DynamicModule[{x, y, ...}, expr] represents an object which maintains the same local instance of the symbols x, y, ... in the course of all evaluations of Dynamic objects in ...

VectorDensityPlot[{{v_x, v_y}, s}, {x, x_min, x_max}, {y, y_min, y_max}] generates a vector plot of the vector field {v_x, v_y} as a function of x and y, superimposed on a ...

DSolve[eqn, y, x] solves a differential equation for the function y, with independent variable x. DSolve[{eqn_1, eqn_2, ...}, {y_1, y_2, ...}, x] solves a list of ...

Texture[obj] is a graphics directive that specifies that obj should be used as a texture on faces of polygons and other filled graphics objects.

LogPlot, ListLogPlot, and related functions have been added to the built-in Mathematica kernel. PolarPlot and ListPolarPlot have been added to the built-in Mathematica ...

Animate[expr, {u, u_min, u_max}] generates an animation of expr in which u varies continuously from u_min to u_max. Animate[expr, {u, u_min, u_max, du}] takes u to vary in ...

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 ...

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

StreamDensityPlot[{{v_x, v_y}, s}, {x, x_min, x_max}, {y, y_min, y_max}] generates a stream plot of the vector field {v_x, v_y} as a function of x and y, superimposed on a ...

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...