Introduction to Multivariable Functions
A multivariable function is a function with several variables. Functions with more than one variable are needed in order to mathematically model complicated physical phenomena, engineering, chemical, agricultural ... systems.
Examples of Multivariable Functions
Example 1A rectangle has a width W and a length L. The area A of the rectangle is given by A = W L. It is clear that if W and L vary, area A depends on two variables: width W and length L. Area A is said to be a function of two variables W and L.
Example 2
A rectangular solid has width W, length L and height H. The volume V of the rectangular solid is given by V = W L H. If W, L and H vary, volume V depends on 3 variables: width W, length L and height H.
Example 3
The volume V of a circular cylinder of radius r and height h is given by V = π r 2 h. If r and h vary, we can say that volume V is a function of two variables r and h.
Example 4
Let T be the temperature in a room. Using a rectangular coordinate system of axes (x,y,z), temperature T can be said to vary with x, y , z and time t and may be written as T(x,y,z,t) as a function of 4 variables.
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