Linear IVPs and BVPs (Mathematica Tutorial)

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

Is the Problem Well-Posed? (Mathematica Tutorial)

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

Casoratian (Built-in Mathematica Symbol)

Casoratian[{y_1, y_2, ...}, n] gives the Casoratian determinant for the sequences y_1, y_2, ... depending on n.Casoratian[eqn, y, n] gives the Casoratian determinant for the ...

ApartSquareFree (Built-in Mathematica Symbol)

ApartSquareFree[expr] rewrites a rational expression as a sum of terms whose denominators are powers of square-free polynomials. ApartSquareFree[expr, var] treats all ...

ContourStyle (Built-in Mathematica Symbol)

ContourStyle is an option for contour plots that specifies the style in which contour lines or surfaces should be drawn.

ExpandDenominator (Built-in Mathematica Symbol)

ExpandDenominator[expr] expands out products and powers that appear as denominators in expr.

NIntegrate Integration Strategies (Mathematica Tutorial)

An integration strategy is an algorithm that attempts to compute integral estimates that satisfy user-specified precision or accuracy goals. An integration strategy normally ...

The Algorithms of Mathematica (Mathematica Tutorial)

The built-in functions of Mathematica implement a very large number of algorithms from computer science and mathematics. Some of these algorithms are fairly old, but the vast ...

InverseEllipticNomeQ (Built-in Mathematica Symbol)

InverseEllipticNomeQ[q] gives the parameter m corresponding to the nome q in an elliptic function.

IVPs with Piecewise Coefficients (Mathematica Tutorial)

The differential equations that arise in modern applications often have discontinuous coefficients. DSolve can handle a wide variety of such ODEs with piecewise coefficients. ...