Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...

NDSolve[eqns, y, {x, x_min, x_max}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range ...

The Graph Utilities Package contains a number of functions useful for graph theory applications. Functions in the Graph Utilities Package. This loads the package.

DistributionFitTest[data] tests whether data is normally distributed. DistributionFitTest[data, dist] tests whether data is distributed according to dist. ...

Product[f, {i, i_max}] evaluates the product \[Product]i = 1 i_max f. Product[f, {i, i_min, i_max}] starts with i = i_min. Product[f, {i, i_min, i_max, di}] uses steps di. ...

Sum[f, {i, i_max}] evaluates the sum \[Sum]i = 1 i_max f. Sum[f, {i, i_min, i_max}] starts with i = i_min. Sum[f, {i, i_min, i_max, di}] uses steps d i. Sum[f, {i, {i_1, i_2, ...

TransformedDistribution[expr, x \[Distributed] dist] represents the transformed distribution of expr where the random variable x follows the distribution ...

"Introduction to Manipulate" and "Introduction to Dynamic" provide most of the information you need to use Mathematica's interactive features accessible through the functions ...

A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...