Introduction to Advanced Numerical ... (Mathematica Tutorial)

The Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...

Numerical Solution of Differential ... (Mathematica Tutorial)

The function NDSolve discussed in "Numerical Differential Equations" allows you to find numerical solutions to differential equations. NDSolve handles both single ...

Tensors (Mathematica Tutorial)

Tensors are mathematical objects that give generalizations of vectors and matrices. In Mathematica, a tensor is represented as a set of lists, nested to a certain number of ...

Tree Drawing (Mathematica Tutorial)

TreePlot lays out the vertices of a graph in a tree of successive layers, or a collection of trees. If the graph g is not a tree, TreePlot lays out its vertices on the basis ...

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 ...

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 ...

Variables and Starting Conditions (Mathematica Tutorial)

All the functions FindMinimum, FindMaximum, and FindRoot take variable specifications of the same form. The function FindFit uses the same form for its parameter ...

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 ...

LineIntegralConvolutionPlot (Built-in Mathematica Symbol)

LineIntegralConvolutionPlot[{{v_x, v_y}, image}, {x, x_min, x_max}, {y, y_min, y_max}] generates a line integral convolution plot of image convolved with the vector field ...

Algebraic Number Fields (Mathematica Tutorial)

Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...