Solutions to Odd-Numbered Exercises

  • George W. Hart


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.


Dimensionless Quantity Multidimensional Analysis Intrinsic Function Dimension Permutation Multiplier Circuit 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • George W. Hart
    • 1
  1. 1.Department of Electrical EngineeringColumbia UniversityNew YorkUSA

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