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Functions and commands 327
Series Returns the series expansion of an expression in the vicinity of
a given equality variable. With the optional third and fourth
arguments you can specify the order and direction of the
series expansion. If no order is specified the series returned is
fifth order. If no direction is specified, the series is
bidirectional.
series(Expr,Equal(var=limit_point),[Orde
r],[Dir(1,0,-1)])
Example:
series((x^4+x+2)/(x^2+1),x=0,5) gives 2+x-2x^2-
x^3+3x^4+x^5+x^6*order_size(x)
Summation Returns the discrete sum of Expr with respect to the variable
Var from Real1 to Real2. You can also use the summation
template in the Template menu. With only the first two
arguments, returns the discrete antiderivative of the expression
with respect to the variable.
sum(Expr,Var,Real1, Real2,[Step])
Example:
sum(n^2,n,1,5) returns 55
Differential
Curl Returns the rotational curl of a vector field. Curl([A B C], [x y
z]) is defined to be [dC/dy-dB/dz dA/dz-dC/dx dB/dx-dA/
dy].
curl([Expr1, Expr2, …, ExprN], [Var1,
Var2, …, VarN])
Example:
curl([2*x*y,x*z,y*z],[x,y,z]) returns [z-x,0,z-
2*x]
Divergence Returns the divergence of a vector field, defined by:
divergence([A,B,C],[x,y,z])=dA/dx+dB/dy+dC/dz.
divergence([Expr1, Expr2, …, ExprN],
[Var1, Var2, …, VarN])
Example:
divergence([x^2+y,x+z+y,z^3+x^2],[x,y,z])
gives 2*x+3*z^2+1