Define a Staircase function in Mathematica
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Given a cosine like "delta function", a continuous and derivable "staircase function" should be defined that grows following the delta function with [Alpha] in each interval 0..Pi (and multiples) and remains constant in the last value with [Alpha] in the intervals Pi..2Pi (and multiples).
When [Alpha] is negative we should get the opposite behavior: constant with in each interval 0..-Pi (and multiples) and decreasing following the delta function with [Alpha] in each interval -Pi..-2Pi (and multiples).
See the notebook for more info.
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I am a physics PhD student and a researcher. "The function will be based on a square Cosine function". The function is ready.
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I am an MIT mathematics student; I'm very familiar with Mathematica. The function will be based on a square Cosine function. This looks easy enough, but I don't believe your test for continuity works correctly.