Works Calculations with MathLib 3.02Document Date: 25 February 1999Welcome to a wonderful improvement upon Apple's Works Calculations for the Newton.  This was made possible by combining Prism Research's MathLib and Apple's Works Calculations.  The power of MathLib that was once reserved for people with programming skills can now be accessed with the simple user interface that could only come from Apple.  There has been added abilities that each one separately could not achieve.  Works Calculations with MathLib has the following special abilities:Handles complex numbers.Handles fractions.Handles Boolean logic.Symbolic Derivatives of ANYTHING.Symbolic Integration of many things.Numerical Calculus of the leftovers.Solve any transcendental equation.Minimize any function.Maximize any function.Fit any polynomial to data.Convert to and from any base.Works Calculations is now every engineer's dream calculator.  Every student of math, science, or engineering would be thrilled at owning this portable powerhouse.  Beam homework pages to your classmates.  Beam them to your colleagues for immediate collaboration.  Teachers can beam homework to their students.System Requirements:If Works Calculations can run, then the MathLib additions can run.MessagePad 2x00eMate 300Newton OS 2.1MathLib can be purchased from Prism Research athttp://members.aol.com/NewtsPrismNewtsPrism@aol.comPrism Research6940 N. Academy Blvd. #332Colorado Springs, Colorado 80918Make check or money order payable to Jonathan Kipling Knight for the amount of US$50.Works Calculations is an Apple product originally released with the eMate but has subsequently been "provided" on the Web in various locations.  Prism Research cannot officially provide a copy of Works Calculations but can let you know where to get one.Functions Reference.The following descriptions are of the additions to Works Calculations and is not a complete listing of functions available.  For the rest of the functions, please refer to the MathLib documentation (MathLib.nwt).List of functions that will not work for graphing:PolynomialEvalabs (including vertical bars |x|)		use fabs insteadInverseCrossGaussJordanIsSymmetricIsSkewSymmetricIsOrthogonalIsHermitianIsUnitaryIfall Boolean functionsany function that returns a complex answer in the range graphedAdditions to Works Calculations:Symbolic Derivatives:Derivatives can be entered in two ways.  The first way is similar to writing derivatives with a pen and paper. The small Greek letter delta "¶" is provided on the Newton keyboard by OPTION-d keystrokes.  An example using the natural way is "¶ sin(Ln(1/x)) {@ 2.3} /¶x" which means "the derivative with respect to x of sin(Ln(1/x)) evaluated at 2.3".  The alternative method for entering derivatives  is "Derive(sin(Ln(1/x)),2.3,x)".  The second method is provided for situation where it would be confusing when using derivatives within integrals and integrals within derivatives.  Multiple derivatives are supported by just nesting one derivative within another.If you don't wish to evaluate the derivative but just want to see what the function looks like then just exclude the {@ 2.3}.  In the above example this would show: "¶sin(Ln(1/x))/¶x -> (cos(Ln(1 / x))) * ((1 / (1 / x)) * (-1 / Square(x)))" after the evaluation tool is picked from the Tools menu.Symbolic Integration:Integrals can be entered in two ways.  The first way is similar to writing integrals with a pen and paper. The integral sign "º" is provided on the Newton keyboard by OPTION-b keystrokes.  An example using the natural way is "º sin(Ln(1/x)) {2.3É°} ¶x" which means "the integral with respect to x of sin(Ln(1/x)) evaluated from 2.3 to infinity".  The alternative method for entering integrals is "Integrate(sin(Ln(1/x)),2.3,°,x)".  The second method is provided for situation where it would be confusing when using derivatives within integrals and integrals within derivatives.  Multiple integrals are supported by just nesting one integral within another.If you don't wish to evaluate the derivative but just want to see what the function looks like then just exclude the {2.3É°}.  In the above example this would show: "ºsin(x) ¶x -> -cos(x)" after the evaluation tool is picked from the Tools menu.If the equation to be integrated is too complicated, then a numerical method is implemented instead of symbolic.Solving Equations:Any equation can be solved with this method.  Solving can be entered in two ways.  The first way is more intuitive. An example using the natural way is "Solve exp(x) = sin(Ln(1/x)) {xÅ2.3}" which means "Solve the the transcendental equation exp(x) = sin(Ln(1/x)) for x near 2.3".  The special character for "approximately" (Å) can be entered from the Newton keyboard by OPTION-x keystrokes.  The alternative method for solving is "Solve(exp(x),sin(Ln(1/x)),x,2.3)".  The second method is provided for situation where it would be confusing when using derivatives and integrals within the solve.Minimizing Functions:Any function can be minimized with this method.  Minimizing can be entered in two ways.  The first way is more intuitive. An example using the natural way is "Minimize sin(Ln(1/x)) {x:2.3É10}" which means "Minimize the function sin(Ln(1/x)) for x between 2.3 and 10".  The special character for "between", also called the ellipsis (É), can be entered from the Newton keyboard by OPTION-; keystrokes.  The alternative method for maximizing is "Minimize(sin(Ln(1/x)),x,2.3,10)".  The second method is provided for situation where it would be confusing when using derivatives and integrals within the Minimize.Maximizing Functions:Any function can be maximized with this method.  Maximizing can be entered in two ways.  The first way is more intuitive. An example using the natural way is "Maximize sin(Ln(1/x)) {x:2.3É10}" which means "Maximize the function sin(Ln(1/x)) for x between 2.3 and 10".  The special character for "between", also called the ellipsis (É), can be entered from the Newton keyboard by OPTION-; keystrokes.  The alternative method for maximizing is "Maximize(sin(Ln(1/x)),x,2.3,10)".  The second method is provided for situation where it would be confusing when using derivatives and integrals within the Maximize.Inverse:This function was provided to Works Calculations to find the inverse of a matrix.  MathLib handles inverse by simply 1/Matrix but Works Calculations handles matrices strangely.  Hence a separate function from division.abs:Abs (absolute value) was provided so that matrices can be evaluated.  Abs(M) would return a number which is the determinant of the matrix M.  Vertical bars can also be used (e.g. |M| ) for abs.  Warning:  never use abs for graphing.  If abs is used in the equation that is graphed, then the wrong graph will appear.  Use fabs(x) instead for graphing.PolynomialEval:Essentially the same as PolyNom in MathLib but has been designed to work with Works Calculations.  PolynomialEval(poly,x) will evaluate the polynomial with coefficients listed in poly, at x.Base Conversion:The ability to convert to and from any base is with the use of the prefix "0x" in front of the number.  Also needed are the two base variables, inBase and outBase.  They have a default value of 16 (hexadecimal) for inBase and 10 (decimal) for outBase.  They can be changed to any Real number greater than 1 and less than 41 - even fractional values!  Numbers to be converted can be fractional as well.  For example, type in:0xF10.00A7pick Evaluate and it returns:0xF10.00A7 -> 3856.00255Provided the default values are used, this means "Convert the hexadecimal number F10.00A7 to a decimal number, hence 3856.00255.The "0x" can be used anytime in any equation enabling algebra in other bases.Exponential notation is also supported.  For example:inBase = 40x3.20210000001e+10 -> 905.00006This is interpreted as (3.20210000001 base 4) multiplied to 4^(10 base 4) is the decimal value of 905.00006.