Instructor:
Below are links to programs I wrote for the TI-85. Clicking on a link should bring up a screen with a text version of the program. You can then save the program as a file onto your computer, and use the TI GRAPH-LINK software and cable (if you have them) to convert this file into a program on your calculator.
If you have a TI-85 or TI-86, you can bring it to class and I will transfer the programs directly from my calculator to yours.
Alternatively, you can try typing the programs into your calculator by hand. If you do this, ignore the first four lines, and the last line, which start with the backslash character \. Also, you will have to figure out how to translate the text version of the program into function keys on your calculator. If you have trouble, check with me.
bisc.asc Bisection method for solving equations.
bisc2.asc Similar to bisc.asc, but prints out all iterations.
newt.asc Newton's method for solving equations.
seca.asc Secant method for solving equations.
node.asc Computes evenly spaced nodes between the values xMin and xMax, and stores the results in XLIST. Also stores the corresponding values of y1 in YLIST. (The function y1 must be defined beforehand.) Prompts for N, which is one less than the number of nodes.
cheb.asc Computes N+1 Chebyshev nodes on the interval [xMin,xMax], stores the results in XLIST, and the corresponding values of y1 in YLIST. Prompts for N.
nint.asc Computes coefficients of Newton interpolating polynomial. Requires XLIST and YLIST to have been created beforehand. Coefficients are stored in Coef.
dvdf.asc Same as nint.asc, but uses the method of divided differences to compute the coefficients.
nval.asc Evaluates Newton form of interpolating polynomial at a given value of x, which must be stored in the variable xc before the program is run. Requires coefficients of the polynomial to have been computed and stored in Coef beforehand. The value of the interpolating polynomial at x is stored in the variable AA.
trap.asc Approximates the integral of f(x) from a to b using the composite trapezoid rule. The function f(x) should be defined as y1 before running the program. The program prompts for a and b, and for the number N of subintervals into which the interval [a,b] is divided. The result is stored in val and displayed.
simp.asc Approximates the integral of f(x) from a to b using the composite Simpson's rule. Uses the same input and output variables as TRAP. Notice, however, that N must be an even number.
romb.asc Approximates the integral of f(x) from a to b using Romberg integration. Again, f(x) should be defined as y1. The program prompts for a and b, and for the number M of columns to produce in the Romberg array. The entries in the Romberg array are stored in the matrix RMAT.
csmp.asc Approximates the integral of f(x) from a to b using an adaptive, recursive Simpson's scheme. The program CSMP sets the problem up initially, prompting for a, b, epsilon (the desired accuracy) and for the maximum number of levels of recursion you want to allow (this prevents infinite recursion). The result is displayed and stored in the variable smprs. The actual recursive procedure is called ADSMP (see below).
adsmp.asc This is the recursive procedure used in CSMP (see above). The procedure is somewhat complicated by the fact that the TI-85 (as well as the TI-86) does not allow local variables or parameter passing in subroutines. If you were to program the procedure on a TI-92, or in any other programming language which does allow these features, the procedure could be written much more simply.