“LIV ING FORCE” INTEGRAL AND REDUCTION OF THE ORDINARY DIFFERENTIAL EQUATION ORDER: METHODICAL PARALLEL BETWEEN TOPICS OF PHYSICS AND MATHEMATICS COURSES

Abstract

The paper considers the justification of the relationship between Newton’s second law and the law of conservation of energy in the simplest case, when we deal with rectilinear motion of a material point under the variable force. The mathematical demonstration of this relationship is compared with the reduction of the differential equation order, the method of solving of differential equations being studied at math classes by junior students – physicists and engineers. The preliminary analysis of modern scientific methodological publications shows the relevance of developing actual methods of linking academic disciplines. The consideration of materials taken from physics and mathematics courses allows us to create a methodical parallel useful both for physical and mathematical studying. Aim. To discover correspondence between algorithms and significations of ordinary differential equations (order reduction) and those of classic mechanics (Newton’s second law and energy conservation). After consideration in general terms the parallel between topics from physics and math courses, we show the solution of a math problem, which could illustrate the detected parallel in math classes. Novelty. The authors have built the methodical parallel between some topics from physics and math courses. This allows demonstrating linking of disciplines rarely shown practically in classes. Methodology and methods. Analysis of modern scientific methodological publications about linking physics and math courses in higher education (physical and
technical study directions); creation of methodical parallel between two linked topics of physics and mathematics courses; analysis of educational examples applying our methodical idea. Results. The analysis of scientific methodological publications shows the problems in physics education noted by professors: it is difficult for students to connect in their mind math methods and their application in physics; math courses are sometimes too formal and far from physics. The paper discusses the methodological approach to solving the problems; gives the example of physics and math reasoning to show how the methodology works.