Module 3 - Circuits & Systems of Equations

This folder contains Live Scripts to compliment physics and math skills applied during a circuits activity.

The first-year engineering program at Hofstra University consists of a computer programming for engineers’ course, and a two-semester sequence of engineering design. Before the fall of 2018, the computer programming for engineers’ course covered algorithms, logic, flowcharting and programming of solutions to engineering problems through the MATLAB® integrated development environment (IDE) [1]. A redesign of the course began in the Fall of 2018 [2] to add Excel and math instruction. Existing hands-on activities were repurposed [3] to serve as and form the foundation of this new, activity centric model learning approach. This is different from incorporating lab experiments as had been done previously [4] in that the activities are designed to be gentler and friendlier for first-year students as well as more easily portable. As students engage in the activity to collect data, they develop collaboration and cooperation skills with their classmates; building a learning support group to help them on their academic journey. The data from the activity is then used to build Excel, math, and MATLAB® skills through more, active learning assignments completed in class. The pedagogy has been created for both first-year engineering students at the university and high school juniors and seniors engaged in the engineering department’s Pathways to Engineering outreach program at four local high schools.

This courseware has been developed by Lynn Albers, PhD at Hofstra University in collaboration with MathWorks.

3) Circuits - where students are introduced to circuits, resistors, breadboards, multimeters, systems of equations, matrices, and their application in engineering. Kirchhoff’s Voltage Law is introduced to build linear equations equivalent to the number of unknowns and solve them by use of a matrix inverse, Cramer’s Rule, and substitution (original activity developed at EGR 1010 at Wright State University).

There are 5 livescripts with accompanying PowerPoint lectures and hands-on activities with circuits, resistors, breadboards and multimeters, and one activity using external courseware - Equations and Systems: Interactive Notebook:

• The first session in this module is using the activity “Equations and Systems: Interactive Notebook” By Pablo López Díez - Colegio Jesuitas León [5]. The course material available here: https://www.mathworks.com/academia/courseware/equations-and-systems.html is used as an introduction to the mathematical topics.
• Module3-1-SystemsOfEquationsMethod1Subs - Systems of Equation in Engineering: The Two-Loop Circuit - Introduction to Kirchhoff’s Voltage Law to build linear equations using substitutions and MATLAB's Symbolic Math Toolbox (original activity developed at EGR 1010 at Wright State University).
• Module3-2-SystemsOfEquationsMethod2MatrixAlgebra - Systems of Equation in Engineering: The Two-Loop Circuit - Introduction to Kirchhoff’s Voltage Law to build linear equations using matrix algebra.
• Module3-3-SystemsOfEquationsMethod3Cramers - Systems of Equation in Engineering: The Two-Loop Circuit - Introduction to Kirchhoff’s Voltage Law to build linear equations using Cramer's rule and MATLAB code.
• Module3-4-SystemsOfEquationsExercise - Systems of Equation in Engineering: The Two-Loop Circuit - Instructions for the associated practical experiment using breadboards, resistors, multimeters and ammeters, where students determine resistances, calculate current and use two methods to compute voltages. After measuring the current, students calculate the error between the experiment and theoretical values, then write a MATLAB script for the entire exercise.
• Module3-5-VectorsQuiz - a short interactive live script quiz to guess column/row vectors and matrix multiplication. Additional activites can be found in the Matrices and Arrays documentation.

Suggested homework for this module includes the following trainings from the Self-Paced Online Courses: Make and Manipulate Matrices + Calculations with Vectors and Matrices + Introduction to Symbolic Math.