##
Mathematics of Periodicity 1

###
Functions

**Function**: procedure which, for any set of **inputs**
in some range, assigns a corresponding **output**
####
Some Non-Periodic Functions (of 1 Variable)

*f(x) = 5*

*f(x) = x*

*f(x) = x^2* ("x squared")

####
Some Periodic Functions

- Continuous periodic functions
*sin (x)*

*cox (x)*

- Discontinuous periodic functions
- Functions with varying periods or amplitudes
*cos (x^2)*

*(cos (x)) / x*

#### Phase

**Phase**: in a periodic process, the point to which the
repeating process has advanced considered in relation to
an assumed starting point
- Phase vs. time: phase ignores absolute time because it
cares only about position within the cycle, independent of
which cycle it is and how long the period is
**Phase angle**: a measure of phase, usually in
radians (0 to 2) or a proportion of a cycle
(0 to 1)
**In phase**: describing two or more periodic processes
whose phases match; that is, the phases of maximum or minimum
amplitude are simultaneous
- Functions in phase with each other
- sin(x), .5 sin(x)

- cos(x), cos(2x)

- Functions out of phase with each other
- sin(x), cos(x)

- sin(x), sin(x+)