Second-Order PDEs (Mathematica Tutorial)

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

The Software Engineering of Mathematica (Mathematica Tutorial)

Mathematica is one of the more complex software systems ever constructed. It is built from several million lines of source code, written in C/C++, Java and Mathematica. The C ...

FrobeniusSolve (Built-in Mathematica Symbol)

FrobeniusSolve[{a_1, ..., a_n}, b] gives a list of all solutions of the Frobenius equation a_1 x_1 + ... + a_n x_n = b.FrobeniusSolve[{a_1, ..., a_n}, b, m] gives at most m ...

The Representation of Textual Forms (Mathematica Tutorial)

Like everything else in Mathematica the textual forms of expressions can themselves be represented as expressions. Textual forms that consist of one-dimensional sequences of ...

Efficient Representation of Many ... (Mathematica Tutorial)

Primitives which can take multiple elements. Some primitives have multi-element forms that can be processed and rendered more quickly by the Mathematica front end than the ...

The Uncertainties of Numerical ... (Mathematica Tutorial)

Mathematica does operations like numerical integration very differently from the way it does their symbolic counterparts. When you do a symbolic integral, Mathematica takes ...

Manipulating Sets of Transformation ... (Mathematica Tutorial)

You can manipulate lists of transformation rules in Mathematica just like other symbolic expressions. It is common to assign a name to a rule or set of rules. This assigns ...

Controlling the Precision of Results (Mathematica Tutorial)

In doing numerical operations like NDSolve and NMinimize, Mathematica by default uses machine numbers. But by setting the option WorkingPrecision->n you can tell it to use ...

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 ...

The Representation of Power Series (Mathematica Tutorial)

Power series are represented in Mathematica as SeriesData objects. The power series is printed out as a sum of terms, ending with O[x] raised to a power. Internally, however, ...