When derivatives cannot be computed symbolically, "Newton's" method will be used, but with a finite difference approximation to the Jacobian. This can have costs in terms of ...

Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...

If you use your computer via a purely graphical interface, you will typically double-click the Mathematica icon to start Mathematica. If you use your computer via a textually ...

MathLink connections between Mathematica sessions. This starts up a link on port number 8000. This connects to the link on port 8000.

Nearest is used to find elements in a list that are closest to a given data point. Nearest function. Nearest works with numeric lists, tensors, or a list of strings.

In doing calculations, you will often need to use previous results that you have got. In Mathematica, % always stands for your last result. Ways to refer to your previous ...

There are many ways to use symbols in Mathematica. Here we use symbols as 'tags' for different types of objects. Working with physical units gives one simple example. When ...

When Mathematica transforms an expression such as x+x into 2x, it is treating the variable x in a purely symbolic or formal fashion. In such cases, x is a symbol which can ...

Module and With allow you to give a specific list of symbols whose names you want to treat as local. In some situations, however, you want to automatically treat certain ...

Basic vector operations. This is a vector in three dimensions. This gives a vector u in the direction opposite to v with twice the magnitude.