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Page 14-1
Chapter 14
Multi-variate Calculus Applications
Multi-variate calculus refers to functions of two or more variables. In this
Chapter we discuss the basic concepts of multi-variate calculus including partial
derivatives and multiple integrals.
Multi-variate functions
A function of two or more variables can be defined in the calculator by using
the DEFINE function („à). To illustrate the concept of partial derivative,
we will define a couple of multi-variate functions, f(x,y) = x cos(y), and g(x,y,z)
= (x
2
+y
2
)
1/2
sin(z), as follows:
We can evaluate the functions as we would evaluate any other calculator
function, e.g.,
Graphics of two-dimensional functions are possible using Fast3D, Wireframe,
Ps-Contour, Y-Slice, Gridmap, and Pr-Surface plots as described in Chapter 12.
Partial derivatives
Consider the function of two variables z = f(x,y), the partial derivative of the
function with respect to x is defined by the limit