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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
y
yyx
x
−=
∂
∂
=
∂
∂
,
• 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
2
+y
2
)
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.]