Kalkulator How-To (December 14, 1996) ===================================== ------------------------------------------------------------------------ NEW TOPICS in the 96/12/14 release: Q-17, Q-18 NEW TOPICS in the 96/11/05 release: Q-15, Q-16 NEW TOPICS in the 96/08/29 release: Q-13, Q-14 ------------------------------------------------------------------------ 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). ------------------------------------------------------------------------ Q-01: How to compute 2/3-3/7 ?? A: Using the keyboard or mouse, enter 2/3-3/7 and hit the Return key. ------------------------------------------------------------------------ Q-02: How to show the result of the previous calculation as a fraction? A: Press Alt-M [Format] and then R [Fraction]. ------------------------------------------------------------------------ Q-03: 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... ------------------------------------------------------------------------ Q-04: 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... ------------------------------------------------------------------------ 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. ------------------------------------------------------------------------ Q-05: 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... ------------------------------------------------------------------------ Q-06: 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. ------------------------------------------------------------------------ Q-07: 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. ------------------------------------------------------------------------ Q-08: 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. ------------------------------------------------------------------------ Q-09: 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. ------------------------------------------------------------------------ Q-10: 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 [Extras | Linear algebra] to bring up 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...). ------------------------------------------------------------------------ Q-11: 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). ------------------------------------------------------------------------ Q-12: 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 [Extras | Polynomial 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. ------------------------------------------------------------------------ Q-13: How to compute an integral of f(x)=x^3*exp(-x) over an interval from 0 to 8? A: First enter the function as an expression line, remembering to use t as the argument: t^3*exp(-t) Then click on [Integ] and type in the limits: 0 and 8, as well as the desired accuracy, say, 1E-9. Click on [OK]. The result will be about 5.745719... ------------------------------------------------------------------------ Q-14: The above approach would not work if the "x^3" above is changed to "x^3.2": I'm getting an error message, why? A: Integration of "t^3.2*exp(-t)" over [0,8] involves computing of 0^3.2, and this is an illegal arithmetic operation (fractional powers of zero are not defined). On the other hand, we know that the function converges to 0 at 0; therefore we may redefine it with use of a conditional function as ifz(t,0,t^3.2*exp(-t)) Type this expression in and repeat the rest of the previous procedure. The result will be 7.35919... ------------------------------------------------------------------------ Q-15: How do I convert the decimal value of -1200 to binary? A: Go to the Computer Math Panel by clicking on [Extras | Computer math] and click on the mode button (on the right, just under the display) to select Signed Decimal. Now you have to choose the word length: click on the bit length button (just below the previous one) and select 16 bits (32 would be OK too, but the number will not fit into an 8-bit word). Type in "1200" and click on the [±] button. The display should read "-1200" now. Click on the mode button again and select Binary. Done: the display should say now "11111011 01010000". ------------------------------------------------------------------------ Q-16: I'm using the Computer Math calculator to multiply 999 by 66. The result is 398. What is wrong and how do I fix it? A: Nothing is wrong. You are obviously working in the Decimal mode (signed or not) and with 16-bit words. The multiplication result, 65934, does not fit into a 16-bit word, so the program does what a computer doing 16-bit math would do: it drops the most significant part of the result. If you want this not to happen, switch to 32-bit words or, even better, use the Main Panel for "regular" (as opposed to "computer") arithmetics. ------------------------------------------------------------------------ Q-17: I would like to define tan(x/4)*(2*sin(x/2)-cos(2x)) as a function of x so that it can be easily used in my calculations. How? A: First, enter the function into the Expression Line, using t (not x!) as the argument: tan(t/4)*(2*sin(t/2)-cos(2*t)) or, using fewer parentheses and multiplication signs tan .25t*(2 sin .5t-cos 2t) Click on the [User] tab in the Function Panel at the left and then on [Define]. Select a slot from the pop-up menu, for example, 1. Type the function name, for example, "trix" into the small box asking you for it. Hit Enter. Note that one of the buttons in the User Function Page will now be marked as [trix]. Now you can use trix as a regular function in your expression; as in trix(30.27)-2*trix(15/2A)+sin(27.333) (obviously, I'm doing this in the Degree mode, but this is not necessary). ------------------------------------------------------------------------ Q-18: Now I would like to define f(x,y) = xy+2*ln(x/y). How do I do it? A: You don't. At present, Kalkulator allows for user-defined functions of just one argument (denoted as t). But if you really do not need a function, but rather just to evaluate the expression a number of times for various x and y, then you can do it: Enter the expression: XY+2 ln(X/Y) Then click on the [Browser] tab in the Variable Panel and set variables X and Y to the values you need, by clicking on [Put], selecting X or Y from the pop-up menu, entering a value and hitting Enter. When X and Y are set, just hit Enter again. The expression value will be computed. Then use [Put} again to enter other combinations of X and Y. By the way, I'm thinking about introducing two-argument user functions in one of the future releases. ------------------------------------------------------------------------ Q-99: How do I get the newest version of Kalkulator? A: Set your browser to my Web page: http://www.freeflight.com/wrotniak/software.html 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. ------------------------------------------------------------------------