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In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
Formulas in the B column multiply values from the A column using relative references, and the formula in B4 uses the SUM() function to find the sum of values in the B1:B3 range. A formula identifies the calculation needed to place the result in the cell it is contained within. A cell containing a formula, therefore, has two display components ...
The substitutions of Euler can be generalized by allowing the use of imaginary numbers. For example, in the integral +, the substitution + = + can be used. Extensions to the complex numbers allows us to use every type of Euler substitution regardless of the coefficients on the quadratic.
Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...
from the formula for the tangent of the difference of angles. Using s instead of r in the above formulas will give the same primitive Pythagorean triple but with a and b swapped. Note that r and s can be reconstructed from a, b, and c using r = a / (b + c) and s = b / (a + c).