PartitionsP[n] gives the number p (n) of unrestricted partitions of the integer n.

PartitionsQ[n] gives the number q (n) of partitions of the integer n into distinct parts.

Refine[expr, assum] gives the form of expr that would be obtained if symbols in it were replaced by explicit numerical expressions satisfying the assumptions assum. ...

Vectors and matrices in Mathematica are simply represented by lists and by lists of lists, respectively. The representation of vectors and matrices by lists. This is a 2×2 ...

The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to ...

MatrixPower[m, n] gives the n\[Null]\[Null]^th matrix power of the matrix m. MatrixPower[m, n, v] gives the n\[Null]^th matrix power of the matrix m applied to the vector v.

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

Plot[f, {x, x_min, x_max}] generates a plot of f as a function of x from x_min to x_max. Plot[{f_1, f_2, ...}, {x, x_min, x_max}] plots several functions f_i.

[1] Butcher, J. C. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods. John Wiley and Sons, 1987. [2] Iserles, A. A First ...

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...