There are many detailed differences between different kinds of computer systems. But one of the important features of Mathematica is that it allows you to work and create ...

Partial differentiation operations. This gives ( ∂ ) / ( ∂x ) x^n. This gives the third derivative.

The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...

Mathematica's notebook interface is a very powerful typesetting system that allows you to enter formulas as they are written in mathematical literature, using two-dimensional ...

The built-in Mathematica iteration functions such as Table and Sum evaluate their arguments in a slightly special way. When evaluating an expression like Table[f,{i,i_max}], ...

A standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With Mathematica, however, you can often get exact results. ...

Mathematica usually pays no attention to whether variables like x stand for real or complex numbers. Sometimes, however, you may want to make transformations which are ...

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...