Multivariable calculus

In calculus, multivariable calculus or multivariate calculus is the extension of regular, one-dimensional calculus to more than one dimension. Most of the concepts from calculus, such as continuity and chain rule, still work in more than one dimension, though sometimes with greater complexity and counter-intuitive result.

Special multivariable uses include partial derivatives, or differentiation with only one dimension at a time, and multiple integration, or integrating over more than one dimension. The gradient operator [math]\displaystyle{ \nabla }[/math], defined in terms of partial derivatives, is used to define higher concepts such as Laplace operator, divergence and curl. By integrating a multivariable function over several variables, one can define an integral over an area, surface or volume as well.

Multivariable Calculus Media

• 

  Plot of the function f(x, y) = (x²y)/(x⁴ + y²)

• 

  Osculating circle of plane curve

• 

  Helicoid curve with 'a = 1'.

• 

  Plot in Mathcad, zelf aangemaakt d.m.v. screenshot

• 

  Plot of the vector field f(x,y) = (-y,x).

Related pages

• Vector calculus