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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.` `` `` `` ``` ``` ``` ``` `` ``` ``` ``` ``` `` ``