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This program calculates a Riemann Sum for a function with two independent variables, taking the form Z = F(x,y); that is to say, it calculates the sum 2D Riemann Sum, approximating the integral Double integral. It is noteworthy in that it allows the use of expressions in the limits of the inner integral, allowing integration of non-rectangular regions; however, it is necessary to specify the order of integration. Values for each rectangular subdivision are calculated at the center of the subdivision.

Note: This program uses the calculator's 'Y0', 'Y9', and 'Y8' graphing functions in it's calculations, and will overwrite any equations previously stored there.








Using the Program:

The following example demonstrates the use of the program to give an approximate solution to the double integral Example 2D sum.

Instructions:
Screen Shot
1) Start the program. The screen depicted at right will appear. Press 'Enter'. Rmn2D Screenshot 1
2) The next screen contains instructions, as shown at right. Rmn2D Screenshot 2
3) As indicated in the equation above, Y is the inner integral. Press '2' to proceed. Rmn2D Screenshot 3
4) Enter the equation at the prompt. Rmn2D Screenshot 4
5) Specify the limit information and subdivisions for the outer integral. (Use a bit of caution here - selecting too high a subdivision count will result in an unacceptably long delay. Just how big a count is too big varies with calculator model and user mood.) Press 'Enter' after entering each value. Rmn2D Screenshot 5
6) Repeat the process for the inner integral. Press 'Enter' after entering each value. Rmn2D Screenshot 6
7) After a delay (the length of which depends on the number of subdivisions calculated), the result is displayed. Rmn2D Screenshot 7
8) Press '2' at this point to quit, and the program exits. Pressing '1' results in the next screen being presented. Rmn2D Screenshot 8
9) Press '1' here and you can enter a new function; press '2' and that step is skipped, and you are prompted for new limit and subdivision values. Rmn2D Screenshot 9

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