4.2 DIFERENTIATION Press to brings the next menu: Function Data Help unction Using this option the user can differentiate analytic functions. The function should be written using Lotus rules (built-in Lotus functions begin with the "@"character like @SIN(X) or the "+" or "-" sign). Press to brings the next screen: ____________________________________________________________________________ A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== EV 1 @cos(var)-var 2 3 4 5 6 7 8 Input or edit the function as a FORMULA and press ENTER .... 9 10 11 12 13 14 ____________________________________________________________________________ The program is now in the Lotus EDIT mode, edit or type a function and than press the ENTER key or just press the ENTER key for no changes. When you are finished editing press ENTER to return to the previous menu. **** WARNING **** Since the program is in the EDIT mode the Lotus keys are operative, however the user is strongly advised to use ONLY the UP, PGUP, DOWN and PGDN keys to scroll between the lines, the program doesn't allow scrolling to the sides by hiding all the columns except the current column. Trying to unhide the columns MAY destroy the program code. For example: if by mistake you have pressed the "/" key press ESC to get back to the READY mode and then press F2 to enter EDIT mode or just continue to type or press ENTER to exit. Type the formula [ @cos(var)-var ] and press ENTER to get the next menu: 1st order 2nd order 3rd order Graph Help The user can have: - 1st order differentiation which uses the formula dy/dx=(Y1-Y0)/h, and works with unevenly spaced data too - 2nd order differentiation which uses the formula dy2/dx2=(Y2-2*Y1+Y0)/h^2 and works only with evenly spaced data - 3rd order differentiation which uses the formula dy3/dx3=(Y3-3*Y2+3*Y1-Y0)/h^3 and works only with evenly spaced data Choosing one of the differentiation order bring the next three prompts Input the lower limit - 0 Input the upper limit - 14 Input the number of steps - 200 For each prompt type the appropriate number and press ENTER. The results for the 1st order differentiation and these inputs are: ____________________________________________________________________________ 1st order 2nd order 3rd order Graph Help Uses the formula dy/dx=(Y1-Y0)/h, works with unevenly spaced data A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1 0 -1.0349857107 -1.0349857107 2 0.9275510003 0.07 -1.104785772 -1.104785772 3 0.8502159962 0.14 -1.1740725927 -1.1740725927 4 0.7680309147 0.21 -1.2425068059 -1.2425068059 5 0.6810554383 0.28 -1.3097532209 -1.3097532209 6 0.5893727128 0.35 -1.3754824648 -1.3754824648 7 0.4930889403 0.42 -1.4393725957 -1.4393725957 8 0.3923328586 0.49 -1.50111068 -1.50111068 9 0.287255111 0.56 -1.5603943243 -1.5603943243 10 0.1780275083 0.63 -1.6169331575 -1.6169331575 11 0.0648421873 0.7 -1.6704502525 -1.6704502525 12 -0.0520893304 0.77 -1.7206834824 -1.7206834824 13 -0.1725371742 0.84 -1.767386805 -1.767386805 14 -0.2962542505 0.91 -1.8103314675 -1.8103314675 ____________________________________________________________________________ Press raph to get the next screen: ____________________________________________________________________________ Before After Data_save Graph_save Help The function before integration [ESC] - Previous menu A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1 0 -1.0349857107 -1.0349857107 2 0.9275510003 0.07 -1.104785772 -1.104785772 3 0.8502159962 0.14 -1.1740725927 -1.1740725927 4 0.7680309147 0.21 -1.2425068059 -1.2425068059 5 0.6810554383 0.28 -1.3097532209 -1.3097532209 6 0.5893727128 0.35 -1.3754824648 -1.3754824648 7 0.4930889403 0.42 -1.4393725957 -1.4393725957 8 0.3923328586 0.49 -1.50111068 -1.50111068 9 0.287255111 0.56 -1.5603943243 -1.5603943243 10 0.1780275083 0.63 -1.6169331575 -1.6169331575 11 0.0648421873 0.7 -1.6704502525 -1.6704502525 12 -0.0520893304 0.77 -1.7206834824 -1.7206834824 13 -0.1725371742 0.84 -1.767386805 -1.767386805 14 -0.2962542505 0.91 -1.8103314675 -1.8103314675 ____________________________________________________________________________ efore - View the original graph fter - View the graph after integration ata_save - Save the data table to a disk a a text (ASCII) file for later use raph_save - Creates a .PIC file of the last displayed graph The column EV includes the function values Y = @cos(var)-var The column EW includes the independent variable (var) The column EY includes the differentiated function values. To see the function before differentiation print the file DIFFBEFO.PIC using Lotus PRINTGRAPH. To see the function after differentiation print the file DIFFAFT.PIC. ata Using this option the user can integrate a function given as a data table. The table should be arranged as two columns of numbers as a text (ASCII) file. The 1st column is F(X) and the 2nd column is X. Press to see the next prompt: input file name - ISRA7.PRN The next screen appears: 1st order 2nd order 3rd order Graph Help ____________________________________________________________________________ A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1200 1195 2 1201 1195.14 3 1201 1195.28 4 1201.5 1195.42 5 1200 1195.56 6 1201 1195.7 7 1201 1195.84 8 1201.5 1195.98 9 1199 1196.12 10 1198 1196.26 11 1197 1196.4 12 1197.5 1196.54 13 1200 1196.68 14 1201 1196.82 ____________________________________________________________________________ Press <1> to create the next screen: ____________________________________________________________________________ 1st order 2nd order 3rd order Graph Help Uses the formula dy/dx=(Y1-Y0)/h, works with unevenly spaced data A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 0.00 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1200 1195 7.1428571429 7.1428571429 2 1201 1195.14 0 0 3 1201 1195.28 3.5714285714 3.5714285714 4 1201.5 1195.42 -10.714285714 -10.714285714 5 1200 1195.56 7.1428571429 7.1428571429 6 1201 1195.7 0 0 7 1201 1195.84 3.5714285714 3.5714285714 8 1201.5 1195.98 -17.857142857 -17.857142857 9 1199 1196.12 -7.1428571429 -7.1428571429 10 1198 1196.26 -7.1428571429 -7.1428571429 11 1197 1196.4 3.5714285714 3.5714285714 12 1197.5 1196.54 17.857142857 17.857142857 13 1200 1196.68 7.1428571429 7.1428571429 14 1201 1196.82 0 0 ____________________________________________________________________________ Press raph to get the next menu: Before After Data_save Graph_save Help Where: efore - View the original graph fter - View the graph after integration ata_save - Save the data table to a disk as a text (ASCII) file for later use raph_save - Creates a .PIC file of the last displayed graph The column EV includes the function values Y = @cos(var)-var The column EW includes the independent variable (var) The column EY includes the integral values. To see the function before integration print the file DINTBEF.PIC using Lotus PRINTGRAPH. To see the function after integration print the file DINTAFT.PIC.