Keyword: «generalized functions»

The paper considers the definition of convexity (up, down) of the graph of function using the method of tangents, chords and analytical method. The author formulates signs and related methods to study functions for bulge graphics using the second derivative and functions of generalization.

The article describes the methodology of the topic "Generalized functions. Generalized derivatives. Delta-Dirac function" presentation in the course of equations of mathematical physics at MSTU named after N.E. Bauman. Delta function was introduced by physicists, trying to formally determine the density of point mass (point charge). Then it was used in the equations of mathematical physics, but without good mathematical reasoning. A general theory of generalized functions was later developed in the works by S.L. Sobolev and L. Schwartz. This mathematical tool is widely used in physics, mathematical physics, electrodynamics, quantum mechanics, acoustics, wave optics, theory of oscillations, the theory of signals and circuits, so it is necessary for students of instrument engineering specialties. However, its academic presentation makes considerable difficulties for the students. The aim of this paper is to propose methodology for academic presentation of generalized functions theory, intelligible to second-year students. Practical methods for calculating generalized derivatives are demonstrated. The article is written on the basis of broad experience in teaching mathematical physics equations and will be useful for students of instrument engineering specialties, as well as for teachers of relevant courses.