Moving the inertial forces to the left gives an expression that can be considered to represent quasi-static equilibrium, but which is really just a small algebraic manipulation of Newton's law:
32.
Equivalently, the momentum equation ( ) can also be cast in the so-called conservation form, through some algebraic manipulations on the Saint-Venant equations, ( ) and ( ).
33.
The general theory of Pell's equation, based on continued fractions and algebraic manipulations with numbers of the form P + Q \ sqrt { a }, was developed by Lagrange in 1766 1769.
34.
As I see it, this was not an arithmetical calculation; it was an algebraic manipulation, performed by a competent editor, posted wrongly twice before he posted an algebraically correct but strictly unsourced formula.
35.
Word problems are a common way to train and test understanding of underlying concepts within a descriptive problem, instead of solely testing the student's capability to perform algebraic manipulation or other " mechanical " skills.
36.
The importance of this algebraic manipulation is notable because it allows linking a measurable and observable magnitudes ( corresponding to the Input-Output analysis ) with more compact magnitudes which have a deeper economic significance for the dynamic analysis.
37.
:: I strongly suspect the solution here is not by a general method, but rather some clever tricks of algebraic manipulation .-- 137.205.236.45 11 : 32, 16 January 2006 ( UTC)
38.
A simple argument, involving only elementary algebraic manipulation, demonstrates that the set of additive maps " f : \ mathbb { Q } \ to \ mathbb { Q } " is identical to the set of linear maps.
39.
For simple domains, it is possible, to impement step 3 of the Fokas method : using the global relations and their invariant properties, it is possible to express all transforms in terms of the given boundary data, using only algebraic manipulations.
40.
This expression is useful for " selecting " any one of the matrices numerically by substituting values of 1, 2, 3 } }, in turn useful when any of the matrices ( but no particular one ) is to be used in algebraic manipulations.
