aGraph bei Google Play
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As example https://graph.tchekov.net/app/fx=sin(x:2)
Starts the application with F(x) = sin(x/2)
|Opens the settings pane.|
|Open the application settings. Scroll up/down to find the needed setting. Tap on it. According to the selection, appropriate change methode will be offered.|
|Opens the settings for 'Work with - Build from'. Here you will find additional view settings such as show derivatives, grid, calculation result etc.|
|Show current calculation results. Here you can copy calculation result for further usage.\nIt is also possible here to create detailed report for the calculations.|
|Creates and shows full function value table. This will take some time, respective progress bar is shown for this period|
|Creates and shows current html report. If the storage permission is granted the report will be also saved.|
|Opens the touch pane.|
|Move both functions together up/down|
|Move F(X) up/down|
|Move G(X) up/down|
|Set the root finding method used for the touch-and-move margin functionality.|
|Touch and move to set the lower margin with previously set root finding method|
|Touch and move to set the upper margin with previously set root finding method|
aGraph is Freeware.
aGraph is called in the following software.
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PGraph uses two approximation methods which I will try to describe. For deep-going information, please look into all good mathematics books.
This text serves only as extension for the PGraph operating instructions, other purposes arenot intended.
The so called "Wrong rule" (or Secant Method) is a procedure for determination of intersections (method for solving equations of finding roots).
We look for the x - value, that makes F(x) to 0 (intersection of F(x) and the x - Axis).
F(x) is replaced by the secant, so the formula:
supplies us an approximate value (the intersection of the secant with the x axis).
If we repeat this procedures often enough with values X1 and X3 or X2 and X3 (aGraph makes this 100 times, or until F(X1)=F(X2)) - we will become an value that is very close to the real one. The approximation is sufficient for ordinary purposes, mathematical is it however NOT correct. These procedure functions only if some basic conditions are given - for further information please look into the appropriate books.
The procedures for numeric determination of surface under function (integration) are based on the same basic principle: The surface must be divided into many strips, finding the surface or every single strip, and then sum of all strips.
The Simpson procedure uses parabola as upper delimitation of the stripes (other procedures use straight lines).
This supplies better approximate values. To define a parabola we needs at least 3 points, also Simpson Method uses double strips.
First the surface is divided at even number of stripes (PGraph - uses 100), then find the strip width h.Double stripes P0, P1, P2
Number of stripes n
Afterwards the three sums are created (Summ1 = first + last strips, Summ2 = sum of the odd strips, Summ3 = sum of the even strips).
Then the last formula is used and we receives a numeric approximate value for the surface under the function.
All further abilities of aGraph, which are based on integration, develop on the Simpson procedure.