$PreRead is a global variable whose value, if set, is applied to the text or box form of every input expression before it is fed to Mathematica.

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 ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Differences[list] gives the successive differences of elements in list. Differences[list, n] gives the n\[Null]^th differences of list. Differences[list, {n_1, n_2, ...}] ...

Rectangle[{x_min, y_min}, {x_max, y_max}] is a two-dimensional graphics primitive that represents a filled rectangle, oriented parallel to the axes. Rectangle[{x_min, y_min}] ...

StandardForm[expr] prints as the standard Mathematica two-dimensional representation of expr.

Ways to construct nested lists. This generates a table corresponding to a 2×3 nested list. This generates an array corresponding to the same nested list.

ForAll[x, expr] represents the statement that expr is True for all values of x. ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond. ...

Function[body] or body & is a pure function. The formal parameters are # (or #1), #2, etc. Function[x, body] is a pure function with a single formal parameter x. ...

Labeled[expr, lbl] displays expr labeled with lbl. Labeled[expr, lbl, pos] places lbl at a position specified by pos. Labeled[expr, {lbl_1, lbl_2, ...}, {pos_1, ...}] places ...