PrivatePaths -> {opt_1 -> val_1, opt_2 -> val_2, ...} is a global option that specifies settings for paths private to the notebook front end.

ShowShortBoxForm is an option for cells that specifies whether box expressions, which are used to represent two-dimensional forms in a cell, are displayed in a more compact ...

SpellingDictionaries -> {opt_1 -> val_1, opt_2 -> val_2, ...} is a global option that specifies settings for spell checking.

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

Solving linear first-order ODEs is straightforward and only requires the use of a suitable integrating factor. In sharp contrast, there are a large number of methods ...

If you want to make use of Mathematica output in an external file such as a program or document, you will often find it useful to "splice" the output automatically into the ...

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, ...

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 ...

JacobianDeterminant[pt] gives the determinant of the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point ...

BesselI[n, z] gives the modified Bessel function of the first kind I_n (z).