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

Daniel Raviv; Daniel Barb; George Roskovich

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Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: Mechanical Engineering: Assorted Topics
Page Count: 24
DOI: 10.18260/1-2--40680
Permanent URL: https://peer.asee.org/40680
Download Count: 451

Paper Authors

biography

Daniel Raviv Florida Atlantic University

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Daniel Raviv received his B.Sc. and M.Sc. degrees from the Technion, and his Ph.D. from Case Western Reserve University in Cleveland, Ohio. He is a professor at Florida Atlantic University (FAU) where he is the Director of the Innovation and Entrepreneurship Lab. In the past he served as the assistant provost for innovation. Dr. Raviv taught at Johns Hopkins University, the Technion, and the University of Maryland, and was a visiting researcher at the National Institute of Standards and Technology (NIST) as part of a group that developed a vision-based driverless vehicle for the US Army (HUMVEE; 65 mph).
His related research work includes exploration of visual invariants that exist only during motion and can be used for real-time closed-loop control systems of cars and drones. He is also interested in teaching and learning innovative thinking, and how to teach innovatively. He is the author of five books: three on learning innovative thinking and two on teaching in visual, intuitive, and engaging ways.

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Daniel Barb

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Daniel is an engineer working in commercial nuclear power. He received his BSME from Florida Atlantic University, and is pursuing an MSME from Pennsylvania State University. He spent six years in the Navy as a nuclear power plant operator aboard a submarine.

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George Roskovich Florida Atlantic University

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Abstract

Abstract

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 and vibrations, and can simplify topics like 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 paper concludes with a related brain teaser.

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.

Citation
Format

Raviv, D., & Barb, D., & Roskovich, G. (2022, August), WIP: A visual and intuitive approach to teaching first order systems to Mechanical Engineering students Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--40680

TY - CPAPER
AB - Abstract

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 and vibrations, and can simplify topics like 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 paper concludes with a related brain teaser.

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.

AU - Daniel Raviv
AU - Daniel Barb
AU - George Roskovich
CY - Minneapolis, MN
DA - 2022/08/23
PB - ASEE Conferences
TI - WIP: A visual and intuitive approach to teaching first order systems to Mechanical Engineering students
UR - https://peer.asee.org/40680
DO - 10.18260/1-2--40680
ER -