WIP: A visual and intuitive approach to teaching first order systems to Mechanical Engineering students.

First Order Differential Equations is a topic prevalent in mathematics and several engineering classes. Mechanical engineering specifically is a field where understanding first order systems is crucial. It is a cornerstone of topics including dynamic systems, vibrations, and fluid dynamics. 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 first order systems. Today's students are exposed to many distractions. If students feel bored or frustrated with a lecture, oftentimes they will browse the internet on their laptops or pull out their phones to entertain themselves with social media (Facebook, Instagram, etc.) or games. They learn differently, more intuitively, experiencing short attention spans. They expect the material and presentation methods to be clear, visual, and intuitive. The goal of this paper is to help instructors explain, and students understand, the fundamental concept of First Order Differential Equations in an intuitive and example-based approach by simplifying the introduction to the topic to something that is clear and easy to intuitively comprehend. To accomplish this, the paper starts with a visual background into first order systems and an explanation of exponential growth vs. exponential decay. It then transitions into: Mechanics examples which are chosen to cover multiple different mechanical engineering topics, such as shock absorbers (vibrations), acceleration rates of different vehicle types (dynamics), and toilet mechanisms (mechanical feedback). Next, the paper moves into thermodynamic examples, such as time constants of different stove types and the cooling rate of a hot coffee cup. Finally, the paper relates the topic to examples from other STEM disciplines, such as charging a cell phone (electrical Engineering), measuring change in pressure between two connected vessels (physics), carbon dating using half-life measurement (chemistry), and DC motors transfer function (electro-mechanical). The point of this approach is to provide students with visual and intuitive examples that relate textbook explanations to real life scenarios. We believe that when using these intuitive examples, students tend to better understand the topic of first order systems. This paper is 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. The contents of this work have been shared with students in a remote (Zoom-based) classroom setting and assessed following the lecture using an anonymous questionnaire. The initial results, based on 40 responses, indicate that this teaching method is effective in helping students comprehend the basic idea behind the concept of First Order Differential Equations. This approach to teaching and learning has been tested in the past for topics in Statics (explaining center of gravity), Statistics (explaining normal distribution), Calculus (explaining integration and explaining derivation by chain, product, and quotient rules), Thermodynamics (explaining entropy), Differential Equations, Control Systems, Digital Signal Processing, Newton's Laws of Motion, and Computer Algorithms. In all of these cases, students found this approach to be very effective for learning, and they highly praised the intuitive and engaging examples. [ABSTRACT FROM AUTHOR]