EulerEquations (Variational Methods Package Symbol)

EulerEquations[f, u[x ], x] returns the Euler\[Dash]Lagrange differential equation obeyed by u[x] derived from the functional f, where f depends on the function u[x] and its ...

FirstIntegral (Variational Methods Package Symbol)

FirstIntegral[u] represents a first integral associated with the variable u in the output of the function FirstIntegrals.

FirstIntegrals (Variational Methods Package Symbol)

FirstIntegrals[f, x[t], t] returns a list of first integrals corresponding to the coordinate x[t] and independent variable t of the integrand f.FirstIntegrals[f, {x[t], y[t], ...

NVariationalBound (Variational Methods Package Symbol)

NVariationalBound[f, u[x ], {x, x_min, x_max}, u_t, {a, a_0}, {b, b_0}, ...] numerically searches for values of the parameters a, b, ... of a trial function u_t, starting ...

VariationalBound (Variational Methods Package Symbol)

VariationalBound[f, u[x ], {x, x_min, x_max}, u_t, {a}, {b}, ...] finds values of the parameters a, b, ... of a trial function u_t that extremize the functional ...

VariationalD (Variational Methods Package Symbol)

VariationalD[f, u[x ], x] returns the variational derivative of the integral \[Integral]f \[DifferentialD]x with respect to u[x], where the integrand f is a function of u, ...

Variational Methods (Variational Methods Package Tutorial)

The basic problem of the calculus of variations is to determine the function u(x) that extremizes a functional F=∫_SubscriptBox[x^StyleBox[min, FontSlant -> Italic], ...

Coordinate Systems (Vector Analysis Package Guide)

Vector Analysis Package (Vector Analysis Package Guide)

Frequently, physical systems exhibit special symmetries or structures that make a particular coordinate system especially useful. In a mathematically elegant solution to ...

ArcLengthFactor (Vector Analysis Package Symbol)

ArcLengthFactor[{f_1, f_2, f_3}, t] gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f_1, f_2, f_3} with respect to the ...