View this file in a text         ____________
editor such as OPL.             /            \
Use the small font and         /              \
turn the status window         ³/  ___  ___  \³
off.                           /  /   ³³   \  \
                               \  \_O//\\O_/  /
Use Ctrl-Menu to turn           \    /__\    /
the status window off.           ³ \      / ³
Use Shift-Psion-Z to zoom.       ³  [[[]]]  ³
                                 \   [[]]   /
                                  \___/\___/
                  ÚÄÄÄÄÄÄÄÄooooOÄÄÄÄ -OO- ÄÄÄÄOooooÄÄÄÄÄÄÄÄ¿
                  ³       GWmaths for Psion Series 3       ³
                  ³          <Version 1.0  1996>           ³
                  ³ Gareth Wild, 53 Woodhouse Lane, Norden ³
                  ³ ROCHDALE, Lancashire, England OL12 7SD ³
 <Scroll Down>    ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ  <Scroll Down>

GWmaths gives help to maths teachers and students to A-level and beyond.
It helps you check answers to simultaneous and quadratic equations as well as
scalar product, Newton-Raphson and complex number calculations. Calculation
of sides and angles of any triangle is easy using the options on the
'Triangle' menu, just enter any three pieces of information and the rest will
be calculated.

GWmaths is freeware. However, it contains the equation input routines from my
shareware application Graph3a. This means you don't have to input functions
with all the * signs in them (see Easy Equation Input section for details).
For this reason GWmaths is protected against reverse translation.
I hope you can find it useful.


These are the files that have been unzipped.
If they are not in the correct directories below you must copy them there.

File          Directory         Comments

Gwmaths10.opa  \APP\          The main program
Gwmaths.txt                   This file


Memory Information:
Gwmaths10.opa is about 11K long and uses about 11K of memory whilst running.

Installation:

1) Install the application in the usual manner by pressing Psion-I and
   selecting Gwmaths10.opa on the correct drive at the dialog.
   
2) You may find it convenient to assign a button to the GWmaths application
   so that you can jump to it quickly from other applications.
   This can be done by placing the cursor on the Graph application on the
   "Systems" screen, pressing Psion-A and then choosing an appropriate
   combination of keys (such as Control-Sheet).
   
MENUS

"Maths1" Menu

1) "Quadratic Equation": (Psion-Q)
   Input A, B and C where AXý+BX+C=0

   This function gives:
      þFactorised version of the equation
      þMin/max point
      þType of roots (real/complex and equal/distinct)
      þSolves the equation
      
2) "Scalar Product": (Psion-A)
   Input the two 3D vectors (A,B,C) [Vector 1]
                        and (D,E,F) [Vector 2]

   This function gives:
      þThe vector mutually perpendicular to Vector 1 and Vector 2
      þMagnitude of Vectors 1 and 2 (also gives this as a square root)
      þThe scalar product
      þThe angle between the two vectors in radians and degrees.

   If you want to input 2D vectors, set A and D, B and E, or C and F to zero.
   

3) "Simultaneous Equations": (Psion-S)
   Input the two equations:
                Ax + By = C
                Dx + Ey = F

   This function gives:
      þSolutions of X and Y for the given equations
   
   
4) "Remainder Theorum": (Psion-R)
   Input the equation of f(x) and a value for x:
   [See section on Easy Equation Input below for help with this]

   This function gives:
      þSolution to f(x)
      
   NB just press Enter after this when "Press Menu" message appears to
   immediately enter another value for x.
   
   
5) "Complex Numbers": (Psion-C)
   Input the two complex numbers:
                A + Bj   [Number 1]
                C + Dj   [Number 2]
                
   This function gives:
      þNumber 1 multiplied by Number 2
      þNumber 1 divided by Number 2
   
   
6) "Newton-Raphson Method": (Psion-W)
   Input the two equations f(x) and fû(x)
   (where fû(x) is the differential of f(x))
   [See section on Easy Equation Input below for help with this]
   Also input a start number

   This function gives:
      þA list of values of X that it has worked through
      þThe value of X for which f(x)=0
   
   
"Maths2" Menu

1) "Equating Functions": (Psion-T)
   Input the two equations f(x) and g(x)
   [See section on Easy Equation Input below for help with this]
   Also input a value for x

   This function gives:
      þSolutions of f(x) and g(x)
   
   NB just press Enter after this when "Press Menu" message appears to
   immediately enter another value for x.
   
