Stiffness Detection (Mathematica Tutorial)

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

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 ...

Compile (Built-in Mathematica Symbol)

Compile[{x_1, x_2, ...}, expr] creates a compiled function that evaluates expr assuming numerical values of the x_i. Compile[{{x_1, t_1}, ...}, expr] assumes that x_i is of a ...

EstimatorGains (Built-in Mathematica Symbol)

EstimatorGains[ss, {p_1, p_2, ..., p_n}] gives the estimator gain matrix for the StateSpaceModel object ss, such that the poles of the estimator are p_i.

FindMaximum (Built-in Mathematica Symbol)

FindMaximum[f, x] searches for a local maximum in f, starting from an automatically selected point.FindMaximum[f, {x, x_0}] searches for a local maximum in f, starting from ...

FRatioDistribution (Built-in Mathematica Symbol)

FRatioDistribution[n, m] represents an F-ratio distribution with n numerator and m denominator degrees of freedom.

InterpolatingPolynomial (Built-in Mathematica Symbol)

InterpolatingPolynomial[{f_1, f_2, ...}, x] constructs an interpolating polynomial in x which reproduces the function values f_i at successive integer values 1, 2, ... of x. ...

Log (Built-in Mathematica Symbol)

Log[z] gives the natural logarithm of z (logarithm to base e). Log[b, z] gives the logarithm to base b.

LQEstimatorGains (Built-in Mathematica Symbol)

LQEstimatorGains[ss, {w, v}] gives the optimal estimator gain matrix for the StateSpaceModel object ss with process and measurement noise covariance matrices w and ...

MardiaKurtosisTest (Built-in Mathematica Symbol)

MardiaKurtosisTest[data] tests whether data follows a MultinormalDistribution using the Mardia kurtosis test.MardiaKurtosisTest[data, " property"] returns the value of " ...