Xor[e_1, e_2, ...] is the logical XOR (exclusive OR) function. It gives True if an odd number of the e_i are True, and the rest are False. It gives False if an even number of ...

ZetaZero[k] represents the k\[Null]^th zero of the Riemann zeta function on the critical line.ZetaZero[k, t] represents the k\[Null]^th zero with imaginary part greater than ...

$IterationLimit gives the maximum length of evaluation chain used in trying to evaluate any expression.

Mathematica stores preference settings and initialization data in two directories, $BaseDirectory and $UserBaseDirectory. Within each of these directories are several ...

Introduction Linear Optimization Numerical Nonlinear Local Optimization

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 ...