With (Built-in Mathematica Symbol)

With[{x = x_0, y = y_0, ...}, expr] specifies that in expr occurrences of the symbols x, y, ... should be replaced by x_0, y_0, ....

Defining Output Formats (Mathematica Tutorial)

Just as Mathematica allows you to define how expressions should be evaluated, so also it allows you to define how expressions should be formatted for output. The basic idea ...

Introduction to Partial Differential ... (Mathematica Tutorial)

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

Inhomogeneous Linear Second-Order ... (Mathematica Tutorial)

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

Generalized Functions and Related ... (Mathematica Tutorial)

In many practical situations it is convenient to consider limits in which a fixed amount of something is concentrated into an infinitesimal region. Ordinary mathematical ...

Graphics Primitives for Text (Mathematica Tutorial)

With the Text graphics primitive, you can insert text at any position in two- or three-dimensional Mathematica graphics. Unless you explicitly specify a style or font using ...

Loops and Control Structures (Mathematica Tutorial)

The execution of a Mathematica program involves the evaluation of a sequence of Mathematica expressions. In simple programs, the expressions to be evaluated may be separated ...

Monitoring and Selecting Algorithms (Mathematica Tutorial)

Functions in Mathematica are carefully set up so that you normally do not have to know how they work inside. But particularly for numerical functions that use iterative ...

Simultaneous Equations (Mathematica Tutorial)

You can give Solve a list of simultaneous equations to solve. Solve can find explicit solutions for a large class of simultaneous polynomial equations. Here is a simple ...

Special Ways to Input Expressions (Mathematica Tutorial)

Mathematica allows you to use special notation for many common operators. For example, although internally Mathematica represents a sum of two terms as Plus[x,y], you can ...