Work

Defined-by-condition Functions

Year: 2025

Type: conference-paper

Abstract: The Implicit Function Theorem is a fundamental result in mathematical analysis with far-reaching implications in differential equations, optimization, and manifold theory. This theorem provides conditions under which a relation defined by an equation can be locally expressed as a function of some variables in terms of others. In this article, we explore the theoretical foundations of the Implicit Function Theorem, its proof, and its applications in various fields, including economics, physics, and engineering. We discuss how the theorem facilitates the study of constrained optimization, implicit differentiation, and the stability of dynamical systems. Additionally, we present illustrative examples to demonstrate its practical utility in solving nonlinear equations and modeling real-world phenomena.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15377900

Author: Nurmanova, Ezoza Ulugbek qizi

Institution: Jizzakh branch of the National University of Uzbekistan named after Mirzo Ulugbek

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6912052525

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