Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems
| Autor: | Christopher Tisdell, Johnny Henderson |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical logic
Well-posed problem Mathematical model Applied Mathematics 010102 general mathematics 05 social sciences 050301 education System of linear equations 01 natural sciences Education Mathematics (miscellaneous) Ordinary differential equation Calculus Initial value problem Boundary value problem 0101 mathematics 0503 education Separable partial differential equation Mathematics |
| Zdroj: | International Journal of Mathematical Education in Science and Technology. 48:794-801 |
| ISSN: | 1464-5211 0020-739X |
| DOI: | 10.1080/0020739x.2017.1285062 |
| Popis: | Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems. |
| Databáze: | OpenAIRE |
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