Dependent variable vs name of function

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Description of bottleneck

In mathematics and in particual in the STEM disciplines one often does not symbolically distinguish the name of a function and its dependent variable.

For example, the time dependence (independent variable, symbolized by <math>t</math>) of an electrical charge <math>q</math> (dependent variable, symbolized by <math>q</math>) might be described by a certain function <math>f(t)</math>, i.e. <math>q = f(t)</math>. Here different symbols have been used for the dependent variable <math>q</math> and the functional relationship <math>f</math> (between <math>t</math> and </q>). It is, however, customary to conflate this and to use <math> q</math> to do denote both dependent variable and functional relationship. This results in the using the experession <math>q(t)</math>.

Interestingly this possible Bottleneck was revealed during an Decoding interview on students' difficulties with describing piecewise defined functions. The interviewers got confused by interviewees simultaneous usage of a symbol as the independent variable of a function and as the name of the functional relation.

People interested in this bottleneck

Peter Riegler