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Concept of an elementary work as introduction to the line integral in engineering studies.

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Title: Concept of an elementary work as introduction to the line integral in engineering studies.
Authors: Aleksandrova, Nelli1 (AUTHOR) nelli@staff.uma.pt, Drumond, Custódia2 (AUTHOR)
Source: International Journal of Mechanical Engineering Education. Jan2025, Vol. 53 Issue 1, p189-210. 22p.
Subjects: Line integrals, Integral calculus, Vector calculus, Mathematical analysis, Vectors (Calculus), Vector fields
Abstract: The paper is devoted to the line integral topic belonging to the section of vector calculus in Mathematical Analysis applied to the undergraduate Mechanical Engineering program. An efficient way of teaching line integrals is proposed and developed based on the elementary work/force principles. By this way, the mathematical concept of the line integral is supposed to be learned in harmony with the elementary mechanics to appreciate its diversity and to set up the right idea about the scientific area covered by Mechanical Engineering and related academic and technical fields. In terms of practical training, the research also offers two new techniques of analytical calculus for line integrals containing singularities and provides a new coherent engineering approach to deal with vector fields as integrands in line integrals. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Concept of an elementary work as introduction to the line integral in engineering studies.
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  Data: <searchLink fieldCode="AR" term="%22Aleksandrova%2C+Nelli%22">Aleksandrova, Nelli</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nelli@staff.uma.pt</i><br /><searchLink fieldCode="AR" term="%22Drumond%2C+Custódia%22">Drumond, Custódia</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Mechanical+Engineering+Education%22">International Journal of Mechanical Engineering Education</searchLink>. Jan2025, Vol. 53 Issue 1, p189-210. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Line+integrals%22">Line integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+calculus%22">Integral calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+calculus%22">Vector calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Vectors+%28Calculus%29%22">Vectors (Calculus)</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink>
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  Label: Abstract
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  Data: The paper is devoted to the line integral topic belonging to the section of vector calculus in Mathematical Analysis applied to the undergraduate Mechanical Engineering program. An efficient way of teaching line integrals is proposed and developed based on the elementary work/force principles. By this way, the mathematical concept of the line integral is supposed to be learned in harmony with the elementary mechanics to appreciate its diversity and to set up the right idea about the scientific area covered by Mechanical Engineering and related academic and technical fields. In terms of practical training, the research also offers two new techniques of analytical calculus for line integrals containing singularities and provides a new coherent engineering approach to deal with vector fields as integrands in line integrals. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Integral calculus
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      – SubjectFull: Vector calculus
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      – SubjectFull: Vectors (Calculus)
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              Text: Jan2025
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