# Fall 2002

Instructor:

John Albert
Office: PHSC 1004, Ext. 5-3782.
Office hours: Mon 10:30 - 11:30 AM; Wed and Thurs, 2:30-3:30 PM (or by appointment)
E-mail: jalbert@ou.edu

## Assignment 1 (due Thurs. Sept. 5)

• section 3.1: #1, 4
• section 3.2: #1, 8, 19 (take k=2 in #19). Note: problem 2 is no longer on the assignment.

## Assignment 2 (due Tues. Sept. 17)

• section 6.1: #1(a,b,c,d), 9, 13, 22

## Assignment 3 (due Thurs. Sept. 26)

• section 3.1 #1 (Redo using bisection method, using calculator only for arithmetic operations.)
• section 6.2: #4, 23, 24

## Assignment 4 (due Tues. Oct. 1)

• section 6.3: #1, 2

## Assignment 5 (due Tues. Oct. 8)

• section 7.1: #6, 7, 15, 17 (For problems #6 and #7, you do not need to derive the formulas; just compute the error terms. For problem #17, find the constants A, B, C, D so that the approximation formula has an error term of O(h^2).)

## Assignment 6 (due Tues. Oct. 21)

• section 7.2: #1, 10, 13

## Assignment 7 (due Tues. Oct. 28)

• section 7.3: #3, 4 (the third problem is removed from this assignment)

## Assignment 8 (due Tues. Nov. 12)

• section 7.4: #4, 7

## Assignment 9 (due Tues. Dec. 3)

• section 8.3: #3, 6, 7

## Assignment 10 (due Tues. Dec. 10)

• section 8.5: #1

## Programs for the TI-85

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
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.
```