 |
Calculus programs on the TI calculator
The Department of Mathematics and Computer Science at Saint Louis University
requires graphing calculators for calculus and precalculus. As the
faculty develop interesting programs for teaching with the calculators,
they will be stored here.
The first program is designed to visually explore Riemann sums.
It is useful for teaching the concept of the definite integral and for
motivating the use of the integral to solve problems that are approximated
by taking sums. The program asks for a function and an upper and lower
bound for x. The program computes an approriate y range for the function.
The program then asks for the number of subintervals and type of sum (min,
max, midpoint, etc.) to be used. The function is drawn along with the
appropriate boxes and the sum is computed.
You can get either the
TI 82 Riemann sum program or the
TI 85 Riemann sum program.
This program
is mainly the work of
Dr. Paul Patterson with some help from
Fr Mike May, S.J.
The second program is designed to compare the various Riemann sums rules.
It is useful for useful for sections looking at numeric integration when the
student wants to see how close the Reimann sum is to the integral. The program
asks for a function, an upper and lower bound for x, and for the number of subintervals.
The program approximates the integral with the right-hand, left-hand, midpoint,
and trapezoid rules, with Simpson's rule, and with the numeric integration key
on the calculator. All 6 values are printed out on the same screen for easy comparison.
You can download either the
TI 82 Riemann sum comparison program or the
TI 85 Riemann sum comparison program.
This program is the work of
Fr. Mike May, S.J.
The third program is designed to see the effect of doubling the number of
subintervals on the Riemann sum.
It is useful for useful for sections looking at numeric integration, particularly when
dealing with convergence of the sum and the size of the error. The program
asks for a function, an upper and lower bound for x, an initial number of subintervals,
and the number of times the number of subinterval is to be doubled. It then compares
the calculator's numeric integral to the various sums achieved.
You can download the
TI 82 Riemann sum subinterval doubler program.
This program is the work of
Fr. Mike May, S.J.
The fourth program is designed to draw contours of a curve by Euler's method.
It is useful both in Calculus I and III. In the first course it gives a justification
for doing implicit differentiation. In the latter course drawing contour maps is
a standard method to visualize surfaces.
You can download the
TI 82 Contours by Euler's method program or the.
TI 85 Contours by Euler's method program .
This program is the work of
Fr. Mike May, S.J.
|
