Keywords
Smooth mapping, Jacobian matrix, differential, rank of a mapping, Euclidean space
How to Cite
Salimova , G. (2026). Smooth Mappings . GLOBAL SCIENTIFIC CONFERENCE ON MULTIDISCIPLINARY RESEARCH, 1(1), 80-83. https://doi.org/10.5281/zenodo.18455042
Abstract
This paper considers smooth mappings between Euclidean spaces and their basic differential properties. A mapping defined on an open set is studied through its coordinate functions, differentiability, and continuity. Special attention is given to the Jacobian matrix, the differential of a mapping, and the concept of rank. Definitions of smooth, infinitely differentiable, and continuous mappings are presented, and illustrative examples are discussed to demonstrate the theoretical results.
References
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