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Warianty tytułu
Nauczanie, modelowanie i wizualizacja równań różniczkowych zwyczajnych
Języki publikacji
Abstrakty
Advances in computer technology and increased interest in dynamical systems influence the way of teaching ordinary differential equations. The paper presents inquiry oriented teaching, usage of modeling, visualisation and interactive web services. Last chapter describes the ways of using MATLAB or public domain software (e.g. Octave) to solve ordinary differential equations.
Postęp w technologii komputerowej oraz wzrost zainteresowania modelowaniem systemów dynamicznych wpływa na sposób nauczania matematyki, w tym równań różniczkowych zwyczajnych. Przedstawiono podejścia: nauczania przez zadawanie pytań, wykorzystanie modelowania, wizualizacji i interaktywnych usług sieci web. Ostatni rozdział opisuje sposoby wykorzystania środowiska MATLAB lub oprogramowania dostępnego jako public domain (np. Octave) do rozwiązywania równań różniczkowych zwyczajnych.
Czasopismo
Rocznik
Tom
Strony
99--111
Opis fizyczny
Bibliogr. 20 poz., wz., wykr., il.
Twórcy
autor
- Faculty of Electrical and Computer Engineering, Cracow University of Technology
Bibliografia
- [1] Boyce W.E, Diprima R.C, Elementary Differential Equations and Boundary Value Problems, (4th Edition), Wiley International, John Wiley & Sons, ISBN 0-471-83824-1, 1986.
- [2] Cariaga E. A., Nualart M. C., Teaching and learning iterative methods for solving linear systems using symbolic and numeric software, Comput Appl Eng Educ 10, 2002, 51—58.
- [3] Interactive Differential Equations, Pearson Addison-Wesley, http://www.aw-bc.com/ide, 2013.
- [4] Kadijevich D., Haapasalo L., Hvorecky J., Using technology in applications and modelling, Teaching Mathematics and its Applications, 24(2-3), 2005, 114—122.
- [5] Kwon O., Rasmussen C., Towards an inquiry approach to undergraduate mathematics Proceedings of the 4th East Asia Regional Conference on Mathematics Education, Penang, Malayasia, 2007, 39—46.
- [6] Kwon, O., at all. Students’ Retention of Mathematical Knowledge and Skills in Differential Equations, School Science and Mathematics, 105(5), 2005, 1—13.
- [7] MATLAB, Simulink, http://www.mathworks.com/products/, 2013.
- [8] Menger K., On the Teaching of Differential Equations, The American Mathematical Monthly, Vol. 51, No. 7 1944, 392—395.
- [9] Modelica and the Modelica Association, http://www.modelica.org, 2014.
- [10] Mrozek B., Mrozek Z., MATLAB i Simulink. Poradnik uzytkownika, Wydanie III, Helion, 2010.
- [11] Nabb K., Inquiry in Differential Equations: A Teacher’s Reflections, 38th AMATYC Annual Conference, http://www.amatyc.org/Events/conferences/2012Jacksonville/proceedings.html, Jacksonville, Florida, 2012.
- [12] Octave, http://www.octave.org and http://octave.sourceforge.net/odepkg
- [13] Padir Taskin, et al., Teaching differential equations in a diverse classroom, 2008 Annual Conference and Exposition, AC 2008-1548, American Society for Engineering Education, 2008.
- [14] Paraskakis I., Rethinking the Teaching of Differential Equations through the Constructivism Paradigm, In: ICALT 2003 - 2003 IEEE International Conference on Advanced Learning Technologies 9-11 July, 2003, Athens, Greece, 2003, 506—510.
- [15] Rasmussen Chris, Whitehead Karen, Learning and Teaching Ordinary Differential Equations, http://www.maa.org/t-and-l/sampler/research-sampler.html, The Mathematical Association of America, RESEARCH SAMPLER, No. 7, January 2003.
- [16] Rasmussen, at all. Capitalizing on advances in mathematics and K-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach differential equations, Asia Pacific Education Review, 7(1), 2006, 85—93.
- [17] Rota Gian-Carlo Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations, http://euler.slu.edu/Dept/Faculty/marks/Pedagogy/RotaOnTeachingDifflEqns.pdf, 1997.
- [18] Teacher package: Differential equations, Plus Magazine, University of Cambridge, http://plus.maths.org/content/teacher-package-differential-equations.
- [19] Wagner J., Speer N., Rossa B., Beyond mathematical content knowledge: A mathematician’s knowledge needed for teaching an inquiry-oriented differential equations course, Journal of Mathematical Behavior 26, 2007, 247––266.
- [20] Zadawanie dobrych pytań http://www.ceo.org.pl/pl/cyfrowaszkola/kurs/zadawanie-dobrych-pytan.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-645415ac-ee3b-45cb-9d81-4b3f8926d8d5