integrateTI82

integrateTI82 - Introduction to the TI-82 The following are...

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Unformatted text preview: Introduction to the TI-82 The following are programs for the TI—82 calculator to do numerical integration, graph slope ﬁelds, demonstrate solutions to differential equations using Euler’s method, and plot trajectories and solutions to systems of differential equations. Notes on Using the TI-82: The commands on the TI-82 are basically the same as on the TI-81, though they may be in different menus. Select ‘PRGM’ to get the program menu, move to ‘NEW’ to enter a new program. You must ﬁrst give it a name (for example, ‘RSUMS’) when prompted; to ﬁnish entering/editing a program, hit 2nd QUIT. To delete a program, press 2nd MEM and select [2:Delete]. The quantity AB represents the product of A and B. Writing Y3 : Y1Y2 deﬁnes Y3 as the product Y1 and Y2. Writing Y3 = Y1(Y2) deﬁnes Y3 as the composition of Y1 and Y2. 127 Numerical Integration Program (Tl-82) This program calculates left- and right-hand Riemann sums, and the trapezoidal, midpoint and Simp- son approximations. Since there’s not room on the calculator to label each approximation separately, we use a compressed method of displaying the results. For instance, the label LEFT/RIGHT indicates that the next two numbers are the left— and right—hand Riemann sums, respectively. Notes: 1. Select ‘PRGM’ to get the program menu, move to ‘NEW’ to enter a new program. You must ﬁrst give it a name (for example, ‘INTEGRAL’) when prompted; to ﬁnish entering/editing a program, hit 2nd QUIT. 2. The function to be integrated must be entered as Y1 (accessed by the “Y =” button). When Y1 occurs in a program, it is evaluated at the current value of X. 3. The lower limit of integration must be less than the upper limit. I S > ( means that the PRGM button must be pushed and then IS > ( selected, not that I , S, > and ( are to be entered separately. ‘Disp’ and ‘Input’ are to be found under PRGM, I/O, pushed while entering a program. 5. To run a program, select PRGM, EXEC. To stop a program while it is running, hit ON. 3 6. Test the program by evaluating / x3 doc = 20, using 100 subdivisions. You should get left— 1 and right-hand sums of 19.7408 and 202608, respectively. For the trapezoid approximation, you should get 20.0008. For the mid point approximation, you should get 199996. For Simpson’s rule, you should get exactly 20. Name: INTEGRAL :Disp “LOWER LIMIT” :Input A :Disp “UPPER LIMIT” :Input B :Disp “DIVNS” :Input N :(B — A) /N —) H :A——>X :O—>L :0—>]\I :1—>I :LblP :L+H*Y1—+L :X+.5H—)X :M+H*Y1——>I\II :X+ .5H—+X :IS>(I,N) :Goto P :Disp “LEFT/RIGHT” :Disp L :L + H * Y1 —> R :A —) X :R — H * Y1 —> R :Disp R :(L + R)/2 -—) T :Disp “TRAP/MID/SIMP” :Disp T :Disp M :(2M + T)/3 —> S :Disp 5' Where to Find The Commands Disp and Input are accessed via PRGM, I/O Enter lower limit of integration. Enter upper limit of integration. Enter number subdivisions. Stores size of one subdivision in H (Note that —) means hit STO button). Start X off at beginning of interval. Initialize L, which keeps track of left sums, to zero. Initialize M, which keeps track of midpoint sums, to zero. Initialize I, the counter for the loop. Label for top of loop. Lbl is accessed via PRGM, CTL. Increment L by Y; H, the area of one more rectangle. (Y1 is accessed via Y—VARS, or 2nd VARS.) Move X to middle of interval. Evaluate Y1 at the middle of interval and increment .M by rectangle of this height. Move X to start of next interval. I S > ( is accessed Via PRGM, CTL. This is the most difﬁcult step in the program: adds 1 to I and does the the next step if I S N (i.e., if haven’t gone through loop enought times); otherwise, skips next step. Thus, if I g N, goes back to Lbl P and loops through again. If I > N, loop is ﬁnished and goes on to print out results. Continue here if I > N, in which case the value of X is now B. Goto is accessed via PRGM, CTL. Jumps back to Lbl P if J g N. L now equals the left sum, so display it. Add on area of right—most rectangle, store in R. Reset X to A. Subtract off area of left-most rectangle. R now equals right sum, so display it. Trap approximation is average of L and R. Display trap approximation. Display midpoint approximation. Simpson is weighted average of M and T. Display Simpson’s approximation. ...
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integrateTI82 - Introduction to the TI-82 The following are...

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