TI-83 Programs

Use the links on the TI-83/TI-84 page for more information about each program.

TI-86 Programs

EULERS.86p

Summary: Uses Euler's method to estimate solution curves to a first-order differential equation. Provides both graphical and numerical data.

Set Up: The expression for dy/dx must be entered in y1. Set WINDOW parameters as desired.

The program will ask you to specify the initial condition (x, y) and the step size Δx. The graph of the approximate solution curve will be displayed as it is generated. Press ENTER to pause the graph at any time. The (x, y) data points for the solution curve (first 99 pairs) are stored in lists LX (x-coordinates) and LY (y-coordinates). The program will run until x exceeds xMax.

GRADSRCH.86p

Summary: Uses the gradient search algorithm to approximate the coordinates of a relative maxima or minima for a differentiable surface f(x, y). Provides numerical data only.

Set Up: The function f(x, y) must be entered (in x and y) as y1.

The program will ask you to specify an initial guess (x, y), the step size, choose a maxima or minima search, and specify the tolerance. The program will run until the magnitude of the gradient is within the tolerance limit, at which time the final estimate of the coordinates of the relative extrema are displayed. The results are stored in four lists. The estimates of the coordinates of the extrema are in lists Ex and Ey, and the components of the gradient at each point are stored in lists Gx (i-component) and Gy (j-component). Use the stat editor to view all four lists.

INTEGRAL.86p

Summary: Calculates Riemann sums for a function over a specified interval. Numerical data only.

Set Up: The function must be entered in y1.

The program will ask you to specify the interval (a, b) and the number of subdivisions N. Select the left endpoint, right endpoint, midpoint, trapezoidal or Simpson's rule. After displaying the result, a second menu will give you the option to change the number of subintervals, to select a different method, to change the interval (a, b), or to quit. The program will continue to run until you select QUIT.

NEWTON.86p

Summary: Newton's Method program. Provides both graphical and numerical data.

Set Up: The function must be entered in y1 and the WINDOW parameters set as desired.

The program will ask you to specify the tolerance (difference between consecutive estimates). You can choose to have the program pause after each iteration; this is recommended as the program runs VERY quickly. Once the graph is displayed the calculator will be in TRACE mode. Move the cursor to the desired initial estimate, then press ENTER. The resulting iterations are shown graphically. If convergence results, press ENTER to see the last estimate. If the method diverges, press ON to stop the program. The resulting estimates are stored in list L1.

RIEMANN.86p

Summary: Calculates Riemann sums for a function over a specified interval. Provides both graphical and numerical results.

Set Up: The function must be entered in y1 and the WINDOW parameters set as desired.

The program will ask you to specify the interval (a, b) and the number of subdivisions N. Select the left endpoint, right endpoint, midpoint or trapezoidal rule. The corresponding rectangles or trapezoids will be displayed. Press enter to see the sum. After displaying the results, a second menu will give you the option to change the number of subintervals, to select a different method, or to quit. The program will continue to run until you select QUIT. If you continue to run the program, you have the option to clear the graph each time or leave the previous results up. This is great for comparing two methods or demonstrating how a larger N will provide a better "fit".

SLOPE.86p

Summary: Draws a slope field for a first-order differential equation.

Set Up: The expression for dy/dx must be entered in y1 and the WINDOW parameters set as desired.

Basically just run the program. The only tricky part can be deciding how to set up the range.

TIMESERS.86p

Summary: Time series program; graphs approximate solutions for x and y given dx/dt and dy/dt. Graphical data only.

Set Up: The expression for dx/dt must be entered in y2 and dy/dt entered in y3. Set the WINDOW parameters as desired.

The program will have you specify the initial condition (x, y) and a step size Δt. The approximate graphs for x vs t and y vs t will be drawn simultaneously. I like to compare the results of this program with those of the TRAJECT program; for example, use the results from one and have the class predict the other.

TRAJECT.86p

Summary: Computes approximate trajectory curves for a system of two first-order differential equations. Provides both graphical and numerical data.

Set Up: The expression for dx/dt must be entered in y2 and dy/dt entered in y3. Set the WINDOW parameters as desired. You may want to run the SLOPE program immediately prior to using this program.

The program will ask you to specify the initial condition (x, y) and a step size Δt. The graph of the trajectory will be drawn. You may press ENTER to pause the graph at any time. The (x, y) data points for the trajectory (first 99 pairs) are stored in lists LX (x-coordinates) and LY (y-coordinates). You must press ON to stop the program.

TI-85 Programs

For Windows users, simply download the files you want and open them with the TI-Graph Link software. For Mac users, simply download the files you want and open them with the TI-Graph Link 2 software.

CONTUR.85p

Summary: Contour graphing program; graphs level curves for a function z = f(x,y).

Set Up: The function f must be defined as y1 (in terms of x and y). Set the RANGE parameters as desired.

The program will ask you to specify the contour factor, delta z, and resolution. The contour factor determines the spacing of the level curves. For example, if this value is four, then level curves will be plotted for values of z which are a multiple of four. Delta z is a tolerance; it determines how "wide" the contour bands will be. More specifically, a point will be plotted if the z value is within delta z of a multiple of the contour factor. The resolution determines which columns of pixels to check. If the resolution is 1, then every column will be evaluated (be prepared- this can be very slow). A resolution of 2 will cause every other column of pixels to be evaluated, etc. The program is very basic and not meant to produce high quality graphs. Keep this in mind! Also, it takes a certain amount of playing with the RANGE settings and program parameters to get a decent graph.

