PDF-Version - am Institut für Baustatik

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> # These are examples of definite sums:
> sum(i, i = -2 .. 5);
12
> sum(x**i, i = 0 .. 3);
2 3
1 + x + x + x
11.3.4 Differentiation and Integration
Differentiation is performed using the diff command:
> # Take the first-order derivative of an expression w.r.t. x:
> diff(3*x^2, x);
6 x
> # Take higher-order partial derivatives by specifying a sequence
> # of variables. Derivatives are taken in the same order as the
> # variable sequence:
> diff(y * x^2 + y, x, y);
2 x
Definite and indefinite integration are performed using the int command, in the same way as described
for the sum command:
> # An example of indefinite integration:
> int( cos(x), x );
sin(x)
> # An example of definite integration:
> int( x^2, x=0..2 );
8/3
When Maple is unable to find the solution to a problem, it returns a "prettyprinted" version of the
original command expression. Sometimes this will be because Maple doesn't know how to solve the
problem, but more often it will be because either no solution exists or the original command/query was
not posed properly.
11.3.5 Series (Reihen)
Maple knows how to generate any finite number of terms of either a Taylor (Laurent) series or an
asymptotic series expansion of some expression. The Maple functions are taylor and asympt
respectively. You specify the number of terms by specifying the "order of truncation". If the terms up to
the x^(n-1) do not make the complete expression, and order term of O(x^n) is added to the end. In the
case of the Taylor series, you can specify the point of expansion for the series.
> # Compute some terms of the Taylor series for cos(z) at z=0:
> taylor(cos(z),z=0);
2 4 6
1 - 1/2 z + 1/24 z + O(z )
> # The default number of terms in the expansion is controlled by
> # the global variable Order, which is initially set to 6:
> Order := 9;
Order := 9
> taylor(cos(z),z=0);
2 4 6 8 9
1 - 1/2 z + 1/24 z - 1/720 z + 1/40320 z + O(z )
> # You can also specify the expansion order to taylor(..):
> taylor(cos(z),z=0,4);
110