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The first three activities provide an active-engagement version of the canonical mathematical and geometric fundamentals for power series. The subsequent activities apply these ideas to physical situations that are appropriate for an upper-division electromagnetism course, using concepts, terminology, and techniques that are common among physicists, but not often taught in mathematics courses. In particular students use the memorized formula for the binomial expansion to evaluate various electrostatic and magnetostatic field in regions of high symmetry. By factoring out a physical quantity which is large compared to another physical quantity, they manipulate the formulas for these fields into a form where memorized formulas apply. The results for the different regions of high symmetry are compared and contrasted. A few homework problems that emphasize the meaning of series notation are included.
Note: The first two activities are also included in ef="https://paradigms.oregonstate.edu/sequences/15" target="_parent">Power Series Sequence (Mechanics) and can be skipped in E&M if already taught in Mechanics.
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“Arms” is an engaging representation of complex numbers. Students use their left arms to geometrically represent numbers in the complex plane (an Argand diagram).
The sequence starts with pure math activities in which students represent a single complex number (using prompts in both rectangular and exponential forms), demonstrate multiplication of complex numbers in exponential form, and act out a number of different linear transformation on pairs of complex numbers. Later activities, relevant to spin 1/2 systems in quantum mechanics, explore overall phases, relative phases, and time dependence.
These activities can be combined and sequenced in many different ways; see the Instructor's Guides for how to introduce the Arms representation the first time you use it.
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