Rethinking pedagogy for second order differential equations: Research for undergraduates

New mathematical / pedagogical research http://dx.doi.org/10.1080/0020739X.20... Enjoy!! In this work, we provided a novel method for well-posedness of second and higher order initial value problems. The innovation involves directly dealing with the second order problem and its equivalent integral equation, rather than transforming the problem to a first order system of differential equations. Within this approach we measure distance between functions through the idea of a weighted distance function (or weighted metric) that involves an exponential function.

As a result of the new ideas herein, students and teachers of differential equations will have a novel pedagogical method for the classroom regarding understanding well-posedness of second and higher order initial value problems. The ideas have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics.

We look forward to measuring the effect that this new avenue has on learning as the next stage in this project.

Please Cite As:
Christopher C. Tisdell (2017) Rethinking pedagogy for second-order
differential equations: a simplified approach to understanding well-posed problems, International Journal of Mathematical Education in Science and Technology, 48:5, 794-801, DOI:
10.1080/0020739X.2017.1285062

http://dx.doi.org/10.1080/0020739X.20...