There are many functions that are built into Mathematica. This tutorial discusses how you can add your own simple functions to Mathematica. As a first example, consider ...

Integration functions. Here is the integral ∫_a^bx^2 dx. This gives the multiple integral ∫_0^adx ∫_0^bd y(x^2+y^2).

Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

You can use the Mathematica function DSolve to find symbolic solutions to ordinary and partial differential equations. Solving a differential equation consists essentially in ...

A typical Mathematica notebook containing text, graphics, and Mathematica expressions. The brackets on the right indicate the extent of each cell. Mathematica notebooks are ...

When you set up mathematical formulas, you often have to introduce various kinds of local objects or "dummy variables". You can treat such dummy variables using modules and ...

When you write down a set of simultaneous equations in Mathematica, you are specifying a collection of constraints between variables. When you use Solve, you are finding ...

Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

When you are putting and getting data via MathLink various kinds of errors can occur. Whenever any error occurs, MathLink goes into a completely inactive state, and all ...