===== Electrostatics and Vector Derivatives ===== Here is a {{workshops:colombia10:Colombia10Derivatives.ppt|link to the powerpoint presentation}} from this session. ---- How can we analyze the way in which scalar and vector fields change? This workshop covered differentiation of scalar and vector fields. In particular, we explored the geometric interpretations of gradient and divergence. * Maple: scalar and vector fields (field lines vs field vectors) * what can change and in which directions? * SG: dr vector in curvilinear * GVC (ss) [[bb>book:math:drvec|The Vector Differential]] * Compare: The Hill * SWBQ: gradient * GVC (ss) [[bb>book:math:gradient|Gradient]] The next three links are a good example of how to sequence different kinds of activities, choosing the different pedagogical strategies depending upon what aspects you are trying to convey. * SWBQ: flux * GVC (ss) [[bb>book:math:flux|Flux]] * Kinesthetic: The concept of flux. A kinesthetic activity in which students use rulers to represent a vector field and a hula hoop to represent a surface. The class discussion focuses conceptually on what contributes to the flux. * Maple: Visualizing Flux. A Maple activity that allows students to explore the flux of the electric field through a cubical surface due to a point charge. The position of the point charge can be varied so that there are different amounts of flux through each of the six surfaces. It is possible to move the point charge source outside of the cube, or even onto the surface of the cube. * Lecture/Overhead: Definition of Divergence * GVC (ss) [[bb>book:math:divergence|Divergence]] * Maple: Visualizing Divergence * Lecture/Overhead: Divergence Theorem * GVC (ss) [[bb>book:math:divthm|The Divergence Theorem]] * Discussion: the Differential form of Gauss's Law * GVC (ss) [[bb>book:physics:maxwell1|Differential Form of Gauss's Law]] ---- Although we did not have time to cover them in this workshop, curl and Stokes' Theorem can be treated analogously to divergence and the Divergence Theorem above. The relevant sections in the activities wiki and Bridge Book are: * GVC (ss) [[bb>book:math:curl2|Curl]] * Visualizing Curl * GVC (ss) [[bb>book:math:stokes|Stokes' Theorem]] * GVC (ss) [[bb>book:physics:maxwell2|Differential Form of Ampère's Law]]