Subsets[list] gives a list of all possible subsets of list. Subsets[list, n] gives all subsets containing at most n elements. Subsets[list, {n}] gives all subsets containing ...

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

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

Supporting a large number of numerical integration methods for differential equations is a lot of work. In order to cut down on maintenance and duplication of code, common ...

Most of the documentation provided for Mathematica is concerned with explaining what Mathematica does, not how it does it. But the purpose of this is to say at least a little ...

SQLCreateTable creates a new table in a database. An alternative, using raw SQL, is described in "Creating Tables with Raw SQL". If you find that the examples in this ...

There are many variants of quasi-Newton methods. In all of them, the idea is to base the matrix B_k in the quadratic model on an approximation of the Hessian matrix built up ...

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...