This function plotter displays some important physics functions, their first and second derivatives and their antiderivative (indefinite integral). The base function y = f(x) may contain up to three continuously variable parameters a, b, c, and one integer parameter p.
At the start of the simulation a normalized Gaussian function (normalized to a definite integral of unit value) is displayed, of variable width (a) and position (b) of its center on the x axis:
y = 1/(a√π) exp(-((x-b)/a)2)
in java- syntax:1/(a * sqrt(pi)) * exp(-((x-b)/a)^2)
Initially the Gaussian is symmetric to x = 1 With sliders a and b width and position can be varied. The end value of the antiderivative (definite integral) of the Gaussian will always be 1 (normalized Gaussian), as the value of this function goes to 0 both for large negative and positive values of x.
Exact coordinates show up at the lower left corner when a point of the curve is marked by the mouse pointer.
The calculated base function is shown in red. Check boxes at the bottom of the window allow you to calculate or hide the reciprocal function (beige) together with the bisecting line (gray) of the coordinate system, the 1. derivative (magenta), the 2. derivative (green) and the antiderivative (indefinite integral) in blue.
The interval of the independent variable x-max< x < xmax is defined in a text field, the interval of the dependent variable y-max < y < ymax in a second one. A third text field defines the initial value y0 of the antiderivative. All text fields are editable; you can input any value. When the curve of a function is not visible, its coordinates may be outside of the defined ranges, and you should adjust those accordingly.
The function formula is editable. You may change it, or formulate your own one. As the plotter does not display stored results, but calculates them anew at every change, it is good for all functions of the type y = f(x). Changes become effective after pressing the ENTER key. At every change old traces are erased and selections are reset to the base function only.
The ComboBox contains a number of preset basic functions of physics and technique. They are described in the Functions page of the Description. With selection of one of them parameters are set to appropriate values, which will appear in the number fields.
Study the effect of sliders by experimenting with the different formulas. In the predefined function slider p is used only with the Poisson distribution. When using p in your own formulas, remember that it creates integer values. In the corresponding text field the p value can be extended beyond the range of the slider.