# Chapter 14 - Multi-variate Calculus Applications; Multi-variate Functions; Partial Derivatives - HP 48gII User Manual

Graphing calculator.

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)
2
2
1/2
= (x
+y
)
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
Page 14-1