Visualization in Mathematical Packages When Teaching with Information Technologies

A method has been obtained for the use of visualization in computer mathematical packages, which is an effective means of overcoming difficult situations that arise for students when mastering such packages and solving computational problems. Depending on the complexity of the problem being solved, either the teacher or the students themselves can create special visual graphic (animation) objects. Such objects allow, initially without going into the intricacies of the functioning of the package and the mathematical apparatus used, to competently describe a complete picture of a difficult situation for students and indicate ways to resolve it. The method is considered through the example of the process of solving systems of equations using the mathematical package Mathcad and the WolframAlpha online resource. Graphical and animated objects are presented that clearly demonstrate the areas of the location of initial approximations, allowing you to numerically obtain all the real roots of systems of trigonometric and nonlinear equations. Similar objects are built to find the critical points of the Himmelblau's special test function. Visualization materials are confirmed by the presented computational calculations. The proposed method is implemented in the form of plans for lectures and practical classes on mathematical modeling using computer technologies. The method was tested with university students at the National Research University Moscow Power Engineering Institute.