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
• = 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
• = 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