Graphing calculator help

[Sarevok]

I have recently received a TI-89 Titanium from the states as a gift. It is a very impressive device compared to the Casios I have used all my life. Currently I have two maths courses at uni, one about calculas and the other involves vectors and matrices.

The calculas one require differentiating and integrating expressions, drawing graphs of functions and inverses, finding limits etc simple stuff. But it gets tedious to do by hand with only a Casio 991MS for aid when doing assigments. Is there some way to rapidly do this with the TI or some programs available for it ?

The vectors and matrices have proved to be harder. It involves finding determinants of matrices of arbitary size, cofactors, gaussian elimination, systems of equations etc. The chapters on vectors are set in eucledean n-space. It involves finding dot product, basis, subspaces, eigenvalues etc. There is also linear transformation involving points in 2D or 3D. I found this very hard at first but I am beginning to understand now. The biggest problem has been how long some large matrix manipulation can be, Any advice on how to use the TI to do these type of problems ? It would be greatly appreciated for this course is driving me mad.

Also any general tips for using the TI ? I never used a graphing calculator before, yesterday I vainly searched for the square root button, that's how n00bish I am at the moment.

[Darth Yoshi]

IIRC, to root on a TI89, you need to input x^1/2.

Also, there should be a graph button on there somewhere, which will automatically graph whatever expression(s) you've inputted. Unfortunately, it's been a few years since I've used one, so I can't be of much more help.

[Bounty]

Square root is "2nd" (the yellow modifier button) + "x" (the x next to "9").

I'm not sure about the 89, but the 83 has a PRGM function to make simple automated programs for things like limits. Check your manual.

Graphs are green modifier button + F3.

[The Jester]

The calculas one require differentiating and integrating expressions, drawing graphs of functions and inverses, finding limits etc simple stuff. But it gets tedious to do by hand with only a Casio 991MS for aid when doing assigments. Is there some way to rapidly do this with the TI or some programs available for it ?

I have an old TI-92 plus, so the syntax for inputting expressions may have changed, but the calculator should be able to handle calculus, etc. without any added programs.

To differentiate: You should have a special "d" character on the keypad somewhere (probably accessed via 2nd). Typing d(expression, variable) will produce the derivative.
E.g. d(x^2, x) will output 2x.

To integrate:
There should be an integration mark somewhere on the keypad. integration_mark(expression, variable, lower limit, upper limit) for definite integrals, integration_mark(expression, variable) for indefinite (note that the integration constant is missing!).
E.g. int_(2x, x) will output x^2
int_(2x, x, 0, 2) will output 4

Limits:
You can probably find limits under the Calc menu, though you could also type "limit" using the character input.
limit(expression, variable, limit)
E.g.
limit(n/(n-1), n, infinity) will output 1
Left and right side limits can be done by adding another parameter to the function which controls from which side the limit is approached depending on whether it is larger or smaller.
E.g.
limit(1/x, x, 0, -2) will output negative infinity
limit(1/x, x, 0, 2) will output infinity

The vectors and matrices have proved to be harder. It involves finding determinants of matrices of arbitary size, cofactors,

There will be an input option in the menus for putting matrices into the system and storing them as variables. It's a bit tedious, but it works.
det(matrix) will find the determinant. The math menu should have a bunch of options for matrix operations. Cofactors cannot be done unless you're willing to program the calculator.

Vectors are denoted using square brackets and can also be saved to variables (use the "->" key followed by the variable name). dotp(v1, v2) and crossp(v1, v2) will calculate the dot product and cross product respectively.

gaussian elimination, systems of equations etc.

Systems of equations can be solved with the simult() function and the appropriate matrices.
simult(coefficients, solutions)

Also any general tips for using the TI ?

Learn the zeros(), czeros(), factor(), expand(), solve(), nsolve(), desolve() and sigma() functions. They help a lot.

[starslayer]

On the TI-89, derivatives are accessed with 2nd+8; integrals 2nd+7. The syntax will be the same as thejester mentioned. Graphing functions is easy; just hit green diamond (the key right below 2nd)+F1, for the Y= window. Under the MODE menu, you can set the calculator to graph functions, parametrics, 3D functions, polar coordinates, sequences, and differential equations.

Limits are in the Calc menu (F3 on the normal screen); thejester covered the syntax. Derivatives have two additional things you do to them in addition to what thejester mentioned; higher-order derivatives can be done as d(expression, var, order); and you can take a derivative at a point by inputting d(blah)lvar=blah. The l between the two things is actually a "with" operator, found to the left of the 7 key.

Most everything else you mentioned is also already programmed into the calculator, just set deeper. To get matrix and vector ops, hit 2nd+5 to bring up the MATH menu, scroll down to Matrix, and a bunch of matrix operations are available. Vector ops (dot and cross products, a unit vector op, and coordinate transforms) are in a menu near the bottom of this list.

To enter the basic matrix ops by hand (+,-,*,-1), enter the matrix like this: [a,b,c;d,e,f;g,h,i]*[etc.], etc. The inverse op is just [matrix]^-1. Left bracket is 2nd+, , right bracket is 2nd+division, and the semicolon is 2nd+9. Vectors are just one row matrices. Gaussian elimination can be done using the augment, ref and rref ops found in the Matrix section of the MATH menu, as can eigenvalues (eigVc, eigVl).

The square root function is 2nd+*; higher-order roots than require either the nRoot function in the CATALOG or, more easily, x^(1/root index). e.g., a cube root is x^(1/3).

As for general trips: READ THE MANUAL IF YOU HAVE IT! It has a complete library of every single function that comes with the calculator, what it means, and how to use it. In addition to the commands thejester mentioned, learn tCollect and tExpand (Algebra menu, under Trig); they will help simply the massive series of trig functions the TI-89 likes to spew for some things. Other useful things include the standard pack of FlashApps the Titanium comes with, and other TI has on their website for free download if the calculator came with the software that allows it to connect to your computer via USB (should be an orange sleeve saying "TIConnect" or something).

Another useful app is called Calculus Tools; this isn't by TI, but it has useful stuff like numerical integration methods, tangent and normal line finders, grad, div, curl, etc. Get it if you can.