Abel Equations (Mathematica Tutorial)

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

Matrix-Based Minimization (Mathematica Guide)

ContourPlot (Built-in Mathematica Symbol)

ContourPlot[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a contour plot of f as a function of x and y. ContourPlot[f == g, {x, x_min, x_max}, {y, y_min, y_max}] plots ...

OutputResponse (Built-in Mathematica Symbol)

OutputResponse[sys, u, t] gives the output response of a TransferFunctionModel or StateSpaceModel object sys to the input u as a function of time t.OutputResponse[sys, u, {t, ...

StateResponse (Built-in Mathematica Symbol)

StateResponse[ss, u, t] gives the state response of the StateSpaceModel object ss to the input u as a function of time t.StateResponse[ss, u, {t, t_min, t_max}] gives the ...

InverseFunction (Built-in Mathematica Symbol)

InverseFunction[f] represents the inverse of the function f, defined so that InverseFunction[f][y] gives the value of x for which f[x] is equal to y. InverseFunction[f, n, ...

NRoots (Built-in Mathematica Symbol)

NRoots[lhs == rhs, var] yields a disjunction of equations which represent numerical approximations to the roots of a polynomial equation.

Symbolic Calculations (Mathematica Tutorial)

Mathematica's ability to deal with symbolic expressions, as well as numbers, allows you to use it for many kinds of mathematics. Calculus is one example. With Mathematica, ...

Decompose (Built-in Mathematica Symbol)

Decompose[poly, x] decomposes a polynomial, if possible, into a composition of simpler polynomials.

Nonlinear Second-Order ODEs (Mathematica Tutorial)

The general form of a nonlinear second-order ODE is For simplicity, assume that the equation can be solved for the highest-order derivative y^ ′′(x) to give There are a few ...