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| Autor/in | Bissell, J. J. |
|---|---|
| Titel | An Elementary Proof by Contradiction of the Exactness Condition for First-Order Ordinary Differential Equations |
| Quelle | In: International Journal of Mathematical Education in Science and Technology, 52 (2021) 6, S.965-971 (7 Seiten)Infoseite zur Zeitschrift
PDF als Volltext |
| Zusatzinformation | ORCID (Bissell, J. J.) |
| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
| ISSN | 0020-739X |
| DOI | 10.1080/0020739X.2020.1817588 |
| Schlagwörter | Validity; Mathematical Logic; Equations (Mathematics); Calculus; Mathematics Instruction; College Mathematics; Undergraduate Study |
| Abstract | The ability to distinguish between exact and inexact differentials is an important part of solving first-order differential equations of the form Adx + Bdy = 0, where A(x,y) [not equal to] 0 and B(x,y) [not equal to] 0 are functions of x and y However, although most undergraduate textbooks motivate the necessary condition for exactness, i.e. the requirement that aA/ay = aB/ax, simple proofs that this condition is sufficient are not always given. Here we demonstrate that the condition is sufficient using a novel proof by contradiction. Our approach is compared to other proofs existing in the literature, and considered in the context of personalized learning. (As Provided). |
| Anmerkungen | Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2022/1/01 |
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