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Differential Equations, Discrete Systems and Control - edition reliée, livre de poche

1997, ISBN: 0792346750

[EAN: 9780792346753], New book, [PU: Springer Netherlands Aug 1997], MATHEMATIK / WIRTSCHAFTS- U. SOZIALWISSENSCHAFTEN; OPTIMIERUNG; VARIATIONSRECHNUNG; OPTIMALCONTROL; DYNAMICOPTIMIZATIO… Plus…

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Differential Equations, Discrete Systems and Control - edition reliée, livre de poche

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This volume presents some of the most important mathematical tools for studying economic models. It contains basic topics concerning linear differential equations and linear discrete-time… Plus…

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Differential Equations, Discrete Systems and Control - edition reliée, livre de poche

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Differential Equations Discrete Systems and Control

This volume presents some of the most important mathematical tools for studying economic models. It contains basic topics concerning linear differential equations and linear discrete-time systems; a sketch of the general theory of nonlinear systems and the stability of equilibria; an introduction to numerical methods for differential equations, and some applications to the solution of nonlinear equations and static optimization. The second part of the book discusses stabilization problems, including optimal stabilization, linear-quadratic optimization and other problems of dynamic optimization, including a proof of the Maximum Principle for general optimal control problems. All these mathematical subjects are illustrated with detailed discussions of economic models. Audience: This text is recommended as auxiliary material for undergraduate and graduate level MBA students, while at the same time it can also be used as a reference by specialists.

Informations détaillées sur le livre - Differential Equations Discrete Systems and Control


EAN (ISBN-13): 9780792346753
ISBN (ISBN-10): 0792346750
Version reliée
Livre de poche
Date de parution: 1997
Editeur: Springer Netherlands
380 Pages
Poids: 0,730 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2008-02-19T10:32:59+01:00 (Paris)
Page de détail modifiée en dernier sur 2023-08-07T06:24:01+02:00 (Paris)
ISBN/EAN: 9780792346753

ISBN - Autres types d'écriture:
0-7923-4675-0, 978-0-7923-4675-3
Autres types d'écriture et termes associés:
Auteur du livre: samuel
Titre du livre: differential equations discrete systems control, theory differential equations, mathematical modelling economics, well control equations


Données de l'éditeur

Auteur: A. Halanay; J. Samuel
Titre: Mathematical Modelling: Theory and Applications; Differential Equations, Discrete Systems and Control - Economic Models
Editeur: Springer; Springer Netherland
360 Pages
Date de parution: 1997-08-31
Dordrecht; NL
Langue: Anglais
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
Available
XVI, 360 p.

BB; Hardcover, Softcover / Wirtschaft/Volkswirtschaft; Wirtschaftstheorie und -philosophie; Verstehen; Optimal control; dynamic optimization; maximum principle; nonlinear systems; optimization; ordinary differential equations; Quantitative Economics; Differential Equations; Difference and Functional Equations; Calculus of Variations and Optimization; Optimization; Differentialrechnung und -gleichungen; Optimierung; BC; EA

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 CapitalAccumulation 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.

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