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2 4
1 - 1/2 z + O(z )
There is also a series function for a more general method of series expansion. See ?series, ?taylor,
and ?asympt for more information on series-expansion facilities.
11.3.6 Limits (Grenzwerte)
Maple can compute limits of a limited (no pun intended) range of expressions. The expression in
question must be an expression in one variable, and any other symbolic unknowns must be real and
nonzero. As with integration, Maple may not be able to find the solution. In this case, the command
expression is returned in the same fashion as what happens with integration. Maple will return
"undefined" (if the limit doesn't exist) or a range (if the limit solution has a range of values).
> limit(cos(x+Pi/2)/x,x=0);
-1
> limit(sin(1/y^2),y=0);
-1 .. 1
> limit(a*cos(x+Pi)/x,x=0);
undefined
11.3.7 Solving Equations (Gleichungen lösen)
There are many Maple functions for solving systems of different kinds of equations. The simplest and
most commonly used of these is solve, which solves algebraic systems of equations:
> # Solve a single equation with one unknown and one solution:
> solve(exp(x) = 1);
0
> # Solve a single equation with a constant, an unknown, and two
solutions:
a , - a
> # An expression like "x+y" is implicitly assumed to be equal to 0:
> solve ({x + y});
{x = -y, y = y}
> # Solve a system of equations simultaneously:
> solve ( {x+2*y=3, y+1/x=1}, {x,y});
{x = -1, y = 2}, {x = 2, y = 1/2}
The function for solving differential equations is dsolve. For full details on using it, see ?dsolve. Here is
a simple example:
> deq := diff(y(x),x) + y(x) = 0;
/ d \
deq := |---- y(x)| + y(x) = 0
\ dx /
> dsolve(deq, y(x));
y(x) = _C1 exp(-x)
As the various solve functions need to specify solution constants, they generate names like "_C1",
"_C2", etc.
11.3.8 Assignment and Substitution (Zuordnung und Substitution)
The function assign is designed to take solution sets of the type produced by solve and actually
perform the variable assignments. To show this applied to a previous example:
> # x and y are mathematical variables:
> x,y;
x, y
> solset := solve({x + 2 * y = 3, y + 1/x = 1}, {x, y});
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