4. SOLVER Using the solver in this program the user can do: o Integration of analytic functions and data tables o Differentiation of analytic functions and data tables o Regression curve fitting - 1st to 8th order Polynomial - 1 to 8 products of powers - Exponential - Multi-linear (8 variables max) o Root finding of non linear equations - Plot and search - Under relaxation - Newton's o Matrix operations and linear equations solving - Invert a matrix (up to 70x70) - Multiply two matrices (up to 70x70) - Solve a set of linear equations (up tp 70 unknown) Press to get the next menu: Integration Differentiation Curve_fit Root_find Help 4.1 INTEGRATION Press to get the next menu: Function Data Help unction Using this option the user can integrate analytic functions. The function should be written using Lotus rules (built-in Lotus functions begin with the "@" character like @SIN(X) or use the "+" or "-" signs). Press to get the next screen: ____________________________________________________________________________ A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | 5.00 | 0.00| 5 ==================================================================== EV EW EX EY EZ 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 the function press ENTER to return to the previous menu. **** WARNING **** Since the program is now 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 mget 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: Rectangle Trapezoid Romberg 1/3 Simpsom 3/8 Simpsom Graph Help Choosing one of the integration methods brings the next the 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 Rectangle method and these inputs are: ____________________________________________________________________________ Rectangle Trapezoid A_Romberg Graph Help Rectangle rule integration [ESC] - Previous menu A B C D E 1 ==================================================================== 2 Units | Output/Input | Memory | 3 ==================================================================== 4 None | -96.49 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1 0 0.07 0.07 2 0.9275510003 0.07 0.06492857 0.13492857 3 0.8502159962 0.14 0.0595151197 0.1944436898 4 0.7680309147 0.21 0.053762164 0.2482058538 5 0.6810554383 0.28 0.0476738807 0.2958797345 6 0.5893727128 0.35 0.0412560899 0.3371358244 7 0.4930889403 0.42 0.0345162258 0.3716520502 8 0.3923328586 0.49 0.0274633001 0.3991153503 9 0.287255111 0.56 0.0201078578 0.4192232081 10 0.1780275083 0.63 0.0124619256 0.4316851336 11 0.0648421873 0.7 0.0045389531 0.4362240868 12 -0.0520893304 0.77 -0.0036462531 0.4325778336 13 -0.1725371742 0.84 -0.0120776022 0.4205002314 14 -0.2962542505 0.91 -0.0207377975 0.3997624339 ____________________________________________________________________________ To see the graphs press the next screen appears: ____________________________________________________________________________ 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 | -96.49 | 0.00| 5 ==================================================================== EV EW EX EY EZ 1 1 0 0.07 0.07 2 0.9275510003 0.07 0.06492857 0.13492857 3 0.8502159962 0.14 0.0595151197 0.1944436898 4 0.7680309147 0.21 0.053762164 0.2482058538 5 0.6810554383 0.28 0.0476738807 0.2958797345 6 0.5893727128 0.35 0.0412560899 0.3371358244 7 0.4930889403 0.42 0.0345162258 0.3716520502 8 0.3923328586 0.49 0.0274633001 0.3991153503 9 0.287255111 0.56 0.0201078578 0.4192232081 10 0.1780275083 0.63 0.0124619256 0.4316851336 11 0.0648421873 0.7 0.0045389531 0.4362240868 12 -0.0520893304 0.77 -0.0036462531 0.4325778336 13 -0.1725371742 0.84 -0.0120776022 0.4205002314 14 -0.2962542505 0.91 -0.0207377975 0.3997624339 ____________________________________________________________________________ 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) values The column EY includes the integral values. To see the function before integration print the file INTBEF.PIC. using Lotus PRINTGRAPH. To see the function after integration print the file INTAFT.PIC. ata Using this option the user can integrate a function given as a data table. The table should be arranged in two columns of numbers as a text (ASCII) file. The first column is F(X) and the second column is X. Press to get the next prompt: Input file name - ISRA7.PRN The next screen appears: ____________________________________________________________________________ Rectangle Trapezoid A_Romberg Graph Help Rectangle rule 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 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 ____________________________________________________________________________ The user can choose 3 integration methods: - Rectangle - Trapezoid - Romberg IMPORTANT: The first two methods can use unevenly spaced data, the third methods MUST HAVE the data points to be evenly spaced to get accurate results. Press to get the next screen: ____________________________________________________________________________ Rectangle Trapezoid Romberg Graph Help Rectangle rule 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 1200 1195 168 168 2 1201 1195.14 168.14 336.14 3 1201 1195.28 168.14 504.28 4 1201.5 1195.42 168.21 672.49 5 1200 1195.56 168 840.49 6 1201 1195.7 168.14 1008.63 7 1201 1195.84 168.14 1176.77 8 1201.5 1195.98 168.21 1344.98 9 1199 1196.12 167.86 1512.84 10 1198 1196.26 167.72 1680.56 11 1197 1196.4 167.58 1848.14 12 1197.5 1196.54 167.65 2015.79 13 1200 1196.68 168 2183.79 14 1201 1196.82 168.14 2351.93 ____________________________________________________________________________ The number 16298.52 in output display is the integration result. Press raph to get the next menu: Before After Data_save Graph_save Help 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.