Rule (Built-in Mathematica Symbol)

lhs -> rhs or lhs -> rhs represents a rule that transforms lhs to rhs.

Symbolic Evaluation (Mathematica Tutorial)

The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...

Check the Results of DSolve (Mathematica How To)

While DSolve usually returns the correct solution to a differential equation it is given, it is common practice to verify the solution returned by any differential equation ...

Create and Use Rules (Mathematica How To)

Transformation rules in Mathematica let you set local values for symbols, functions, and all other types of expressions. Using rules provides a powerful and extensible method ...

MapAll (Built-in Mathematica Symbol)

MapAll[f, expr] or f //@ expr applies f to every subexpression in expr.

Solve an Equation (Mathematica How To)

Mathematica has many powerful features which enable you to solve many kinds of equations.

With (Built-in Mathematica Symbol)

With[{x = x_0, y = y_0, ...}, expr] specifies that in expr occurrences of the symbols x, y, ... should be replaced by x_0, y_0, ....

Find Available Options (Mathematica How To)

The default behavior for a function in Mathematica is carefully chosen to be suitable for the vast majority of cases. Mathematica also gives you fine-grained control over the ...

Solve a Partial Differential Equation (Mathematica How To)

Mathematica 's differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms ...

DiscreteShift (Built-in Mathematica Symbol)

DiscreteShift[f, i] gives the discrete shift DiscreteShift[f(i), i] == f(i + 1). DiscreteShift[f, {i, n}] gives the multiple shift \[DiscreteShift]_i^n\ f.DiscreteShift[f, ...