One significant advantage Mathematica provides is that it can symbolically compute derivatives. This means that when you specify Method->"Newton" and the function is ...

In just one Mathematica command, you can easily specify a calculation that is far too complicated for any computer to do. For example, you could ask for ...

IntegerString[n] gives a string consisting of the decimal digits in the integer n. IntegerString[n, b] gives a string consisting of the base b digits in the integer n. ...

The standard way in which Mathematica works is to take any expression you give as input, evaluate the expression completely, and then return the result. When you are trying ...

Export["file. ext", expr] exports data to a file, converting it to the format corresponding to the file extension ext. Export[file, expr, " format"] exports data in the ...

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

RiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the continuous algebraic Riccati equation ConjugateTranspose[a].x + x.a - ...

LinearSolve[m, b] finds an x which solves the matrix equation m.x == b. LinearSolve[m] generates a LinearSolveFunction[...] which can be applied repeatedly to different b.

Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...