HP 48gII Graphing Calculator Instrukcja Użytkownika Pobierz pdf (Strona 469)

100

101

Page 14-8

The resulting matrix has elements a

= ∂

φ/∂X

= 6., a

= ∂

φ/∂X

= -2.,

and a

= a

= ∂

φ/∂X∂Y = 0. The discriminant, for this critical point s2(1,0)

is ∆ = (∂

f/∂x

)⋅ (∂

f/∂y

)-[∂

f/∂x∂y]

= (6.)(-2.) = -12.0 < 0, indicating a

saddle point.

Multiple integrals

A physical interpretation of an ordinary integral,

∫

dxxf )( , is the area

under the curve y = f(x) and abscissas x = a and x = b. The generalization

to three dimensions of an ordinary integral is a double integral of a function

f(x,y) over a region R on the x-y plane representing the volume of the solid

body contained under the surface f(x,y) above the region R. The region R

can be described as R = {a<x<b, f(x)<y<g(x)} or as R = {c<y<d, r(y)<x<s(y)}.

Thus, the double integral can be written as

∫∫∫∫∫∫

dydxyxdydxyxdAyx

)(

),(),(),( φφφ

Calculating a double integral in the calculator is straightforward. A double

integral can be built in the Equation Writer (see example in Chapter 2). An

example follows. This double integral is calculated directly in the Equation

Writer by selecting the entire expression and using function @EVAL. The result

is 3/2. Step-by-step output is possible by setting the Step/Step option in the

CAS MODES screen.

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