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- W1477834 abstract "This chapter describes implicit functions and implicit differentiation. Not every equation, even of polynomial type, can be solved directly for its unknown. If two variables are related by an equation that cannot be solved algebraically for one of the variables, then one can only discover the relationship between the two variables numerically. To be specific, if X and Y are related by the equation Y↑2 + 3 * X * Y − 6 * X↑3 * Y = 5, then by treating this as a quadratic in Y and applying the quadratic formula, one has Y = (-3 * X + -SQR(9 * X↑2 + 4 * (5 + 6 * X↑3)))/2. Thus, in this case, one is able to solve the equation relating X and Y to obtain an explicit relationship between the two variables. If the polynomial relating X and Y had been of degree 5 or greater in both of the variables, then it would in general be impossible to obtain an explicit relationship between the two variables. In that case, the relationship can be called implicit." @default.
- W1477834 created "2016-06-24" @default.
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- W1477834 date "1981-01-01" @default.
- W1477834 modified "2023-09-27" @default.
- W1477834 title "IMPLICIT FUNCTIONS AND DIFFERENTIATION" @default.
- W1477834 doi "https://doi.org/10.1016/b978-0-12-304365-8.50008-x" @default.
- W1477834 hasPublicationYear "1981" @default.
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