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Page 12-1

Chapter 12

Multi-variate Calculus Applications

Multi-variate calculus refers to functions of two or more variables. In this

Chapter we discuss basic concepts of multi-variate calculus: partial derivatives

and multiple integrals.

Partial derivatives

To quickly calculate partial derivatives of multi-variate functions, use the rules

of ordinary derivatives with respect to the variable of interest, while

considering all other variables as constant. For example,

() ()

)sin()cos(),cos()cos( yxyx

yyx

−=

∂

• You can use the derivative functions in the calculator: DERVX, DERIV,

∂, described in detail in Chapter 11 of this Guide, to calculate partial

derivatives (DERVX uses the CAS default variable VX, typically, ‘X’).

Some examples of first-order partial derivatives are shown next. The

functions used in the first two examples are f(x,y) = SIN(y), and

g(x,y,z) = (x

)

1/2

sin(z). Added the following note after this blank

line. [Note: not all lines will be visible when done with the exercises

in the following figures.]

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HP 48gII Manuale Utente Pagina 143