eLecture: Zykloide (englische Version) скачать в хорошем качестве

eLecture: Zykloide (englische Version)

This is an example of an electronic course (e-lecture). The theme of cycloids was chosen because while it is clear and complete in itself, there are connections to other areas of mathematics such as vector algebra, geometry, calculus, differential equations and the calculus of variations. The mathematical depth ranges from easy to challenging, so there is something for everyone. Finally, it also has practical applications in mechanics and mechanical engineering. The e-lecture is suitable for self-study and consists of a video lecture, an eBook with formulas and explanations an interactive tool for the cycloid to "explore" and visualize and a self-test to check the acquired knowledge. Mathematical relationships which are presented in the video are derived in detail in the e-book. Necessary knowledge, as far as it goes beyond a lecture course mathematics for engineers, is provided, e.g. in the chapters A.1 Parameter curves and A.2 Introduction to the calculus of variations. In order to understand the different cycloids high-school mathematics is sufficient, whereas Chap. 2, Properties of the cycloid, applies to readers who are already familiar with differential equations. It was not intended to cover all known facts about cycloids as completely as possible, but rather, this selection is based on the personal taste of the author. More can be found in the thesis of Diana Heuer, and of course in Wikipedia. You can move freely between the units. For example, it can be useful while reading the books to trace the origin of the curves with the simulation tool, or to look up something in the eBook while you make the self-test. Have fun! Axel Kilian ******************************************************************** Produziert am Medienkompetenzzentrum der Hochschule Merseburg am Fachbereich Soziale Arbeit.Medien.Kultur Medienkompetenzteam: Dipl.Kult.Päd. Kai Köhler-Terz (Leitung). Thomas Grabmann (Technische Gesamtleitung). Filmproduktion Aleksandar Turuntas, Kamera Matthias Greiß, Montage Unterstützung: Finanzielle Unterstützung erhält das Vorhaben durch das interdisziplinäre HSP-Projekt „eLeture“ (Leitung: Prof. Dr. A. Kilian/K. Köhler-Terz), das vom Prorektorat für Studium und Lehre der Hochschule Merseburg, verantwortlich Prof. Dr. Heike Mrech, gefördert wurde. © Hochschule Merseburg 2015 bis 2016