Ботаника

This textbook covers quantitative methods in economics, ranging from linear algebra to dynamic programming. It provides theoretical foundations and practical applications for students. The content is designed to aid in economic analysis and decision-making, and focuses on using mathematical tools to solve real-world problems.

Asosiy mavzular

Chiziqli algebra: This section covers matrices, determinants, and systems of linear equations. It discusses operations with matrices, methods for calculating determinants, and techniques for solving systems of linear equations. Emphasis on how these concepts are utilized to model economic relationships.
Chiziqli dasturlash: Introduces linear programming, including mathematical modeling, graphical solutions, the simplex method, and duality. It includes topics such as sensitivity analysis and economic interpretations of the models, with a focus on the practical application of linear programming techniques.
Butun sonli chiziqli dasturlash: Presents methods for solving linear programming problems with integer constraints. Topics include Gomory's cutting plane method, and branch and bound techniques, with examples illustrating their use in various economic decision-making scenarios.
Transport masalalari: Deals with transportation problems, including the formulation of the problem, methods for finding initial basic feasible solutions, and the potential method for optimization. Considers special cases and provides detailed algorithmic procedures for solving these problems.
Matritsali o'yinlar: Introduces game theory, focusing on matrix games and their applications. Topics include pure and mixed strategies, the minimax theorem, and methods for solving matrix games. Explains how these concepts can be applied to analyze strategic interactions in economics.
Bimatritsali o'yinlar: Extends game theory concepts to bimatrix games, where players have different payoff matrices. Explores the concept of Nash equilibrium and methods for finding equilibrium in these games. Provides insights into strategic interactions where players' interests are not perfectly aligned.
Chiziqsiz dasturlash: Covers nonlinear programming, including quadratic forms, unconstrained and constrained optimization. Discusses methods for finding extrema of nonlinear functions, such as the method of Lagrange multipliers. Also explores the use of computer software to solve these types of problems.
Qavariq dasturlash: Presents convex programming, including convex sets and convex functions. Covers the Karush-Kuhn-Tucker (KKT) conditions for optimality and provides an overview of methods for solving convex programming problems.
Dinamik dasturlash: Deals with dynamic programming, including Bellman's equation, and its applications to resource allocation, shortest path problems, and equipment replacement. Emphasizes the principle of optimality and provides recursive formulations for solving dynamic optimization problems.
Transport va chiziqsiz dasturlash masalalarini kompyuterda yechish: Presents an overview of several commonly used software packages such as PER, TORA, LINGO, and Maple, their special features, and examples for how to use them in a step by step manner in order to solve and test these various optimization techniques, for both linear and nonlinear applications.