Details of Mathematica Functions Understood by TILU

The Mathematica (tm) computer algebra system has a user syntax that is supposed to look like mathematics, but has some very significant differences. This page attempts to outline them. For additional examples directly from WRI, the vendor of Mathematica, visit . While you are there, you might also try out their own (so far, free) trial integration program, which uses the algorithms in Mathematica 4.0.

Function application is signified by using square brackets. That is, sin x is typed Sin[x]. Parentheses are used only for grouping, and the multiplication operation, *, is optional. Consequently, Sin(x) means the same as "Sin x" which is merely the product of Sin*x, where Sin is some constant. And when you integrate it, you get 1/2*sin*x^2. This is probably not what you wanted. If you integrate Sin[x] you'll get the expected answer.

Here is a list of the operations we now accept for integration. Their presence in this list should not be taken to assume that they appear prominently (or at all) in our current formula list.

* + - / Abs ArcCos ArcCot ArcCsc ArcSec ArcSech ArcSin ArcSinh ArcTan
ArcTanh ArcCosh ArcCoth ArcCsch BesselI BesselJ BesselK BesselY
ChebyshevT ChebyshevU Cos Cot Csc Csch EllipticE EllipticF EllipticK
Erf Erfc Exp Laguerre Legendre Log Power Sec Sech Sin Sinh Sqrt Tan Tanh

In Mathematica infix functions such as + * / -and their arguments are combined in a way that may require insertion of extra parentheses to specify precedence. The expressions a+b*c and (a+b)*c are both valid, but mean different things. These can also be written a+b c and (a+b) c since the asterisk (*) is in most cases optional.
For another example, x^2*Exp[a*x] and x^2 Exp[a x] are the same.
The expression Log[x] is the natural logarithm, the trigonometric and arctrigonometric functions are in radians. At the moment, we require that you use Exp[x] rather than E^X.
"Real Numbers" (floating-point) are not recommended. Since you can make up a name for any such constants this should not be a problem. Rational numbers like 1/2 are acceptable.
We are not prepared to do NUMERICAL integration. Our intention has been to supply a different facility, namely TABLE LOOKUP. Given the number of people trying to use Tilu for either calculus homework or elementary numerical problems, maybe we should put up a numerical integration engine too!

Additional notes for users of special functions