What are some applications of smoothing a piecewise polynomial?
For example, I am interested in learning from you: 1) In what future areas of my math studies will this be useful? and 2) Are there common real world applications of this technique?
This topic is presented as a worked example following the lecture on the product rule in Calculus I (see note below), at the following link: MIT OCW 18.01 SC Worked Example of Smoothing a Piecewise Polynomial
Hopefully, awareness of future applicability will help me learn this idea well enough to remember it permanently.
I look forward to your thoughts on the topic.
Note: The formal name of the MIT OCW class is presented here to facilitate searching by other participants interested in the same material: MIT OCW Math 18.01 SC Single Variable Calculus // MIT Open Courseware Math 18.01 OCW Scholar Single Variable Calculus