ArcSinh[z] gives the inverse hyperbolic sine sinh -1 (z) of the complex number z.

FactorSquareFreeList[poly] gives a list of square-free factors of a polynomial, together with their exponents.

LaguerreL[n, x] gives the Laguerre polynomial L_n (x). LaguerreL[n, a, x] gives the generalized Laguerre polynomial L_n^a(x).

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...

FindInstance[expr, vars] finds an instance of vars that makes the statement expr be True. FindInstance[expr, vars, dom] finds an instance over the domain dom. Common choices ...

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

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 ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Numerical algorithms for constrained nonlinear optimization can be broadly categorized into gradient-based methods and direct search methods. Gradient search methods use ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...