InverseSeries[s] takes the series s, and gives a series for the inverse of the function represented by s. InverseSeries[s, x] uses the variable x in the inverse series.

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

Unicode: F431. Alias: Esc == Esc. Infix operator with built-in evaluation rules. x  y is by default interpreted as Equal[x,y] or x==y. \[Equal] is drawn longer than ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

FindArgMax[f, x] gives the position x_max of a local maximum of f.FindArgMax[f, {x, x_0}] gives the position x_max of a local maximum of f, found by a search starting from ...

ChineseRemainder[{r_1, r_2, ...}, {m_1, m_2, ...}] gives the smallest non-negative x that satisfies all the integer congruences x mod m_i = r_i mod m_i.

FindArgMin[f, x] gives the position x_min of a local minimum of f.FindArgMin[f, {x, x_0}] gives the position x_min of a local minimum of f, found by a search starting from ...

A Diophantine polynomial system is an expression constructed with polynomial equations and inequalities combined using logical connectives and quantifiers where the variables ...

DiscreteLQRegulatorGains[ss, {q, r}, \[Tau]] gives the optimal discrete-time state feedback gain matrix with sampling period \[Tau] for the continuous-time StateSpaceModel ...

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 ...