Mathematica Notation for functions and numbers.

Kenneth Levasseur
Mathematical Sciences
UMass Lowell
Kenneth_Levasseur@uml.edu

Functions

If f is a function, then to evaluate f with however many arguments as is appropriate, you use the notation [Graphics:Images/mmnotes_gr_1.gif].   Even standard mathematical functions like exponentiation have this form:  [Graphics:Images/mmnotes_gr_2.gif] is [Graphics:Images/mmnotes_gr_3.gif], but x^k is also accepted.

Here are a few more  common examples

[Graphics:Images/mmnotes_gr_4.gif] [Graphics:Images/mmnotes_gr_5.gif]
[Graphics:Images/mmnotes_gr_6.gif] [Graphics:Images/mmnotes_gr_7.gif]
[Graphics:Images/mmnotes_gr_8.gif] [Graphics:Images/mmnotes_gr_9.gif]
[Graphics:Images/mmnotes_gr_10.gif] [Graphics:Images/mmnotes_gr_11.gif]
[Graphics:Images/mmnotes_gr_12.gif] [Graphics:Images/mmnotes_gr_13.gif]
[Graphics:Images/mmnotes_gr_14.gif] [Graphics:Images/mmnotes_gr_15.gif]
[Graphics:Images/mmnotes_gr_16.gif] [Graphics:Images/mmnotes_gr_17.gif]
[Graphics:Images/mmnotes_gr_18.gif] [Graphics:Images/mmnotes_gr_19.gif]
[Graphics:Images/mmnotes_gr_20.gif] [Graphics:Images/mmnotes_gr_21.gif]
[Graphics:Images/mmnotes_gr_22.gif] [Graphics:Images/mmnotes_gr_23.gif]

Numbers

Within Mathematica, traditional symbols such as π and e can entered, but webMathematica input is usually plain text:

Also,  [Graphics:Images/mmnotes_gr_27.gif] = Sqrt[a]    and  [Graphics:Images/mmnotes_gr_28.gif]

Numbers can be exact or approximate.   Approximate numbers are generally characterized by the presence of a decimal point.   The number 1/3 is exact and the product [Graphics:Images/mmnotes_gr_29.gif]  will be exactly 1, while 3.0 [Graphics:Images/mmnotes_gr_30.gif] will only be as close to 1.0 as machine precision will allow.  Working with exact numbers has the advantage of producing exact numbers, but the down side is that working with exact numbers is often much slower.  In large problems, error propagation can be a problem using approximate numbers.

Even complex numbers can be either exact or approximate:
    3/5 +  4/5  I    and  Cos[Pi/9] + Sin[Pi/9] I
both happen to be exact numbers with modulus 1, but    0.5 + Sqrt[3.0]/3 I is approximate.


Converted by Mathematica      November 28, 2001