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Have You Seen an Integral? Visual, intuitive and Relevant Explanations of Basic Engineering-related Mathematical Concepts

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2018 ASEE Annual Conference & Exposition


Salt Lake City, Utah

Publication Date

June 23, 2018

Start Date

June 23, 2018

End Date

July 27, 2018

Conference Session

Mathematics Division Technical Session 2

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Paper Authors


Daniel Raviv Florida Atlantic University

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Dr. Raviv is a Professor of Computer & Electrical Engineering and Computer Science at Florida Atlantic University. In December 2009 he was named Assistant Provost for Innovation and Entrepreneurship.

With more than 25 years of combined experience in the high-tech industry, government and academia Dr. Raviv developed fundamentally different approaches to “out-of-the-box” thinking and a breakthrough methodology known as “Eight Keys to Innovation.” He has been sharing his contributions with professionals in businesses, academia and institutes nationally and internationally. Most recently he was a visiting professor at the University of Maryland (at Mtech, Maryland Technology Enterprise Institute) and at Johns Hopkins University (at the Center for Leadership Education) where he researched and delivered processes for creative & innovative problem solving.

For his unique contributions he received the prestigious Distinguished Teacher of the Year Award, the Faculty Talon Award, the University Researcher of the Year AEA Abacus Award, and the President’s Leadership Award. Dr. Raviv has published in the areas of vision-based driverless cars, green innovation, and innovative thinking. He is a co-holder of a Guinness World Record. His new book is titled: "Everyone Loves Speed Bumps, Don't You? A Guide to Innovative Thinking."

Dr. Daniel Raviv received his Ph.D. degree from Case Western Reserve University in 1987 and M.Sc. and B.Sc. degrees from the Technion, Israel Institute of Technology in 1982 and 1980, respectively.

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Today’s students are exposed to information presented in visual, intuitive and concise ways. They expect explanations for why a subject is important and relevant, as well as for its potential use. In order to adapt to students’ learning preferences and styles, efforts must be made to further modify teaching methods to include relevance of the material to daily life experiences. The material should also be presented in easy-to-comprehend, visual, and intuitive ways. This is most relevant in math courses that are usually taught with little or no connection to other disciplines, and in particular engineering.

This paper focuses on introducing basic math concepts by linking them to daily experiences using relevant analogy-based examples, to be introduced prior to delving into purely mathematical explanations and proofs. The paper shows tangible physical explanations of concepts in calculus, specifically on topics such as:

(a) Integration and differentiation. To explain these concepts, the paper uses several examples such as (1) relations between steering wheel angle of a car and the physical angle of the car in world coordinates, (2) relations between water flow and its accumulation in a container, (3) elevator directional motion, and (4) energy and its temporal rate-of-change during running, walking, sitting, and sleeping. It also shows some unexpected examples that relay to very basic daily observations such as the relation between moving shadows to differentiation and integration.

(b) First order differential equation and time constant of first order system. Based on accumulated teaching experience, some helpful examples are: (1) battery charging a mobile phone at different initial charging values, and (2) cooling rate of coffee. There are of course many other examples, but not all of them are as impactful (e.g., radioactive decay and carbon dating). These ideas are shared so that instructors can use them to enhance understanding of engineering-related math concepts, and to show their relevance.

We refer to this approach as “work in progress.” When using the above examples (and many others), students have demonstrated better, clearer understanding of difficult concepts. Even though this was not an official assessment, based on similar experience that was gained and assessed by the author multiple times in other engineering related subjects (Control Systems, Digital Signal Processing, Computer Algorithms, and Physics), it is believed that the approach has a great potential.

Raviv, D. (2018, June), Have You Seen an Integral? Visual, intuitive and Relevant Explanations of Basic Engineering-related Mathematical Concepts Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. 10.18260/1-2--30572

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