A Hands-on Application-Based Tool for STEM Students to Understand Differentiation

The main goal of this project is to illustrate to college students in science, technology, engineering, and mathematics (STEM) fields some fundamental concepts in calculus. A high-level technical computing language MATLAB, is the core platform used in the construction of this project. A graphical user interface (GUI) is designed to interactively explain the intuition behind a key mathematical concept: differentiation. The GUI demonstrates how a derivative operation (as a form of kernel) can be applied on one-dimensional (1D) and two-dimensional (2D) images (as a form of vector). The user can interactively select from a set of predetermined operations and images in order to show how the selected kernel operates on the corresponding image. Such interactive tools in calculus courses are of great importance and need, especially for STEM students who seek an intuitive and visual understanding of mathematical notions that are often presented to them as abstract concepts. In addition to students, instructors can greatly benefit from using such tools to elucidate the use of fundamental concepts in mathematics in a real world context.