Advertisement

Solutions to Odd-Numbered Exercises

  • George W. Hart

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

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

Personalised recommendations