Simplifying with assumptions. Mathematica does not automatically simplify this, since it is only true for some values of x. Sqrt[x^2] is equal to x for x≥0, but not otherwise.

Solving equations involving power series. Here is a power series. This gives an equation involving the power series.

You can tell a lot about what "type" of expression something is by looking at its head. Thus, for example, an integer has head Integer, while a list has head List. In a ...

Testing and searching for elements of lists. "Getting Pieces of Lists" discusses how to extract pieces of lists based on their positions or indices. Mathematica also has ...

Expressions corresponding to cells. Here is a notebook containing a text cell and a Mathematica input cell. Here are the expressions corresponding to these cells.

The essence of most methods is in the local quadratic model that is used to determine the next step. The FindMinimum function in Mathematica has five essentially different ...

There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

[AN96] Adams, L. and J. L. Nazareth. (Eds.) Linear and Nonlinear Conjugate Gradient-Related Methods. SIAM, 1996. [Br02] Brent, R. P. Algorithms for Minimization without ...

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 ...