Functions for constructing matrices. This generates a 2×2 matrix whose i,j^th entry is a[i,j]. Here is another way to produce the same matrix.

When you do symbolic calculations, it is quite easy to end up with extremely complicated expressions. Often, you will not even want to see the complete result of a ...

In doing numerical operations like NDSolve and NMinimize, Mathematica by default uses machine numbers. But by setting the option WorkingPrecision->n you can tell it to use ...

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...

Converting between numbers and lists or strings of digits. Here is the list of base 16 digits for an integer. This gives a list of digits, together with the number of digits ...

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]. ...

There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

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 ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...