Erschienen in:

1995 | OriginalPaper | Buchkapitel

Solutions to Odd-Numbered Exercises

verfasst von : George W. Hart

Erschienen in: Multidimensional Analysis

Verlag: Springer New York

Enthalten in: Professional Book Archive

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With x a length: (a) the Taylor series $$ 1 + x + {x^2} + {x^3} + \ldots $$ is the sum of a dimensionless quantity, a length, an area, a volume, etc.; (b) the formula 1 + x/n sums a dimenslonless quantity and a length; (c) the derivative $$ \frac{d}{{dx}}\,f(x) $$ has dimensions of [f/length] and so can not equal [f]; (d) the condition that [f]=[f2] requires that f be dimensionless, but according to a result in §1.2.6, there can be no intrinsic function from lengths to dimensionless quantities.

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