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Divergence, Gradient, and Curl

Faculty Commons material developed by Troy Messina - Published July 14, 2023

This is the second of a series of computational/graphing activities on scalars and vectors designed for the intermediate Electricity & Magnetism course using a text such as Griffiths “Introduction to Electrodynamics”. These activities are
1. Scalar and Vector Fields
2. Div, Grad, Curl
3. Vector Fields
Div, Grad, Curl is an in-class set of activities that introduce students to computational methods for calculating vector mathematics. These are meant to follow the Vector and Scalar Fields activities that can be found at https://teaching.smp.uq.edu.au/fiveminutephysics/index.html#course=phys2055&lecture=Fields, and a Python version submitted by me to PICUP. This Div, Grad, Curl activity introduces symbolic mathematics, e.g., the dot product, cross product, gradient, etc. from the Python SymPy library and puts those tools to use in the context of vectors and vector fields to help students visualize how these operations result in scalars or vectors depending on the input vectors.
Learning Outcomes: Students develop a deeper understanding of the differences between scalar and vector fields. Students learn to computationally calculate divergence, gradient, and curl. Students learn to graphically visualize the results of these computations. Students develop a better understanding of the mathematical operations divergence, gradient, and curl.

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