Abstract
The paper deals with a comprehensive analysis of existing mathematical criteria for conservative vector fields including algebraic and geometrical interpretation of Extended Green’s Theorem. Special attention is devoted to the fields containing a point singularity, which represents the primary challenge both in teaching Calculus and in carrying out scientific research in general in computer engineering. Examples of real-world physical fields such as gravitational, electric and magnetic ones are used to appreciate the proposed clarification while teaching various interchangeable disciplines such as mathematics, physics and engineering. Other examples from scientific research literature are provided as well to support the necessity of the study. The detailed analysis of Extended Green’s theorem has been also performed to avoid frequent misunderstandings arising in various topics of vector calculus, mechanics, physics and pure mathematics. The research conducted has as a main objective to improve university curricula in engineering majors based on the current requirement of joining science, technology, engineering and mathematics (STEM curriculum). Besides, it contributes to a more efficient way of approaching geometrical singularities, which is extremely important in any computer programing.
Recommended Citation
Aleksandrova, Nelli
(2025).
(R2084) Clarification of Mathematical Criteria for Conservative Forces and Vector Fields with a Point Singularity in Engineering Studies,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
2, Article 9.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss2/9