If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

NMinimize, NMaximize, Minimize, and Maximize employ global optimization algorithms, and are thus suitable when a global optimum is needed. Minimize and Maximize can find ...

Whenever Mathematica draws a three-dimensional object, it always effectively puts a cuboidal box around the object. With the default option setting Boxed->True, Mathematica ...

When you set up a graphics object in Mathematica, you give coordinates for the various graphical elements that appear. When Mathematica renders the graphics object, it has to ...

Palettes are like extensions of your keyboard. They can be used to perform many actions in Mathematica, including entering typesetting characters, styling notebooks, and ...

Finding the date and time. This gives the current date and time. The Mathematica DateList function returns whatever your computer system gives as the current date and time. ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...

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 ...

The first argument given to DSolve is the differential equation, the second argument is the unknown function, and the last argument identifies the independent variable. Here ...

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 ...