The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Applications of Functions of Two Or More Variables

Here are some examples of functions of two or more variables arising in applications.

Geometry:

  • ab = area of a rectangle of sides a and b
  • abc = volume of a rectangular solid
  • ½bh = area of a triangle with base b and height h
  • πr2h = volume of a cylinder with circular base of radius r and height h
  • ⅓πr2h = volume of a cone with circular base of radius r and height h
  • 01_real_and_hyperreal_numbers-53.gif = distance from the origin to (x, y)

Physics:

  • F = ma = force required to give a mass m an acceleration a
  • ρ(x,y, z) = density of a three-dimensional object at the point (x, y, z)
  • F = Gm1m2/s2 = gravitational force between objects of mass m1 and m2 at distance s
  • 01_real_and_hyperreal_numbers-54.gif= relativistic mass of an object with rest mass m0 and velocity v

Economics:

  • c(x, y) = cost of x items of one commodity and y items of another commodity
  • D1(p1, p2) = demand for commodity one when commodity one has price p1 and commodity two has price p2


Last Update: 2006-11-09