EULER.85p

Summary: Uses Euler's method to estimate solution curves to a first-order differential equation. Provides both graphical and numerical data.

Set Up: The expression for dy/dx must be entered in y1. Set RANGE parameters as desired.

The program will ask you to specify the initial condition (x, y) and the step size Δx. The graph of the approximate solution curve will be displayed as it is generated. Press ENTER to pause the graph at any time. The (x, y) data points for the solution curve (first 99 pairs) are stored in the matrix PNTS. The first column contains the x values and the second column the y values. The program will run until x exceeds xMax.

GRADSRCH.85p

Summary: Uses the gradient search algorithm to approximate the coordinates of a relative maxima or minima for a differentiable surface f(x,y). Provides numerical data only.

Set Up: The function f(x,y) must be entered (in x and y) as y1.

The program will ask you to specify an initial guess (x,y), the step size, choose a maxima or minima search, and specify the tolerance. The program will run until the magnitude of the gradient is within the tolerance limit, at which time the final estimate of the coordinates of the relative extrema are displayed. The results are stored in four lists. The estimates of the coordinates of the extrema are in lists Ex and Ey, and the components of the gradient at each point are stored in lists Gx (i-component) and Gy (j-component). Use the stat editor to view all four lists.

INTEGRAL.85p

Summary: Calculates Riemann sums for a function over a specified interval. Numerical data only.

Set Up: The function must be entered in y1.

The program will ask you to specify the interval (a, b) and the number of subdivisions N. Select the left endpoint, right endpoint, midpoint, trapezoidal or Simpson's rule. After displaying the result, a second menu will give you the option to change the number of subintervals, to select a different method, to change the interval (a, b), or to quit. The program will continue to run until you select QUIT.

RIEMANN.85p

Summary: Calculates Riemann sums for a function over a specified interval. Provides both graphical and numerical results.

Set Up: The function must be entered in y1 and the RANGE parameters set as desired.

The program will ask you to specify the interval (a, b) and the number of subdivisions N. Select the left endpoint, right endpoint, midpoint or trapezoidal rule. The corresponding rectangles or trapezoids will be displayed. Press enter to see the sum. After displaying the results, a second menu will give you the option to change the number of subintervals, to select a different method, or to quit. The program will continue to run until you select QUIT. If you continue to run the program, you have the option to clear the graph each time or leave the previous results up. This is great for comparing two methods or demonstrating how a larger N will provide a better "fit".

SLOPE.85p

Summary: Draws a slope field for a first-order differential equation.

Set Up: The expression for dy/dx must be entered in y1 and the RANGE parameters set as desired.

Basically just run the program. The only tricky part can be deciding how to set up the range.

TABLE.85g

Summary: A table program that (roughly) simulates the table features of the TI-82.

Set Up: Define up to four functions in y1 through y4.

The program will ask you to specify one or two functions from among y1 through y4. If you only want a table for one function, select it then press TABLE. If you want a table containing two functions, select them and then the program will automatically proceed. Choose AUTO or ASK mode. ASK mode will allow you to specify the x values. Enter the number of x values you want for the table (up to six), then enter the x values themselves. The table will appear on the screen, along with some options. Select NEW X to enter some more x values, NEW y to change to a different function (or functions), or STOP to quit the program. With AUTO mode the calculator will fill in the table using equally spaced x values. The program will ask you to specify TblMin, which is the initial x value, and ΔTbl which is the Δx, or spacing between x values. The table will appear on the screen, along with some options. Select NEW T to change the TblMin and ΔTBL settings, NEW Y to change to a different function (or functions), MORE to scroll down, BACK to scroll up, or STOP to quit the program. The program will crash if a zero division occurs, so try to plan around the possibility. Also, there are two subroutines called by the program, which are TBL1 and TBL2. These must be loaded into the calculator for the main program to function, but you will never need to access them directly.

TIMESERS.85p

Summary: Time series program; graphs approximate solutions for x and y given dx/dt and dy/dt. Graphical data only.

Set Up: The expression for dx/dt must be entered in y2 and dy/dt entered in y3. Set the RANGE parameters as desired.

The program will have you specify the initial condition (x, y) and a step size Δt. The approximate graphs for x vs t and y vs t will be drawn simultaneously. I like to compare the results of this program with those of the TRAJECT program; for example, use the results from one and have the class predict the other.

TRAJECT.85p

Summary: Computes approximate trajectory curves for a system of two first-order differential equations. Provides both graphical and numerical data.

Set Up: The expression for dx/dt must be entered in y2 and dy/dt entered in y3. Set the RANGE parameters as desired. You may want to run the SLOPE program immediately prior to using this program.

The program will ask you to specify the initial condition (x, y) and a step size Δt. The graph of the trajectory will be drawn. You may press ENTER to pause the graph at any time. The (x, y) data points for the trajectory (first 99 pairs) are stored in the matrix PNTS. The first column contains the x values and the second contains the y values. You must press ON to stop the program.