
                  Kalkulator How-To (May 12, 1996)
                  ================================

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NOTE: in these examples we assume you are currently in the Kalkulator
Main Panel and that the Expression line has been cleared (hit Escape to
clear it if necessary).

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Q: How to compute 2/3-3/7 ??

A: Using the keyboard or mouse, enter

      2/3-3/7
      
   and hit the Return key.
   
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Q: How to show the result of the previous calculation as a fraction?

A: Press Alt-M [Format] and then R [Fraction].

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Q: How to convert 120 watts into horsepower units?

A: Enter 120 and hit Return. Press Alt-N [Convert]. Select "Power" from
   the top selector, then "watts" from the middle one, then
   "horsepower(MKS)" from the bottom one. Click on [OK]. The result
   should be 0.16...

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Q: A box-shaped container is 2 feet 2.5 inches tall, 1 foot 2 1/3 
   inches wide and 10 3/8 inches deep. What is its volume in gallons?
   
A. Thank you for asking. First let us compute the volume in cubic feet;
   type
   
       ft(2,2.5)*ft(1,2+1/3)*ft(0,10+3/8)
       
   and hit the Enter key. The displayed result should be 2.28...
   Next, click on [Convert]. Then click on the "Convert" combo box and
   select "Volume". Click on the "From" combo and select "cu.feet",
   then on "To" and select "gallons(US)". Click on [OK]. The converted
   result will be 17.059...
      
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NOTE: if your needs are limited to simple tasks as shown above, you
may like to shrink the Kalkulator: select [Options | Panel Options]
from the menu, then select "Minimal" from the top selector and uncheck
the "Menu and Title Bar" box. This way you get a small, simple and
friendly calculator, with the more advanced features not getting into
your way. You may also choose "Basic" instead of "Minimal".

As an alternative, you may consider using Kalkulator's offspring, the
Midget. It will handle these problems just fine, is smaller and less
expensive.

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Q: How to solve an equation x+exp(x)=2 ?

A: First express the equation as f(t)=0; to do this, enter f(t) as

     t+exp t-2
     
   Next, click on [Zero]. When asked for the solution limits and
   accuracy, enter something reasonable, like 0, 100 and 1E-8 
   (or .00000001). Click on [OK]. The result should be 0.44...
   
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Q: How to compute an integral of f(x)=1/(x+4) from 0 to 2?
   
A: Enter f(t) as

     1/(t+4)
     
   into the Expression Line. Click on [Integ]. When the dialog box
   prompts you for integral limits and accuracy, enter 0, 2 and 1E-6
   (or another accuracy value), respectively. Click on [OK]. The
   result, 0.405..., will be stored in the Temporary Variable, t.
   
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Q: How to graph a function, e.g. f(x)=exp(-abs(x))*sin(1/x) for x
   between -2 and 2 ??

A: Enter the expression using t as the function argument

     exp(-abs t)*sin(1/t)
   
   and click on [Graph]. Enter -2 and 2 as x-limits. Click on [Find]
   and [Round], then on [OK].
   
   Note: this is a very unpleasant function to graph. You may want
   to increase the graph precision by selecting the [Options|Graph
   Options] menu and checking the "Fine Detail" box (do it before
   clicking on [Graph], of course). Then find any other function
   graphing program and see what job it will do. Bingo.
   
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Q: How to fit a square regression curve through a series of XY points?

A: Click on [Edit]. If necessary, click on [Mode] to set the buffer
   to the XY mode. Make sure the buffer is clear (use [Clear] if
   necessary). Type your points into the yellow box: X on the
   left, Y on the right; use arrow, Tab and Return keys as needed.
   Click on Exit. In the Main Panel click on [Regr] and select
   "2nd degree". When asked about the plot, click on [Yes]. 
   In the Graph Range dialog, click on [Find] and [Round]. Done.
   
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Q: How to compare visually a square regression curve from the example
   above with a linear regression line?
   
A: If the graph generated above is still visible, press Escape.
   Click on [Regr] and select "1st degree", but answer [No] to the
   question on drawing the line. Clear the Expression Line (press
   Escape), and enter
   
     poly t
     
   Click on [Show], then on [Add]. Enjoy.
   
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Q: How to solve a system of three linear equations:

      2*x1 -  x2             = 3
      -x1  + 1.5*x2 - 0.3*x3 = -7
             x2     - x3     = 1
                          
A: Click on [Lin] to bring the Linear Algebra Panel. Click on [Size]
   and select "3". Click on [Edit] and select "a". Enter the matrix
   so that the input grid contains:
  
      2    -1     0
     -1   1.5  -0.3
      0     1    -1
      
   and click on [OK]. Then click on [Edit] again and select "u".
   Enter the vector:
  
      3
     -7
      1
      
   and click on [OK] again.
  
   From the keyboard enter "a/u=v".
  
   To view the solution, click on [Edit] and select "v". The result
   will be (-2.64..., -8.28..., -9.28...).
  
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Q: How do I know that this is the right solution?

A: There are three ways:

   (1) Trust me. 
   
   (2) In the Linear Algebra Panel, enter "a*v=w", then use [Edit]
       and "w". The vector w should be the same as u.
       
   (3) The hard way: exit the Linear Algebra Panel and
       compute the following three expressions in the Main Panel:
   
          2v#1-v#2
          
          -v#1+1.5v#2-.3v#3
          
          v#2-v#3
          
       The results should be 3, -7 and 1, respectively.
       
    The recommended method is (1).
    
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Q: How to solve a cubic equation:

   2*x^3-9*x^2+x+5=0

   storing the largest real root as variable U?
   
A: First, get into the Root Panel by clicking on [Roots]. Enter the
   polynomial coefficients into the yellow data grid at the left so
   that the grid looks like
   
         5
         1
        -9
         2
         
   Click on [Solve]. The solution display at the right will show three
   real roots: t1=-0.649..., t2=4.243... and t3=0.906...
   Click the left mouse button on the largest one (t2) and select U
   from the pop-up menu.
   
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Q: How do I get the newest version of Kalkulator?

A: Set your browser to my Web page:

     http://www.freeflight.com/wrotniak/
     
   This Web page contains both 16- and 32-bit versions of Kalkulator.
   They are virtually identical, except that the 32-bit one is somewhat
   faster under Windows 95.

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