Читать книгу All sciences. №3, 2023. International Scientific Journal - Sultonali Mukaramovich Abduraxmonov - Страница 7

Aliev Ibratjon Khatamovich

2nd year student of the Faculty of Mathematics and Computer Science of Fergana State University

Ferghana State University, Ferghana, Uzbekistan

Аннотация. Изучение математической теории, способной в качестве отдельного инструмента описывать наблюдаемый мир весьма необходимо не только для исследователей в данной области, но и для всех представителей человеческой цивилизации, не говоря уже о тех, кто хочет производить описания математических теорий, ради этих же математических теорий. Особенной в данной части является такой метод исследования, как использование тройного или трёхкратного интеграла, наряду с отдельными операциями с элементами под знаком этого же тройного интеграла.

Ключевые слова: трёхкратные интегралы, математический анализ, исследования, определение, вычисление, научная новизна.

Annotation. The study of a mathematical theory capable of describing the observable world as a separate tool is very necessary not only for researchers in this field, but also for all representatives of human civilization, not to mention those who want to produce descriptions of mathematical theories for the sake of these same mathematical theories. Special in this part is such a method of research as the use of a triple or triple integral, along with separate operations with elements under the sign of the same triple integral.

Keywords: triple integrals, mathematical analysis, research, definition, calculation, scientific novelty.

The need to determine the volume, therefore, based on density and mass, along with the number of components and other derivatives of these quantities for objects that cannot be determined practically, a vivid example of this is the determination of the mass of a mountain, huge details for which it is not possible or too costly to use the Archimedes method, but it is necessary to calculate the volume or even when determining parameters of the whole planet.

The object of the study is a three-fold integral. The subject of the study is the process of calculating a triple integral, as well as operating with it when replacing variables of this triple integral. As a result of the study, some hypothesis is put forward that asserts the possibility of using triple integrals in calculating the parameters of linear accelerators relative to the internal particles of smooth electromagnetic waveguides of linear accelerators.

The objectives of the study are:

· Definition of the concept of a triple integral;

· Study of the process of replacing variables in a triple integral;

· Showing a model for calculating parameters by means of a three-fold integral for a linear accelerator waveguide.

The objectives of the study are:

· Study of the concept of a three-fold integral in the general understanding and some coordinate systems, indicating general concepts in a brief form;