Meike Akveld (a) & Wigand Rathmann (b)
meike.akveld@math.ethz.ch; wigand.rathmann@fau.de
(b) Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Department Mathematik
Abstract
Traditionally advanced engineering courses cover more dimensional analysis in a one semester course in the first or second year. Understanding of the gradient is the basis for optimization algorithms and for explaining stochastic gradient methods used in machine learning. Computing the gradient itself is not hard, but a deeper understanding can be hard to obtain and often visualisations prove to be useful. The module, we will present and which is work in progress, consists of texts and quizzes, both enhanced with interactive visualisations. The goal is to deepen the geometric understanding of easily computed concepts like partial derivatives, tangent planes, directional derivatives, and in particular the gradient, so that these concepts can be generalised more easily to higher dimensional spaces or for more abstract purposes. In the last part of the module students are introduced to classical descend methods used in (constrained) optimisation which are based on gradients. This self-study module will be provided for Moodle and ILIAS as LMS using the STACK question type. The visualisation in the text and quizzes is realized using JSXGraph.
Keywords
Engineering Math, STACK, JSXGraph, interactive self-study module, multivariable calculus
Links
STACK Website: https://stack-assessment.org
JSXGraph Website: https://jsxgraph.org