KleinInvariantJ[\[Tau]] gives the Klein invariant modular elliptic function J(\[Tau]).

Norm[expr] gives the norm of a number, vector or matrix. Norm[expr, p] gives the p-norm.

Thread[f[args]] "threads" f over any lists that appear in args. Thread[f[args], h] threads f over any objects with head h that appear in args. Thread[f[args], h, n] threads f ...

Transpose[list] transposes the first two levels in list. Transpose[list, {n_1, n_2, ...}] transposes list so that the k\[Null]^th level in list is the n_k\[Null]^th level in ...

WorkingPrecision is an option for various numerical operations that specifies how many digits of precision should be maintained in internal computations.

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

In many kinds of numerical computations, it is convenient to introduce approximate functions. Approximate functions can be thought of as generalizations of ordinary ...

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...