HP 49g+ Graphing Calculator Bedienungsanleitung PDF herunterladen (Seite 141)

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 manual, 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) = x cos(y), and g(x,y,z) = (x

)

1/2

sin(z).

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HP 49g+ Graphing Calculator Bedienungsanleitung Seite 141