Linear—Quadratic Optimization on Finite Horizon -- 8.1 Continuous Time -- 8.2 Applications -- 8.3 Discrete Time -- 8.4 Applications in Discrete Time -- 8.5 A Tracking Problem -- 8.6 A Simple Differential Game -- 8.7 Notes and References -- 9 Some Unconstrained Dynamic Optimization Problems -- 9.1 The Simplest Problem of the Calculus of Variations -- 9.2 A Macroeconomic Growth Model -- 9.3 A Discrete — Time Variational Problem -- 9.4 An Application -- 9.5 Unrestricted Optimal Control Problem in Discrete Time -- 9.6 An Application -- 9.7 Optimization with Linear Dynamics and Linear Cost. Continuous Time -- 9.8 Some Microeconomic Models -- 9.9 Optimization with Linear Dynamics and Linear Cost. Discrete Time -- 9.10 Applications -- 9.11 Notes and References -- 10 General Problem of Optimal Control -- 10.1 Problem Statement. General Theorems -- 10.2 Optimum Capital Accumulation under the Minimum Time Objective -- 10.3 Reduction of Problems with Free Initial and Final Time to Problems on Fixed Horizon -- 10.4 An Abstract Multiplier Rule -- 10.5 Proof of Theorem 10.1 -- 10.6 Notes and References -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-015-8915-4
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Difference and Functional Equations . Difference equations . Differential Equations . Economic theory . Economic Theory/Quantitative Economics/Mathematical Methods . Economics . Functional equations . Mathematical optimization . Optimization . Ordinary differential equations . Authors: Halanay, Aristide . Samuel, Judita . Corporate Authors: SpringerLink (Online service) . Series: Mathematical modelling : theory and applications . Classification: 330.1 .

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Differential Equations, Discrete Systems and Control: Economic Models /

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