Mathematica Tutorial

Numerical Functions

IntegerPart[x]	integer part of x
FractionalPart[x]	fractional part of x
Round[x]	integer x closest to x
Floor[x]	greatest integer x not larger than x
Ceiling[x]	least integer x not smaller than x
Rationalize[x]	rational number approximation to x
Rationalize[x,dx]	rational approximation within tolerance dx

Functions relating real numbers and integers.

x	IntegerPart[x]	FractionalPart[x]	Round[x]	Floor[x]	Ceiling[x]
2.4	2	0.4	2	2	3
2.5	2	0.5	2	2	3
2.6	2	0.6	3	2	3
-2.4	-2	-0.4	-2	-3	-2
-2.5	-2	-0.5	-2	-3	-2
-2.6	-2	-0.6	-3	-3	-2

Extracting integer and fractional parts.

IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left and right of the decimal point. Round[x] is often used for forcing numbers that are close to integers to be exactly integers. Floor[x] and Ceiling[x] often arise in working out how many elements there will be in sequences of numbers with non-integer spacings.

Sign[x]	1 for x>0, -1 for x<0
UnitStep[x]	1 for x≥0, 0 for x<0
Abs[x]	absolute value x of x
Clip[x]	x clipped to be between -1 and + 1
Rescale[x,{x_min,x_max}]	x rescaled to run from 0 to 1
Max[x₁,x₂,...] or Max[{x₁,x₂,...},...]
	the maximum of x₁, x₂, ...
Min[x₁,x₂,...] or Min[{x₁,x₂,...},...]
	the minimum of x₁, x₂, ...

Numerical functions of real variables.

x+Iy	the complex number x+iy
Re[z]	the real part Re z
Im[z]	the imaginary part Im z
Conjugate[z]	the complex conjugate z^* or
Abs[z]	the absolute value z
Arg[z]	the argument such that z=zeⁱ

Numerical functions of complex variables.