Gauss–Newton Methods (Mathematica Tutorial)

For minimization problems for which the objective function is a sum of squares, it is often advantageous to use the special structure of the problem. Time and effort can be ...

Special Functions (Mathematica Tutorial)

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

Plotting Search Data (Mathematica Tutorial)

The utility functions FindMinimumPlot and FindRootPlot show search data for FindMinimum and FindRoot for one- and two-dimensional functions. They work with essentially the ...

Plot the Results of NDSolve (Mathematica How To)

NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot ...

LaTeX (Mathematica Import/Export Format)

MIME type: application/x-tex LaTeX typesetting system and programming language. Commonly used for typesetting mathematical and scientific publications. Plain text format. ...

MapThread (Built-in Mathematica Symbol)

MapThread[f, {{a_1, a_2, ...}, {b_1, b_2, ...}, ...}] gives {f[a_1, b_1, ...], f[a_2, b_2, ...], ...}. MapThread[f, {expr_1, expr_2, ...}, n] applies f to the parts of the ...

Min (Built-in Mathematica Symbol)

Min[x_1, x_2, ...] yields the numerically smallest of the x_i. Min[{x_1, x_2, ...}, {y_1, ...}, ...] yields the smallest element of any of the lists.

SpokenString (Built-in Mathematica Symbol)

SpokenString[expr] gives a string of text corresponding to a spoken representation of the expression expr.

Linear Second-Order ODEs with Rational ... (Mathematica Tutorial)

The hypergeometric functions play a unifying role in mathematical analysis since many important functions, such as the Bessel functions and Legendre functions, are special ...

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 ...