Решение задач экономики средствами пакетов Maple and MathCad

Решение задач экономики средствами пакетов  Maple and MathCad

Plan

1. Introduction.
2. The main part.

1. Getting acquainted with the program Maple.
2.  Construction and visualization of complex graphics functions using the program Maple, held in secondary schools in Kazakhstan.
3. Construction of a mathematical model of a problem of economic statistics by using Maple.

1. Conclusion
2. Used literature.

Introduction

You need to solve a math problem quickly, efficiently and without errors in an analytical form (of course, if at all possible) - should be addressed to the program Maple. If a solution is possible only in a numerical way.

Maple - a software package, a computer algebra system. It is a product of Waterloo Maple Inc. (English) Russian., which produces software products since 1984, focused on complex mathematical calculations, data visualization and modeling.

The system is designed to Maple symbolic computation, although it has a number of tools for the numerical solution of differential equations and finding integrals. It has developed graphical tools, has its own programming language that resembles Pascal.

In this project we consider the possibility of output function graphs in program Maple. There were shown the construction and visualization of complex graphics functions using the program Maple, held in secondary schools in Kazakhstan.A specific example of economic statistics and technical statistics were examined and were calculated using the program Maple and MathCAD.

2.2. Construction and visualization of complex graphics functions using the program Maple, held in secondary schools in Kazakhstan.

Let’s show an example of fractional-linear function: у=[pic 1]

[pic 2]

The following graph trigonometric functions [pic 3].

Also demonstrate the possibility to combine the two programs Maple different functions on the same graph        [pic 4],[pic 5],[pic 6]

[pic 7]

The following example consists of several different functions on the same graph, made by using Maple:

[pic 8],[pic 9],[pic 10]

[pic 11],[pic 12],[pic 13],[pic 14]

[pic 15]

        In the following example, the function chart data, a sequence of coordinates of individual points. Then the segments connecting these points, we obtain the graph of fractional-linear function.

[pic 16]

[pic 17]

Schedule 3-dimensional image is shown in the graph below, and the function is given by the following equation: [pic 18]

[pic 19]

2.3. Construction of a mathematical model of a problem of economic statistics by using Maple.

For enterprise managers, it is important to know the theory and practical tools to wield economic and mathematical modeling, using this science, anyone who has knowledge can build and calculate the economic-mathematical model that can help in any situation when you need to make the right decision. Mathematical model can help to take into account many different factors and characteristics that can affect this problem. When analyzing this model, you can find the best plan for dealing respectively minimizes costs. EMM includes methods of various sciences such as Computer Science, Economics, Statistics, etc. Through the development of science and technology now, all calculations take less time than before. Strong advancement of mathematical theories (linear algebra, analysis, probability theory, correlation and regression analysis, differential equations, etc.) provides for our services is very powerful and developed mathematical apparatus.

Of course, in the use of mathematical methods has its weaknesses. When you try to formalize the economic situation can get very complicated mathematical problem. To simplify it, we must introduce new assumptions are often not justified from an economic perspective. Therefore, the researchers engaged in danger of mathematical analysis technique instead of true economic situation. The only way to combat this is the usage of computers with a set of programs. In the course of this robot, we discuss how we can simplify the mathematical part EMM tasks, using a software package for example Maple.        

Under the economic-mathematical model is meant a mathematical description of the economic process and the test object. This model expresses the regularity of the economic process in abstract form using mathematical relationships. Using mathematical modeling in economics allows quantitative economic analysis to deepen and expand the area of economic information, intensify economic calculations.

Economical and mathematical modeling, as a rule, based on linear programming techniques. Linear programming is called to find an optimal plan in problems with linear structure. For solving linear programming problems, usually used the simplex method, which in general terms is that by successive iterative procedures is the solution satisfying the optimality.

In general, for such tasks must go through the following steps

1. Clarification of the economic substance of the tasks and the system is variable.

2. Analysis and formalization of all constraints of the problem.

3. Finding the objective function and the optimality criterion.

4. Mathematical formalization of all input data and search for the solution.

The fourth stage can be carried out in two ways

1. Finding a solution manually

2. And with the usage of the software package Maple

According to all the parameters, the second method is most convenient; because it reduces the time you spend on searching the solution of tasks, provides the necessary clarity of the information and the possibility of correction of the initial data. Modern economic process characterized by high intensity and the large volume of the information reported in the unit of time that imposes special requirements to the processes. In particular, improving the efficiency of EMMA in the modern conditions is impossible without using of computer mathematics.