Total differentiation operations. When you find the derivative of some expression f with respect to x, you are effectively finding out how fast f changes as you vary x. Often ...

DistributeDefinitions[s_1, s_2, ...] distributes all definitions for the symbols s_i to all parallel kernels.DistributeDefinitions["context"] distributes definitions for all ...

Typical command-line options for Mathematica executables. If the Mathematica front end is called with a notebook file as a command-line argument, then this notebook will be ...

The Notation Package allows you to extend Mathematica so it understands and functions correctly with new typeset notations. Typically, new notations are defined by ...

VariationalBound[f, u[x ], {x, x_min, x_max}, u_t, {a}, {b}, ...] finds values of the parameters a, b, ... of a trial function u_t that extremize the functional ...

Important points to remember in Mathematica. If you have used other computer systems before, you will probably notice some similarities and some differences. Often you will ...

"Defining Functions" discusses how you can define functions in Mathematica. In a typical case, you would type in f[x_]=x^2 to define a function f. (Actually, the definitions ...

Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient-based methods use first ...

In any interactive session, Mathematica effectively operates in a loop. It waits for your input, processes the input, prints the result, then goes back to waiting for input ...

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...