MATHEMATICAL MODELING IN DESIGNING EQUATIONS CONTAINING UNKNOWN QUANTITY UNDER THE SIGN OF MODULE WITH MAPLETECHNOLOGIES

Abstract

      The technology of designing equations and inequalities containing unknown quantity under the sign of module based on mathematical modeling is established. We consider the following key steps of constructing equations containing unknown under the sign of module: 1) Statement of a problem (finding the type of mathematical object and its properties, such as the type and properties of the equation, 2) creating or finding a scientific approach to create a mathematical model, for example in the form of ideas; 3) creation of mathematical model it’s research and adjustments; 4) creation or finding a scientific approach to solve the mathematical model and the creation of a scientific approach based on the method of solving mathematical model; 5) creation of algorithm based on the method for solving mathematical model; 6) creation of algorithm program according to specific algorithmic language of the algorithm (we have Maple); 7) adjustment of the program and the program execution; 8) analysis of the results and their broadcast on the problem. Note that at every stage there are situations of necessary adjustments, then you should go back to the previous steps and make adjustments to them. The different cases of equations, the number of solutions are investigated: equation has three, two, one, none, plenty solutions. The appropriate mathematical models are constructed which are then investigated and resolved. When solving mathematical models in the form of equations and inequalities bulky conversion and calculations are performed in Maple-technology, which significantly improved the quality of such changes, retained considerable ime and allowed the computer to perform experiments without much effort. Established algorithm and program according to the designed method allow to get enough of similar tasks with answers options to create tests or individual tasks.