Teaching First-order Systems to Electrical Engineering Students Using Visual and Intuitive Examples

Abstract Teaching first order systems to Electrical Engineering students using visual and intuitive examples Abstract First order differential equations is a topic that is prevalent in mathematics and is foundational to several engineering classes. Electrical engineering specifically is a field where understanding first order systems is crucial; it is a cornerstone of topics such as transient electrical systems including RC and RL circuits. Despite this, many students struggle with conceptual understanding of this subject. The equations and mathematics can be overwhelming and frustrating, in part because it is often hard to visualize the concept. Today's students have plenty of distractions at their fingertips. Especially in the midst of the COVID-19 pandemic, which has resulted in more online-learning, students will oftentimes browse the internet or pull out their phones if they begin feeling bored or frustrated with a topic. Simply put, today's students learn differently – more intuitively and with shorter attention spans – and lessons should compensate for this with presentation methods that are clear, visual, and intuitive. The primary focus of this work is to help teachers explain, and learners to understand, the fundamental concepts of first order differential equations through the use of intuitive and example-based approaches as they relate primarily to electrical engineering. This paper seeks to simplify the introduction to the topic of first order differential equations into something that is clear and easy to comprehend. To accomplish this, the paper starts with a visual background of first order systems and an explanation of exponential growth vs. exponential decay. It then moves into (1) electrical examples, including the charging rate a cell phone and the idea of transient response in electrical systems such as RC and RL circuits, (2) electromechanical examples, including DC motors and heat transfer rates of different types of stoves, (3) various topics from other STEM disciplines, such as vehicle accelerations (dynamics), diffusion (physics), and currency depletion (economics). The paper concludes with a related brain teaser. The goal of this approach is to provide students with examples that translate textbook explanations to real life and help in understanding the material. We believe that when using these intuitive examples students tend to better understand first order systems, especially as they relate to the field of electrical engineering. This paper should be considered a work in progress. The presented information is meant to be supplemental in nature and not to replace existing textbooks or other teaching and learning methodologies. This intuitive and engaging approach to teaching and learning has been tested in the past for many topics including Control Systems, Digital Signal Processing, Computer Algorithms, Statics, Thermodynamics, Calculus, Statistics, and Newton's Laws of Motion. In all of these cases, students highly praised the approach and found it to be very effective for learning.