When you set up mathematical formulas, you often have to introduce various kinds of local objects or "dummy variables". You can treat such dummy variables using modules and ...

IntegerPartitions[n] gives a list of all possible ways to partition the integer n into smaller integers. IntegerPartitions[n, k] gives partitions into at most k integers. ...

Just as the equation x^2+3x==2 asserts that x^2+3x is equal to 2, so also the inequality x^2+3x>2 asserts that x^2+3x is greater than 2. In Mathematica, Reduce works not only ...

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...

StateResponse[ss, u, t] gives the state response of the StateSpaceModel object ss to the input u as a function of time t.StateResponse[ss, u, {t, t_min, t_max}] gives the ...

Integers represents the domain of integers, as in x \[Element] Integers.

f' represents the derivative of a function f of one argument. Derivative[n_1, n_2, ...][f] is the general form, representing a function obtained from f by differentiating n_1 ...

One of the important features of Mathematica is its ability to give you exact, symbolic, results for computations. There are, however, computations where it is just ...

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

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...