
                  Kalkulator How-To (April 21, 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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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".

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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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