Functions of Two Variables

  • John Gilbert
Part of the Macmillan Mathematical Guides book series (MG)


We have studied functions of one variable and vector functions of one variable. In each case, the value of the variable defines the value of the function. We now turn to functions of two variables, where the values of two variables must be given before we can evaluate the function. As in the case of a function of one variable, we define a function f of two variables, x and y, say, by its value at all points of the domain. Now, however, ranges of values for both x and y must be specified. For example, the domain of f might consist of values of x and y satisfying axb and cyd. Instead of referring to x and y separately, we shall often refer to them as a point (x, y); then we can talk about f being evaluated at the point (x, y), while the domain of f is the rectangle in the xy plane defined by the above inequalities.


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Copyright information

© John Gilbert 1991

Authors and Affiliations

  • John Gilbert
    • 1
  1. 1.Department of MathematicsUniversity of LancasterBailrigg, LancasterUK

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