Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

Unicode: F520. Alias: Esc sq Esc. Prefix operator.  x is by default interpreted as Square[x]. Used in mathematical physics to denote the d'Alembertian operator. Sometimes ...

Convergents[list] gives a list of the convergents corresponding to the continued fraction terms list.Convergents[x, n] gives the first n convergents for a number ...

RootReduce[expr] attempts to reduce expr to a single Root object.

The basis for a nonlinear conjugate gradient method is to effectively apply the linear conjugate gradient method, where the residual is replaced by the gradient. A model ...

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...

MathieuC[a, q, z] gives the even Mathieu function with characteristic value a and parameter q.

MathieuS[a, q, z] gives the odd Mathieu function with characteristic value a and parameter q.

Exists[x, expr] represents the statement that there exists a value of x for which expr is True. Exists[x, cond, expr] states that there exists an x satisfying the condition ...

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.