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 ``` ``` ```Using &kmplot; ``` ``` ``` ```&kmplot; deals with named functions, which can be specified in ``` ```terms of Cartesian coordinates (called explicit ``` ```functions), polar coordinates or as parametric functions. To ``` ```enter a function, choose ``` ```PlotEdit ``` ```Plots... . You can also enter new functions ``` ```in the Function equation text box in the main ``` ```&kmplot; window. The text box can handle explicit and polar ``` ```functions. Each function you enter must have a unique name (&ie;, a ``` ```name that is not taken by any of the existing functions displayed in ``` ```the list box). A function name will be automatically generated if you ``` ```do not specify one. ``` ``` ``` ```For more information on &kmplot; functions, see . ``` ``` ``` ``` ``` ``` ``` ```Here is a screenshot of the &kmplot; welcome window ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` Screenshot ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Function Types ``` ``` ``` ``` ``` ```Explicit Functions ``` ```To enter an explicit function (&ie;, a function in the form y=f(x)) into &kmplot;, just enter it in the ``` ```following form: ``` ``` ``` ```f(x)=expression ``` ``` ``` ```Where: ``` ``` ``` ``` ``` ``` f is the name of the function, and can be any ``` ```string of letters and numbers you like, provided it does not start with any of ``` ```the letters x, y or r (since these are used for parametric and polar ``` ```functions). ``` ``` ``` ``` ``` ``` ``` ```x is the x-coordinate, to be used in the expression ``` ```following the equals sign. It is in fact a dummy variable, so you can use any ``` ```variable name you like, but the effect will be the same. ``` ``` ``` ``` ``` ``` ``` ```expression is the expression to be plotted, ``` ```given in appropriate syntax for &kmplot;. See . ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```As an example, to draw the graph of y=x2+2x, ``` ```enter the following into the functions dialog of &kmplot;: ``` ``` ``` ```f(x)=x^2+2x ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Parametric Functions ``` ```Parametric functions are those in which the x and y coordinates are ``` ```defined by separate functions of another variable, often called t. To enter a ``` ```parametric function in &kmplot;, follow the procedure as for an explicit ``` ```function, but prefix the name of the function describing the x-coordinate with ``` ```the letter x, and the function describing the y-coordinate with the letter ``` ```y. As with explicit functions, you may use any variable name you wish for the ``` ```parameter. To draw a parametric function, you must go to PlotNew Parametric Plot.... A function name will be created automatic if you do not specify one. ``` ```As an example, suppose you want to draw a circle, which has parametric ``` ```equations x=sin(t), y=cos(t). In the &kmplot; functions dialog, do the ``` ```following: ``` ``` ``` ```Open the parametric plot dialog with ``` ```PlotNew Parametric Plot... ``` ```. ``` ``` ``` ```Enter a name for the function, say, ``` ```circle, in the Name ``` ```box. The names of the x and y functions change to match this name: the ``` ```x function becomes xcircle(t) and the y function ``` ```becomes ycircle(t). ``` ``` ``` ``` ``` ```In the x and y boxes, enter the appropriate equations, &ie;, ``` ```xcircle(t)=sin(t) and ``` ```ycircle(t)=cos(t). ``` ``` ``` ``` ``` ```Click on OK and the function will be drawn. ``` ``` ``` ```You can set some further options for the plot in this dialog: ``` ``` ``` ``` ``` ``` ``` ```Hide ``` ``` ``` ```If this option is selected, the plot is not drawn, but &kmplot; ``` ```remembers the function definition, so you can use it to define other ``` ```functions. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Custom plot minimum-range ``` ```Custom plot maximum-range ``` ``` ``` ```If this options are selected, you can change the maximum and ``` ```minimum values of the parameter t for which the function is plotted ``` ```using the Min: and Max: ``` ```boxes. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Line width: ``` ``` ``` ```With this option you can set the width of the line drawn on the ``` ```plot area, in units of 0.1mm. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Color: ``` ``` ``` ```Click on the color box and pick a color in the dialog that ``` ```appears. The line on the plot will be drawn in this color. ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Entering Functions in Polar Coordinates ``` ``` ``` ```Polar coordinates represent a point by its distance from the origin ``` ```(usually called r), and the angle a line from the origin to the point makes ``` ```with the x-axis (usually represented by the Greek letter theta). To enter ``` ```functions in polar coordinates, use the menu entry ``` ```PlotNew Polar Plot... ``` ```. In the box labeled r, complete the ``` ```function definition, including the name of the theta variable you want ``` ```to use, ⪚, to draw the Archimedes' spiral r=theta, enter: ``` ``` ``` ``` ``` ```(theta)=theta ``` ``` ``` ``` ``` ```so that the whole line reads r(theta)=theta. Note that ``` ```you can use any name for the theta variable, so ``` ```r(foo)=foo would have produced exactly the same output. ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Combining Functions ``` ```Functions can be combined to produce new ones. Simply enter the functions ``` ```after the equals sign in an expression as if the functions were variables. For ``` ```example, if you have defined functions f(x) and g(x), you can plot the sum of f ``` ```and g with: ``` ``` ``` ``` ``` ```sum(x)=f(x)+g(x) ``` ``` ``` ``` ``` ``` ``` ```Note that you can only combine functions of the same type, ⪚ an ``` ```explicit function cannot be combined with a polar function. ``` ``` ``` ``` ``` ``` ``` ```Changing the appearance of functions ``` ``` ``` ```To change the appearance of a function's graph on the main plot ``` ```window, select the function in the Edit Plots ``` ```dialog, and click on the Edit button. In the ``` ```dialog which appears, you can change the line width in the text box, ``` ```and the color of the function's graph by clicking on the color button ``` ```at the bottom. If you are editing an explicit function, you will see a ``` ```dialog with three tabs. In the first one you specify the equation of ``` ```the function. The Derivatives tab lets you draw ``` ```the first and second derivative to the function. With the ``` ```Integral tab you can draw the integral of the ``` ```function which is calculated using Euler's method. ``` ```Another way to edit a function is to right click on the ``` ```graph. In the popup menu that appears, choose ``` ```Edit ``` ``` ``` ```For more information on the popup menu, see . ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Popup menu ``` ``` ``` ```When right-clicking on a plot function or a single-point parametric plot function a popup menu will appear. ``` ```In the menu there are five items available: ``` ``` ``` ``` ``` ``` ``` ```Hide ``` ``` ``` ``` ``` ```Hides the selected graph. Other plots of the graph's function will still be shown. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Remove ``` ``` ``` ``` ``` ```Removes the function. All its graphs will disappear. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Edit ``` ``` ``` ``` ``` ```Shows the editor dialog for the selected function. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Copy ``` ``` ``` ``` ``` ```Copies the graph to another running &kmplot; instance. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Move ``` ``` ``` ``` ``` ```Moves the graph to another running &kmplot; instance. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```For plot functions the following four items are also available: ``` ``` ``` ``` ``` ``` ``` ```Get y-Value ``` ``` ``` ``` ``` ```Opens a dialog in which you can find the y-value corresponding to ``` ```a specific x-value. The selected graph will be highlighted in the ``` ```dialog. Enter an x value in the X: box, and click ``` ```on Calculate (or press &Enter;). The corresponding y ``` ```value will be shown under Y:. ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Search for Minimum Value ``` ``` ``` ``` ``` ```Find the minimum value of the graph in a specified range. The ``` ```selected graph will be highlighted in the dialog that appears. Enter ``` ```the lower and upper boundaries of the region in which you want to ``` ```search for a minimum, and click Find. The x and ``` ```y values at the minimum will be shown. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Search for Maximum Value ``` ``` ``` ``` ``` ```This is the same as Search for Minimum ``` ```Value above, but finds maximum values instead of minima. ``` ``` ``` ``` ``` ``` ``` ``` ``` ```Calculate Integral ``` ``` ``` ``` ``` ```Select the x-values for the graph in the new dialog that appears. ``` ```Calulates the integral and draws the area between the graph and the x-axis in the ``` ```selected range in the color of the graph. ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ```