Ebook: Differential Equations, Discrete Systems and Control: Economic Models

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.

---

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.
Content:
Front Matter....Pages i-xvi
Linear and Affine Differential Equations. Equations with Separated Variables....Pages 1-22
Linear Differential Equations with Constant Coefficients....Pages 23-73
Linear Systems with Constant Coefficients....Pages 74-102
General Theory of Nonlinear Systems. Stability....Pages 103-143
Numerical Solution of Differential Equations....Pages 144-170
Control Systems. Stabilization of Linear Systems....Pages 171-197
Optimal Stabilization....Pages 198-227
Linear-Quadratic Optimization on Finite Horizon....Pages 228-269
Some Unconstrained Dynamic Optimization Problems....Pages 270-305
General Problem of Optimal Control....Pages 306-350
Back Matter....Pages 351-359

---

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.
Content:
Front Matter....Pages i-xvi
Linear and Affine Differential Equations. Equations with Separated Variables....Pages 1-22
Linear Differential Equations with Constant Coefficients....Pages 23-73
Linear Systems with Constant Coefficients....Pages 74-102
General Theory of Nonlinear Systems. Stability....Pages 103-143
Numerical Solution of Differential Equations....Pages 144-170
Control Systems. Stabilization of Linear Systems....Pages 171-197
Optimal Stabilization....Pages 198-227
Linear-Quadratic Optimization on Finite Horizon....Pages 228-269
Some Unconstrained Dynamic Optimization Problems....Pages 270-305
General Problem of Optimal Control....Pages 306-350
Back Matter....Pages 351-359
....