ArcTan (Built-in Mathematica Symbol)

ArcTan[z] gives the arc tangent tan -1 (z) of the complex number z. ArcTan[x, y] gives the arc tangent of y/x, taking into account which quadrant the point (x, y) is in.

Ceiling (Built-in Mathematica Symbol)

Ceiling[x] gives the smallest integer greater than or equal to x. Ceiling[x, a] gives the smallest multiple of a greater than or equal to x.

Wronskian (Built-in Mathematica Symbol)

Wronskian[{y_1, y_2, ...}, x] gives the Wronskian determinant for the functions y_1, y_2, ... depending on x.Wronskian[eqn, y, x] gives the Wronskian determinant for the ...

Nonlinear Second-Order ODEs (Mathematica Tutorial)

The general form of a nonlinear second-order ODE is For simplicity, assume that the equation can be solved for the highest-order derivative y^ ′′(x) to give There are a few ...

Polynomial Factoring & Decomposition (Mathematica Guide)

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Im (Built-in Mathematica Symbol)

Im[z] gives the imaginary part of the complex number z.

Re (Built-in Mathematica Symbol)

Re[z] gives the real part of the complex number z.

Resolve (Built-in Mathematica Symbol)

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...

GroebnerBasis (Built-in Mathematica Symbol)

GroebnerBasis[{poly_1, poly_2, ...}, {x_1, x_2, ...}] gives a list of polynomials that form a Gröbner basis for the set of polynomials poly_i. GroebnerBasis[{poly_1, poly_2, ...

Eliminate (Built-in Mathematica Symbol)

Eliminate[eqns, vars] eliminates variables between a set of simultaneous equations.