PROGRAMMING YOUR CALCULATOR Ref: TI-83 Guidebook – Chapter 16 § 3.2 (and later parts of Chapter 3)

In preparation for our next class meeting, you will need to add the RSUM program to your calculator. You will need this program to compute the left and right Riemann sums that are required in some of the homework problems starting in § 3.2.

The RSUM program listing (for both TI-82 and TI-83) is on the back of this handout. The program can also be copied from the calculator that is on reserve in the Mathematics Library (LeConte College, 3rd floor). If you are using another calculator, you are on your own.

INTRO to PROGRAMMING

The basic instructions for programming are the same for all programs. The actual lines of the programs will differ. The basic steps are:

1. Reset: 2nd MEM 5: Reset 2: Default 2: Reset 2. Create a program:

Select PRGM . An alphabetical list of all programs on your calculator will be displayed. Highlight NEW by pressing ◀ and ▶ . Select 1: Create New .

3. Name your program:

After Name=, type in the name (up to 8 letters) of your new program, then press ENTER . The flashing A after Name= indicates that the calculator is already in alpha mode. (This means that you will see the green character that appears above the key that is pressed.)

4. Enter your program:

Each line in the program begins with the character : . You will enter one command per line and use ENTER to move to the next line. If you need to delete a character, use DEL . If you need to insert a character, use 2nd INS . If you need to move to a different line in a program, use ▲ and ▼ . When you have finished typing in all the program lines (in the proper order), press 2nd QUIT .

5. Execute a program:

Press PRGM to enter program mode. Select the program to be executed (by number or by using ▲ and ▼) Your display will show prgm followed by the name of the program that was selected.

On this handout, any word in a program line that begins with an uppercase letter is actually a command and must be retrieved from a menu or key. For example:

X is X,T,θ,n

Y1 is VARS then Y-VARS then 1: Function then 1: Y_{1}

→ is STO⇒

Disp is PRGM then I/O then 3:Disp IS>( is PRGM then CTL then A:IS>

RSUM

Create a program named RSUM that will compute the right- and left-hand sums for the function Y_{1} on a specified interval with n subdivisions.

1. Under INTRO to PROGRAMMING , follow steps 1 – 3 .

2. Under INTRO to PROGRAMMING , follow step 4, enter the program:

: Disp "LOWER LIMIT"
: Input A
: Disp "UPPER LIMIT"
: Input B
: Disp "DIVISIONS"
: Input N
: A → X
: 0 → S
: (B-A)/N → H
: 1 → I
: Lbl P
: S+H*Y_{1} → S
: X+H → X
: IS>(I,N)
: Goto P
: Disp "LEFT SUM"
: Disp S
: B → X
: S+H*Y_{1} → S
: A → X
: S-H*Y_{1} → S
: Disp "RIGHT SUM"
: Disp S

3. To use RSUM: enter the function-to-be-evaluated under Y= as Y_{1} press 2nd QUIT to return to main screen select PRGM #: RSUM (# is the number corresponding to RSUM in the list of programs) prgmRSUM should appear on your main screen, begin execution by pressing ENTER LOWER LIMIT will appear on one line; type the lower limit (a) of the interval of integration

after the ?, then press ENTER

UPPER LIMIT will appear on the next line; type the upper limit (b) of the interval of integration after the ?, then press ENTER

DIVISIONS will appear on the next line; type the number of subintervals (n) that should be used in determining the sums after the ?, then press ENTER

Voilà! For example, you should find that the left- and right-hand sums for ∫_{1}^{3} x^{3} dx with 100 subin-

tervals are 19.7408 and 20.2608, respectively.