What’s here.

A slew of programs and functions for the TI-89, TI-92, and TI-92 Plus calculators. Everything is organized into eight folders:

(single variable calculus)calc(multivariable calculus and optimization)mv(linear algebra)lin(differential equations)de(probability)pr(Gaussian quadrature)quad(special functions)sp(general stuff)gnrlDocumentation

Each program contains a very brief description of how to use it and what it does. This can be seen by pressing Contents... (F6) in VAR-LINK. Unfortunately that only shows the first several lines, so in some cases you'll need to open the program/function in the program editor to see it all.In the Contents section below, there are links to thorough pages of examples.

Downloading and Installation

The folders can be downloaded all at once as a zipped file. There are two versions: (1) old-fashioned TI-92groupfiles with .9Xg extensions, and (2) normal folders containing functions/programs with .89f/.89p extensions, which have a few minor changes for the TI-89's smaller screen. Here are the download links:

9Xgfiles.zip 89fpfiles.zip Once you have the unzipped files on your computer, you need the TI Graph-Link cable and TI Connect Software to communicate with your calculator.

To install the .9Xg files, just drag them onto the window of the TI Device Explorer program after you've connected with your calculator. To install a folder containing .89p/.89f files, first open the folder and select all the files in it, and then drag them onto the Device Explorer window. The enclosing folder will be created automatically. (At least that works for me.)

Important: If you change the folder structure, you're going to have to do some modifications in many of the programs.

Disclaimer

These programs were not written to be particularly user friendly. In particular, there is little or no checking for bad user input. Also, many of the programs use other programs, so the folder structure needs to be left intact, unless you want to do some troubleshooting and modification.Though effort has been made to ensure the accuracy of these programs, no guarantee of accuracy is stated nor implied. No one but yourself is responsible for anything that might happen as a result of using these programs. None of these programs should be used in mission-, life-, or grade-critical applications without extensive testing, for which you alone are responsible.

LinksAsk a question of the TI-89/92 Discussion Group at TI

Ray Kremer’s ticalc.org

Brooks/Cole have made my TI-89/92 “CalcLabs” manual available as a free PDF. Enjoy.

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Contents

Single Variable Calculus

sgnchng

searches for a sign change in the values of a functionsecgraph

plots the graph of a function along with a collection of secant linestangraph

plots the graph of a function along with a collection of tangent linesderlist

computes a list of the first n derivatives of a functionnewt

finds a root of a function and displays a table of the iteratesnewtfn

root found by Newton's Method as a function of the initial guessgrphnewt

creates a graphical display of the Newton's Method iterationleftbox

creates a graphical display of the left-endpoint approximation to the area under a curverightbox

creates a graphical display of the right-endpoint approximation to the area under a curvemidbox

creates a graphical display of the midpoint approximation to the area under a curvetrapez

creates a graphical display of the trapezoidal approximation to the area under a curvesimpson

computes the Simpson's Rule approximation to the integral of a functionwincheck

a boring utility## Multivariable Calculus and Optimization

arrow

plots an arrow to represent a vector in the planeshowvecs

plots a collection of vectors in the planevpproj

computes the projection of a point in 3D onto a “viewing plane”view3d

plots a 3d parametric curve (a “space curve”)viewmore

basically the same as view3D; used inparasurfparasurf

plots a 3D parametric surfacevecfield

plots a 2D vector field (with arrowheads!)grad

computes the gradient of a function of any number of variablesdiv

computes the divergence of a vector field of any number of variablescurl

computes the curl of a 3D vector fieldlaplace

computes the Laplacian of a function of any number of variableshessian

computes the hessian matrix (2nd derivative) of a function of any number of variablesevalgrad

evaluates a vector function at a given pointevalhesnevaluates a matrix function at a given point

jacobian^{ }

computes the Jacobian matrix of a vector field (or transformation fromR^{n}toR^{n})newtstep^{ }

computes one step of Newton's Method for finding a zero of a vector field (or transformation

fromR^{n}toR^{n})qapprox^{ }

computes the quadratic approximation to a function of any number of variables at a given pointwincheck^{ }## Linear Algebra

lufac

computes the LU factorization of a matrixlusolve

solves LUx = bcholfac^{ }

computes the Cholesky factorization LL^{T}of a symmetric, positive definite matrixcholsol^{ }

solves Ax = b by means of the Cholesky factorization of A, if A is symmetric and positive definitenullsp

returns a description of the null space of a matrixnullvecs

returns a basis for the null space of a matrixeignvals

computes the eigenvalues of a matrix by the least efficient method possibleeignvecBug alert!

computes the eigenvector(s) of a matrix corresponding to a particular eigenvalueqrfac

computes the QR factorization of a matrixqform

decodes the result ofqrfacto display Qqrsolve

solves Ax = b by means of the QR factorization of Agschmidt

orthogonalizes the columns of a matrix## Differential Equations

slopefld

plots the slope (direction) field of a differential equation (or pair of equations)imeuf, imeug

functions for using the Improved Euler's (a.k.a. Heun's) Method to plot approximate

solutions of a pair of differential equationsrkstep2

computes one step of 4th-order Runge-Kutta for a pair of differential equationsndsolve2

computes an array of points along an approximate solution of a pair of differential

equations (usesrkstep2)ndplot2

plots an approximate solution of a pair of differential equations (usesndsolve2)## Probability

bin,cbin

binomial and cumulative binomial probabilities, resp.poisson,cpoisson

Poisson and cumulative Poisson probabilities, resp.nrml

cumulative probabilities from the standard normal distributionnrmlpctl

percentiles of the standard normal distribution (a great application of Newton's Method!)zalpha

critical z values associated with tail areazcntrl

critical z values associated with central areatdist

cumulative probabilities from Student's t-distribution with r degrees of freedomtpctl

percentiles of Student's t-distribution with r degrees of freedomtalpha

critical t values associated with tail area in Student's t-distribution with r degrees of freedomtcntrl

critical t values associated with central area in Student's t-distribution with r degrees of freedomchi2

cumulative probabilities from the chi-square distribution with r degrees of freedomchi2pctl

percentiles of the chi-square distribution with r degrees of freedom

gauss5

five-point Gaussian quadraturegauss7

seven-point Gaussian quadraturegauss11

eleven-point Gaussian quadraturecmpgauss

composite Gaussian quadrature based ongauss11## A Few Special Functions

dblfac

“double factorial” n(n-2)(n-4) ... (2 or 1)gamma

the Gamma function. Gamma(x) is defined for all reals except the negative integers.

If n is a positive integer, then Gamma(n) = (n-1)!expint1

the “exponential integral” functionbesselj

the Bessel function J_{n}(“first kind”)bessely

the Bessel function Y_{n}(“second kind”)## General

circles

draws random circles on the screenpolygon

plots a triangulated regular polygonmakelist

computes an array of points (x_{k}, f(x_{k})), k = 1, ..., nnestlist

computes an array of recursively defined points (x_{k+1},y_{k+1}) = (f(x_{k},y_{k}), g(x_{k},y_{k})), k = 1, .. nlistplot

creates a piecewise linear graph from an array of points as returned bymakelistornestlist

This work is dedicated to the numerical analysts at NCSU who corrupted me in grad school.