Innovative methods and technologies while examining equations of mathematical physics

Abstract

Abstract Teaching disciplines of physics and mathematics in the age of information technology requires innovative teaching methods application. These methods complement traditional forms; they are aimed at developing the systematic and creative thinking of students. The disciplines of the physical and mathematical profile include such discipline as “Equations of Mathematical Physics”. They help students develop skills in creating mathematical models of physical processes and phenomena. It is advisable to apply software packages to create computer models of situational problems when studying the discipline “Equations of Mathematical Physics”. The mathematical packages application makes it possible to take various situations by changing the input parameters of the model on the basis of computer models of physical processes. The problems of mathematical physics are based on the study of the second-order partial differential equations of three main types: hyperbolic, elliptic, and parabolic. The paper discusses the mathematical package MathCad application in the study of free and forced vibrations of a string. Mathematical models of free and forced oscillations are presented. The d’Alembert formula for solving equations of hyperbolic type is presented. The authors describe stages of the study of free vibrations of the membrane in MathCad. Bessel functions are constructed. Membrane surface animation has been created. Observations of membrane vibrations were carried out.