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Mathematical Dependent vs Independent Variables

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Mathematics
In calculus, a function is a map whose action is specified on variables. Take x and y to be two variables. A function f may map x to some expression in x. Assigning gives a relation between y and x. If there is some relation specifying y in terms of x, then y is known as a dependent variable (and x is an independent variable).
Statistics
In a statistics experiment, the dependent variable is the event studied and expected to change whenever the independent variable is altered.[1]
Modelling
In mathematical modelling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In the simple stochastic linear model the term is the i th value of the dependent variable and is i th value of the independent variable. The term is known as the "error" and contains the variability of the dependent variable not explained by the independent variable.
With multiple independent variables, the expression is: , where n is the number of independent variables.
Simulation
In simulation, the dependent variable is changed in response to changes in the independent variables.
Statistics Synonyms

Independent variable
An independent variable is also known as a "predictor variable", "regressor", "controlled variable", "manipulated variable", "explanatory variable", "exposure variable" (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or an "input variable."[2][3]
"Explanatory variable" is preferred by some authors over "independent variable" when the quantities treated as "independent variables" may not be statistically independent.[4][5]
Independent variable(s) may be of these kinds: continuous variable(s), binary/dichotomous variable(s), nominal categorical variable(s), ordinal categorical variable(s), among others.
Dependent variable
A dependent...

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