SETTING THE INITIAL VALUE FOR ODEs

Instead of typing in the initial value for a differential-equation approximate solution, as described in the differential equations topic, you can also select the coordinates using the mouse.

First, type in a dif-eq or select one from the equations combobox to modify. Choose the Set Initial Value item from the Point menu. The mouse cursor will change to a crosshair. Click the left mouse button to choose a point on the graph screen as the initial value (or use the arrow keys and press enter to choose a point). Graphmatica will insert the text representation of this choice into the currently selected equation, replacing any IV specification that it contained already. Now press enter in the equation editor or click the Graph button to graph the solution.

For second-order or higher ODEs, you can also specify the first derivative using the mouse. After you click on the IV point, Graphmatica displays a "rubber band" line from this point to the current mouse position until you click on a second point. The coordinates of the first point are then taken to be the t and x values for the, and dx/dt is initially set to the slope of the line between the two points. Thus on a square grid, drawing a line at a 45° angle yields a slope of 1. But, since the slope is calculated based on the logical coordinates of the line segment, if the grid is compressed or logarithmic along one axis, this will not always be the case. To make things easier, the slope of the current line is displayed numerically in the status bar while you move the cursor.

For systems of ODEs, this function allows you to click on 2, 3, or 4 initial value points, one for each equation in the system. Since all IVs are required to be at the same coordinate for t, after selecting the first IV you are restricted to selecting points on the vertical line defined by the t-coordinate of your first click. Graphmatica marks each IV as you select it so that you will not forget how many IVs you have placed already and how many you have left.

Be aware that, like the coordinate cursor, the accuracy of this function is limited by the resolution of your display; on the default grid, the granularity may be as much as 0.05 graphing units.

The Set Initial Value menu item is only available when Graphmatica detects that an equation with one of the differential "variables" (dX) is selected.