   
2) "Fractions": (Psion-F)
   Input the numerator and denominator (numerator > denominator)

   This function gives:
      þThe number input as a true fraction
   
   
3) "Summation": (Psion-M)
   Input f(x) and a starting value for x
   [See section on Easy Equation Input below for help with this]

   This function gives:
      þCalculates f(x) then adds one to x
      þForms a list of f(x+K) where K is the number of key presses
      
 NB press Esc to exit this option.


4) "Integration": (Psion-I)
   Input f(x), min and max values, and the number of strips to use
   [See section on Easy Equation Input below for help with this]
   The greater the number of strips the greater the accuracy of the
   calculation but the longer it takes to calculate.

   This function gives:
      þThe arae under the graph of f(x) from Min to Max
      þAccuracy is proportional to the number of strips
      

"Triangle" Menu

Explanation:

Angles must be entered in degrees.
Angle answers are given in degrees.
The included angle is between the two sides input.
The unincluded angle is one outside the two sides input.
The included side is between the two angles input.
The unincluded side is one outside the two angles input.
[  < means angle  ]
<A is opposite side A
<B is opposite side B
<C is opposite side C

1) "3 Sides": (Psion-Y)
   Input the lengths of sides A, B and C

   This function gives:
      þ<A, <B and <C
      

2) "Included Angle, 2 Sides": (Psion-N)
   Input the lengths of sides A and B, and enter angle C (in degrees)

   This function gives:
      þ<A, <B and length of side C


3) "Unincluded angle, 2 Sides": (Psion-U)
   Input the lengths of sides A and C, and enter angle C (in degrees)

   This function gives:
      þthe are two possible values for each angle/side (<A, <B and side B)


4) "2 Angles, Included Side": (Psion-D)
   Input the length of side A, and enter angles B and C (in degrees)

   This function gives:
      þ<A and the lengths of sides B and C


5) "2 Angles, Unincluded side": (Psion-L)
   Input the length of side B, and enter angles B and C (in degrees)

   This function gives:
      þ<A and lengths of sides A and C



"Special" Menu

1) "Beep On/Off": (Psion-B)
   Turns error beep on/off.
   
2) "Version": (Psion-V)
   Displays information about the author and the version code.
   
3) "Exit": (Psion-X)
   Exits the program and save the present settings.
   Exiting can also be done from the 'System' screen, if the program is not
   busy, by pressing Delete on the highlighted GWmaths name, or by pressing
   Esc in the main body of the program (both cases require a confirmation and
   will save the present settings).


NOTE: Throughout GWmaths if you press Enter when the "Press Menu" busy
      message is flashing, the last option you used will be executed again

Easy Equation Input:

This program uses the same type of equation input as my shareware application
Graph3a.
You can type in equations with or without * and **.
Equations may be written in upper or lower case letters:
eg 2SIN(3X), 2*sin(3*x) and 2Sin(3*X) are all equivalent

Xü would be written as X3 (or X**3)
Xý would be written as X2 (or X**2)

So 3Xü+4Xý+9X+1 could be written as:   3X3+4X2+9X+1
                                    or 3*X**3+4*X**2+9*X+1
                                    
I think is easy to see which one is more simple to type and easier to read.

The syntax for functions is the same as in the calculator eg COS(X), SQR(X)
(ie you must put the expression to be executed by the function in brackets)
cosx, sin3x etcare NOT valid expressions

All trigonometrical functions are executed in radians.

GWmaths will execute equations with multiple brackets eg

(x+1)x(x-1)(x-2) ..is a valid expression
4(2x-1)2 ..........is a valid expression (ie 4(2x-1)ý)

If you put letters together and they are not interpreted as a function then
GWmaths will multiply them eg

xxx .............executed as x*x*x
ii ..............executed as i*i

If you keep getting an 'Unexpected name' error message on an equation you
really want to enter, type it in long hand ie with * and **.

NB this method uses the M9 Calc memory. Do not use M9 as a storage memory in
the Calc application if you are using GWmaths.

Legal Bit:
This program comes with no warranty of any kind.
Reverse translation of this program is prohibited.
GWmaths is protected against reverse translation.
Bug reports to the address at the start of this file.