Solutions to Odd-Numbered Exercises

George W. Hart
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George W. Hart: Columbia University, Department of Electrical Engineering

Chapter 9 in Multidimensional Analysis, 1995, pp 223-226 from Springer

Abstract: Abstract 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.

Keywords: Dimensionless Quantity; Multidimensional Analysis; Intrinsic Function; Dimension Permutation; Multiplier Circuit (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4612-4208-6_10

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