Making Power Series Expansions (Mathematica Tutorial)

Functions for creating power series. Here is the power series expansion for exp(x) about the point x0 to order x^4. Here is the series expansion of exp(x) about the point ...

The Representation of Solution Sets (Mathematica Tutorial)

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...

Compiled Function Operation (Compiled Function Tools Tutorial)

The Mathematica compiler generates a CompiledFunction expression that contains a sequence of simple instructions for evaluating a Mathematica computation. The compiled ...

BooleanCountingFunction (Built-in Mathematica Symbol)

BooleanCountingFunction[k_max, n] represents a Boolean function of n variables that gives True if at most k_max variables are True.BooleanCountingFunction[{k}, n] represents ...

Lie Symmetry Methods for Solving ... (Mathematica Tutorial)

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

SparseArray (Built-in Mathematica Symbol)

SparseArray[{pos_1 -> val_1, pos_2 -> val_2, ...}] yields a sparse array in which values val_i appear at positions pos_i. SparseArray[{pos_1, pos_2, ...} -> {val_1, val_2, ...

Naming and Finding Files (Mathematica Tutorial)

The precise details of the naming of files differ from one computer system to another. Nevertheless, Mathematica provides some fairly general mechanisms that work on all ...

TransferFunctionModel (Built-in Mathematica Symbol)

TransferFunctionModel[m, var] represents the model of the transfer-function matrix m with complex variable var.TransferFunctionModel[{num, den}, var] specifies the numerator ...

GraphData (Built-in Mathematica Symbol)

GraphData[name] gives a graph with the specified name.GraphData[name, " property"] gives the value for the specified property for a named graph.GraphData["class"] gives a ...

DiscretePlot3D (Built-in Mathematica Symbol)

DiscretePlot3D[expr, {i, i_min, i_max}, {j, j_min, j_max}] generates a plot of the values of expr when i runs from i_min to i_max and j runs from j_min to ...