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328 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 u 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. Specifically, returns a vector whose first element is
u(x)*v(x) and whose second element is v(x)*u'(x). 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(f(Var), u(Var), [Var], [Real1],
[Real2])
Example:
ibpu(x*ln(x), x) returns [x^2*ln(x) –x*ln(x)-x]
By Parts v 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. Specifically, returns a vector whose first element is
u(x)*v(x) and whose second element is v(x)*u'(x). 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(f(Var), v(Var), [Var], [Real1],
[Real2])
Example:
ibpdv(ln(x),x) gives [x*ln(x),-1]