There are many ways to use symbols in Mathematica. Here we use symbols as 'tags' for different types of objects. Working with physical units gives one simple example. When ...

The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathematica function NDSolve, on the other hand, is a general numerical differential ...

Introduction ODE Integration Methods Partial Differential Equations

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

ContinuousWaveletTransform[{x_1, x_2, ...}] gives the continuous wavelet transform of a list of values x_i.ContinuousWaveletTransform[data, wave] gives the continuous wavelet ...

RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.

Numerical solution of differential equations. This generates a numerical solution to the equation y^′(x)y(x) with 0<x<2. The result is given in terms of an ...

For ordinary polynomials, Factor and Expand give the most important forms. For rational expressions, there are many different forms that can be useful. Different kinds of ...

Matrix representations of graphs go back a long time and are still in some areas the only way to represent graphs. Adjacency matrices represent adjacent vertices and ...

Mathematica not only has systemwide support for arbitrary Unicode characters, but also includes nearly a thousand carefully designed characters for mathematical notation and ...