A Framework for an ICT-Based Study of Parametric Integrals
| Autor: | Thierry Dana-Picard, David G. Zeitoun |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
05 social sciences 050301 education 0102 computer and information sciences Symbolic computation Darboux integral 01 natural sciences Volume integral Order of integration (calculus) Algebra Computational Mathematics Computational Theory and Mathematics 010201 computation theory & mathematics Integro-differential equation Slater integrals Representation (mathematics) 0503 education Mathematics Parametric statistics |
| Zdroj: | Mathematics in Computer Science. 11:285-296 |
| ISSN: | 1661-8289 1661-8270 |
| DOI: | 10.1007/s11786-017-0299-z |
| Popis: | We describe working session for the study of 1-parameter families of definite integrals in a technology-rich environment. The joint usage of paper-and-pencil work together with a Computer Algebra System and eventually a web based database may lead to closed forms for the integrals, to the derivation of combinatorial identities, and other kinds of output. This joint usage applied to parametric integrals lead to mathematical expressions rather than graphic representation. This permits a new learning process in the teaching of mathematics, physics and engineering. We begin with a short survey of classical cases, using telescopic methods. Then we show a new example where the integrals depend not only on an integer parameter, but also on a real variable. In this last case, the study of the parametric integral involves the study of a recurrence differential equation. |
| Databáze: | OpenAIRE |
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