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2. Free variables and bound variables - Wikipedia

   en.wikipedia.org/wiki/Free_variables_and_bound...

   Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n. In the lambda calculus, x is a bound variable in the term M = λx. T and a free variable in the term T. We say x is bound in M and free in T. If T contains a subterm λx. U then x is rebound in this term.

3. de Bruijn index - Wikipedia

   en.wikipedia.org/wiki/De_Bruijn_index

   A variable n is bound if it is in the scope of at least n binders (λ); otherwise it is free. The binding site for a variable n is the nth binder it is in the scope of, starting from the innermost binder. The most primitive operation on λ-terms is substitution: replacing free variables in a term with

4. Change of variables - Wikipedia

   en.wikipedia.org/wiki/Change_of_variables

   Variable changes for differentiation and integration are taught in elementary calculus and the steps are rarely carried out in full. The very broad use of variable changes is apparent when considering differential equations, where the independent variables may be changed using the chain rule or the dependent variables are changed resulting in ...

5. Imputation (statistics) - Wikipedia

   en.wikipedia.org/wiki/Imputation_(statistics)

   When substituting for a data point, it is known as "unit imputation"; when substituting for a component of a data point, it is known as "item imputation". There are three main problems that missing data causes: missing data can introduce a substantial amount of bias , make the handling and analysis of the data more arduous , and create ...

6. Substitution (logic) - Wikipedia

   en.wikipedia.org/wiki/Substitution_(logic)

   A substitution σ is called a flat substitution if xσ is a variable for every variable x. A substitution σ is called a renaming substitution if it is a permutation on the set of all variables. Like every permutation, a renaming substitution σ always has an inverse substitution σ −1 , such that tσσ −1 = t = tσ −1 σ for every term t .

7. Tangent half-angle substitution - Wikipedia

   en.wikipedia.org/.../Tangent_half-angle_substitution

   The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .

8. Change of variables (PDE) - Wikipedia

   en.wikipedia.org/wiki/Change_of_variables_(PDE)

   Advice on the application of change of variable to PDEs is given by mathematician J. Michael Steele: [1] "There is nothing particularly difficult about changing variables and transforming one equation to another, but there is an element of tedium and complexity that slows us down.

9. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   Here z is the free variable, while x and y are dependent on z. Any point in the solution set can be obtained by first choosing a value for z, and then computing the corresponding values for x and y. Each free variable gives the solution space one degree of freedom, the number of which is equal to the dimension of the solution set.