Keyword: «function continuity concept»

The limit of function and continuity of function concepts are among the most difficult-to-digest concepts of school mathematics, and often cause difficulties for students. This work suggests a methodology for the presentation of the topic "The function continuity concept " in the courses of algebra and analysis in high school and mathematical analysis course for University first-year students. The aim of this work is to substantiate this concept with examples from physics, to provide deep understanding of continuity concept by high school and University students, to figure out the physical and geometric meaning of this concept. The work summarizes basic theoretical knowledge, typical examples and tasks for proof. The article is based on the experience of teaching mathematical analysis in technical university and it will be useful both for teachers in conducting practical classes and for students in their independent work on the topic.