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

When Mathematica reads the text x^y, it interprets it as x raised to the power y. In a notebook, you can also give the two-dimensional input x^y directly. Mathematica again ...

Ways to label two-dimensional plots. Here is a plot, using the default Axes->True. Setting Frame->True generates a frame with axes, and removes tick marks from the ordinary ...

You can enable logging in two ways. The log file records messages as they occur, building up a detailed record of license activity over a period of time. Logging supports ...

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 Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...

Expressions corresponding to notebooks. Here is a simple Mathematica notebook. Here is the expression that corresponds to this notebook.

Here is one way to get multiple minima: call NMinimize multiple times with different random seeds, which will cause different optimization paths to be taken. This defines a ...

Ways to change the overall options for a notebook. This creates a notebook displayed in a 40×30 window with a thin frame. Style options for a notebook.

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.