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 ...

Outer (Built-in Mathematica Symbol)

Outer[f, list_1, list_2, ...] gives the generalized outer product of the list_i, forming all possible combinations of the lowest-level elements in each of them, and feeding ...

Partition (Built-in Mathematica Symbol)

Partition[list, n] partitions list into non-overlapping sublists of length n. Partition[list, n, d] generates sublists with offset d. Partition[list, {n_1, n_2, ...}] ...

PolynomialReduce (Built-in Mathematica Symbol)

PolynomialReduce[poly, {poly_1, poly_2, ...}, {x_1, x_2, ...}] yields a list representing a reduction of poly in terms of the poly_i. The list has the form {{a_1, a_2, ...}, ...

Table (Built-in Mathematica Symbol)

Table[expr, {i_max}] generates a list of i_max copies of expr. Table[expr, {i, i_max}] generates a list of the values of expr when i runs from 1 to i_max. Table[expr, {i, ...

Developing an Import Converter (Mathematica Tutorial)

Mathematica provides functions that allow users to write their own file format converters and integrate them with the Mathematica Import and Export framework. You can ...

Nonlinear PDEs (Mathematica Tutorial)

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

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 ...

Generalized Input (Mathematica Tutorial)

The fundamental paradigm of most computer languages, including Mathematica, is that input is given and processed into output. Historically, such input has consisted of ...

Introduction to Graph Drawing (Mathematica Tutorial)

Mathematica provides functions for the aesthetic drawing of graphs. Algorithms implemented include spring embedding, spring-electrical embedding, high-dimensional embedding, ...