On the Presentation of the Physical and Mathematical Solutions Process of Problems in Physics to Engineering Students

Basile Panoutsopoulos

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Conference: ASEE Zone 1 Conference - Spring 2023
Location: State College,, Pennsylvania
Publication Date: March 30, 2023
Start Date: March 30, 2023
End Date: April 12, 2023
Tagged Topic: Diversity
Page Count: 7
DOI: 10.18260/1-2--45072
Permanent URL: https://strategy.asee.org/45072
Download Count: 44

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Paper Authors

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Basile Panoutsopoulos Community College of Rhode Island (CCRI)

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Basile Panoutsopoulos (M’80–SM’01) holds a Ph.D. from the Graduate Center of the City University of New York, a ME in Electrical Engineering from The City College of the City University of New York, a MS in Applied Mathematics, and a BS in Electrical Engineering from New Jersey Institute of Technology. He is a Life Senior Member of IEEE.
He joined the Department of Physics and Engineering, CCRI in the Fall 2013. He was with the School of Engineering and Technology at Central Connecticut State University during the period 2010-2013. Previously, he worked for Naval Undersea Warfare Center, initially in New London, CT, and later in Newport, RI, from 1992 to 2010. He has taught courses in Physics, Mathematics, and Electrical Engineering and Technology. His interests concentrate on Electromagnetics and Applications, Bioelectromagnetics, Energy Systems, Electric Circuits, Applied Mathematics, and Pedagogy (especially methodology and strategies in Problem-Solving techniques). He volunteers in Robotics and Mathcounts clubs. Dr. Panoutsopoulos may be reached at Basile.Panoutsopoulos@ieee.org and BPanoutsopoulos@ccri.edu .

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Abstract

On the Presentation of the Physical and Mathematical Solutions Process of Problems in Physics to Engineering Students

The solution to problems is both a techne and a technique. To teach and train engineering students (our future engineers and colleagues) on how to solve problems (engineers solve problems) we presented them with the solution process using two approaches. One characteristic of both approaches is that we show all the steps of the solution process so the student concentrates on understanding the application of principles than trying to guess how the various results come into existence. To distinguish the two approaches, are called the Mathematical and Physical/Mathematical. In the newly developed Mathematical approach, the mathematical steps of the solution process are organized in a diagrammatic approach. All steps of the mathematical solution process are presented logically, clearly indicating the necessary derivations and substitutions, until to get a final formula that to the left of the equality sign has the unknown quantity and to the right all the known quantities. This approach has the advantage of including interactive dialogs (questions and answers, comments) which take place during class time, but requires the presence of the instructor. The physical explanation of every step was provided during the presentation (lecture/recitation) using an interactive screen by the instructor. The presentation (video and audio) was recorded and made available to the students in the Collaborate part of Blackboard. It is ideal for class discussion. Other problems were presented using the Physical/Mathematical approach that includes both physical explanation and mathematical presentation. The one line of the text is followed by the next line corresponding equation, and so on, until to get the final formula in which to the left of the equality sign has the unknown quantity and to the right all the known quantities. This approach has the advantage that does not require the presence of the instructor. It is ideal for self-study. Both approaches were presented to the students during the past year. In class, discussions took place during the semester on the preferable and possibly more beneficial approach by the students. They embraced the physical/mathematical more because it suits for self-study. Furthermore, it does not require the need to watch the recorded lecture/recitation which takes considerably more time. But they suggested that the first approach is beneficial for fast review (preparation for examination) after they have mastered the classical solution. To assist the student in their study an effort is underway to prepare problem-solution processes that include both the above-discussed approaches; the physical/mathematical is the main solution process while the mathematical is presented under Summary.

NOTE: THE FORMULAS BELOW CANNOT BE PASTED ON A TEXTBOX!

Example: Let us consider a point charge Q. Determine an expression for the electric field E at every point of the space. Solution Process:

Mathematical approach Physical / Mathematical approach To find the electric field intensity around a charge Q, we shall use the definition of the electric field: The force on the test charge due to the charge is given by Coulomb’s law: The distance is denoted by in the spherical coordinate system we are using to solve this problem. Substituting the force equation into the electric field equation, we get: We conclude that the electric field has an component when the source charge is positive and the test charge is, by definition, positive. The force will have orientation along the line connecting the two points and sense away from the charge . Why?

Citation
Format

Panoutsopoulos, B. (2023, March), On the Presentation of the Physical and Mathematical Solutions Process of Problems in Physics to Engineering Students Paper presented at ASEE Zone 1 Conference - Spring 2023, State College,, Pennsylvania. 10.18260/1-2--45072

TY - CPAPER
AB - On the Presentation of the Physical and Mathematical Solutions Process of Problems in Physics to Engineering Students

The solution to problems is both a techne and a technique. To teach and train engineering students (our future engineers and colleagues) on how to solve problems (engineers solve problems) we presented them with the solution process using two approaches. One characteristic of both approaches is that we show all the steps of the solution process so the student concentrates on understanding the application of principles than trying to guess how the various results come into existence. To distinguish the two approaches, are called the Mathematical and Physical/Mathematical.
In the newly developed Mathematical approach, the mathematical steps of the solution process are organized in a diagrammatic approach. All steps of the mathematical solution process are presented logically, clearly indicating the necessary derivations and substitutions, until to get a final formula that to the left of the equality sign has the unknown quantity and to the right all the known quantities. This approach has the advantage of including interactive dialogs (questions and answers, comments) which take place during class time, but requires the presence of the instructor. The physical explanation of every step was provided during the presentation (lecture/recitation) using an interactive screen by the instructor. The presentation (video and audio) was recorded and made available to the students in the Collaborate part of Blackboard. It is ideal for class discussion.
Other problems were presented using the Physical/Mathematical approach that includes both physical explanation and mathematical presentation. The one line of the text is followed by the next line corresponding equation, and so on, until to get the final formula in which to the left of the equality sign has the unknown quantity and to the right all the known quantities. This approach has the advantage that does not require the presence of the instructor. It is ideal for self-study.
Both approaches were presented to the students during the past year. In class, discussions took place during the semester on the preferable and possibly more beneficial approach by the students. They embraced the physical/mathematical more because it suits for self-study. Furthermore, it does not require the need to watch the recorded lecture/recitation which takes considerably more time. But they suggested that the first approach is beneficial for fast review (preparation for examination) after they have mastered the classical solution.
To assist the student in their study an effort is underway to prepare problem-solution processes that include both the above-discussed approaches; the physical/mathematical is the main solution process while the mathematical is presented under Summary.

NOTE: THE FORMULAS BELOW CANNOT BE PASTED ON A TEXTBOX!

Example: Let us consider a point charge Q.
Determine an expression for the electric field E at every point of the space.
Solution Process:

Mathematical approach Physical / Mathematical approach

To find the electric field intensity around a charge Q, we shall use the definition of the electric field:

The force on the test charge due to the charge is given by Coulomb’s law:

The distance is denoted by in the spherical coordinate system we are using to solve this problem.
Substituting the force equation into the electric field equation, we get:

We conclude that the electric field has an component when the source charge is positive and the test charge is, by definition, positive. The force will have orientation along the line connecting the two points and sense away from the charge . Why?

AU - Basile Panoutsopoulos
CY - State College,, Pennsylvania
DA - 2023/03/30
PB - ASEE Conferences
TI - On the Presentation of the Physical and Mathematical Solutions Process of Problems in Physics to Engineering Students
UR - https://strategy.asee.org/45072
DO - 10.18260/1-2--45072
ER -