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326 Functions and commands
Gradient Returns the gradient of an expression. With a list of variables
as second argument, returns the vector of partial derivatives.
grad(Expr,LstVar)
Example:
grad(2*x^2*y-x*z^3,[x,y,z]) gives [2*2*x*y-
z^3,2*x^2,-x*3*z^2]
Hessian Returns the Hessian matrix of an expression.
hessian(Expr,LstVar)
Example:
hessian(2*x^2*y-x*z,[x,y,z]) gives [[4*y,4*x,-
1],[2*2*x,0,0],[-1,0,0]]
Integral
By Parts v(x) Performs integration by parts of the expression f(x)=u(x)*v'(x)
with f(x) as the first argument and v(x) (or 0) as the second
argument. With the optional third, fourth and fifth arguments
you can specify a variable of integration and bounds of the
integration. If no variable of integration is provided, it is taken
as x.
ibpdv(Expr(f(x)),Expr(v(x)),[Var(x)],[Re
al(a)],[Real(b)])
Example:
ibpdv(ln(x),x) gives [x*ln(x),-1]
By Parts u(v) Performs integration by parts of the expression f(x)=u(x)*v'(x)
with f(x) as the first argument and u(x) (or 0) as the second
argument. With the optional third, fourth and fifth arguments
you can specify a variable of integration and bounds of the
integration. If no variable of integration is provided, it is taken
as x.
ibpu(Expr(f(x)),Expr(u(x))[,Var(x)[,[Rea
l(a),[Real(b)]])
Example:
ibpu(Expr(f(x)),Expr(u(x)),[Var(x)],[Real(a)]
,[Real(b)])