Simple Mathematica Expressions

Mathematica can be used to calculate variables for the fitter "on the fly" by entering Mathematica expressions into the appropriate fields in the Fit Setup screen. Here we give a brief overview of some of the more common Mathematica expressions. We assume that the dataset has two variables named voltage and temp.

**Arithmetic Expressions**
Name	Symbol	Example
Plus	+	voltage + temp
Minus	-	voltage - temp
Times	*	*voltage temp**
Divide	/	voltage / temp
Power	^, Power	voltage^2 or Power[voltage,2]
Square root	Sqrt	Sqrt[temp] or temp^0.5

In the power and square root examples above, we see an example of three general principles of Mathematica:

All built-in functions begin with an upper case letter.
Arguments to the function are enclosed in square brackets.
Multiple arguments are separated by commas.

**Common Transcendental Functions**
What	Examples
exponential function, e^temp	Exp[temp]
natural logarithm, ln(temp)	Log[temp]
logarithm to base b, log_b(temp)	Log[b, temp]
trigonometric functions (arguments in radians)	Sin[temp], Cos[temp], Tan[temp], Csc[temp], Sec[temp], Cot[temp]
sine of "theta" when theta is in degrees	Sin[theta Degree]
inverse trigonometric function, returning results in radians	ArcSin[temp], ArcCos[temp], ArcTan[temp], ArcCsc[temp], ArcSec[temp], ArcCot[temp]
inverse sine of temp in degrees	ArcSin[temp] / Degree
argument of *temp + ivoltage** where i is the square root of -1.	ArcTan[temp, voltage]
hyperbolic functions	Sinh[temp], Cosh[temp], Tanh[temp], Csch[temp], Sech[temp], Coth[temp]
inverse hyperbolic functions	ArcSinh[temp], ArcCosh[temp], ArcTanh[temp], ArcCsch[temp], ArcSech[temp], ArcCoth[temp]

**Miscellaneous**
What	Example
A pseudo-random number between 0 and 1.	Random[]
The square root of temp squared plus voltage squared. (This is not a Mathematica built-in, but is part of the Experimental Data Analyst package which is the "engine room" for the fitter.)	Quadrature[temp, voltage]

This document was written by David Harrison, October 1999.