An example on E-learning contents for engineering students to self-study and focus on mathematics

Abstract

Until recently, without proper visualization tools, mathematics education researchers haven't focused on the development of visualization for symbols and graphs. Using paper based materials or physical things is not enough to provide dynamic understanding of the mathematics theories for students. those materials are very limited to be modeled and, specially, paper based materials are so 'static' that it doesn't have any room for drawing the motivation out from students. This thesis aims for engineering students to get motivation on studying engineering mathematics and focusing on their mathematics classes by representing visualized examples and explaining mathematical theories using Mathematica, a CAS system which provides visual mathematical graphs and symbols. webMathematica is an effective CAS package for building a mathematics related website, providing dynamic calculations, visualizing function and so forth. Also, this package is able to publish all the presented mathematics contents from Mathematica to be the one, a web version. In this thesis, we will use webMathematica for engineering students to study mathematics via the contents we provide. First, we will evaluate their motivation by, in advance, showing the visualized result graph which shows the concept of differential and integral calculus. Then, for letting students to form the concept given above, we will explain the definition by providing numerical formulae and text to help student's understanding. By providing the process of answering with examples, students can understand the concept of differential and integral calculus. Using the programmed package we built, students will be able to understand the concept of differential and integral calculus by typing only essential variables to get answers from the web. Followed by exercise questions, students can check if they perfectly understood. This thesis will provide contents of Newton Method and Rieman Sum for engineering students.