RevolutionPlot3D (Built-in Mathematica Symbol)

RevolutionPlot3D[f_z, {t, t_min, t_max}] generates a plot of the surface of revolution with height f_z at radius t.RevolutionPlot3D[f_z, {t, t_min, t_max}, {\[Theta], ...

SphericalPlot3D (Built-in Mathematica Symbol)

SphericalPlot3D[r, \[Theta], \[Phi]] generates a 3D plot with a spherical radius r as a function of spherical coordinates \[Theta] and \[Phi].SphericalPlot3D[r, {\[Theta], ...

ParametricPlot3D (Built-in Mathematica Symbol)

ParametricPlot3D[{f_x, f_y, f_z}, {u, u_min, u_max}] produces a three-dimensional space curve parametrized by a variable u which runs from u_min to u_max. ...

Introduction to Manipulate (Mathematica Tutorial)

The single command Manipulate lets you create an astonishing range of interactive applications with just a few lines of input. Manipulate is designed to be used by anyone who ...

NDSolve (Built-in Mathematica Symbol)

NDSolve[eqns, y, {x, x_min, x_max}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range ...

SingularValueDecomposition (Built-in Mathematica Symbol)

SingularValueDecomposition[m] gives the singular value decomposition for a numerical matrix m as a list of matrices {u, w, v}, where w is a diagonal matrix and m can be ...

Linear Systems of ODEs (Mathematica Tutorial)

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

Incompatible Changes since Mathematica ... (Mathematica Tutorial)

Every new version of Mathematica contains many new features. But careful design from the outset has allowed nearly total compatibility to be maintained between all versions. ...

Delay Differential Equations (Mathematica Tutorial)

A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

Some Notes on Internal Implementation (Mathematica Tutorial)

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...