Sunday, March 2, 2008

Calculus with TI89 calculator

I love my TI-89 calculator - but I hate the manual that came with it.

Dont get me wrong, maybe it is just that I have a really old version and it has been improved since my version was released - or maybe the manual is supposed to be a "reference" book instead of a user guide.

Anyway, I'm doing Calculus at University and so I decided to spend some time going through the manual and summarising the functions that I use the most.

Remembering the function names

All of the functions shown below can be accessed from the "Catalog" menu or the "Math" menu. The "Math" menu is much better as it groups all of the functions by their usage. (EG Matrix, Calculus etc)

Unfortunately the "Math" menu does not provide the (limited) help that the "catalog" menu provides. After using the commands for a while, you quickly get used to the available parameters.

Calculus

Differenciation

Use the F3 function key (option 1) or 2nd + 8 keys

d(x^2+2x,x) - Differenciate the function x^2+2x
d(x^2+2x,x,2) - Get the second differencial of the function

Integrals

Use the F3 function key (option 2) or 2nd + 7 keys

S(2x+2,x) - Get the integral of 2x+2 dx
S(2x+2,x,1,5) - Get the area under the function between 1 and 5

Local Minimum and Maxima (turning points)

fMin(x^2,x) - Get the min candidates of the function x^2
fMax(x^2,x) - Get the max candidates of the function x^2

Limits

limit(1/x^2,x,0) - Find the limit of 1/x^2 as x approaches 0
limit(1/x,x,0,1) - Find the limit of 1/x as x approaches 0 from above
limit(1/x,x,0,-1) - find the limit of 1/x as x approaches 0 from below

Algebra

Intercepts

To find the x intercepts, use the zeros function.

zeros((x+2)^2-2 , x) - List where the function crosses the x axis

To find where the function crosses the y axis, we use the "with" operator to set x equal to zero. The with operator is a vertical bar (on the button above the EE button)

(x+2)^2+2 | x=0

Solving Inequalities

solve( abs(2x+2)+1 < 5 )

Solving Quadratics

"factor" and "expand" are opposites of each other.

solve( x^2+4x+2=0 , x) - Find the values of x that make the equation true
factor( x^2+3x+2 ) - Find the factors [ eg (x+1)(x+2) ] of the equation
expand( (x+1)(x+2) ) - Convert the factors into an equation

Matrices and Vectors

Use ; to seperate rows and commas to seperate columns

[1,2,3;4,5,6] x [3,2;4,5;6,7] - Find the multiple of two matrices

ref( [1,2,3;4,5,6] ) - Convert to row echelon form
rref( [1,2,3;4,5,6] ) - Convert to reduced row echelon form

Transpose a matrix

Use the catalog button to get access to the letter T used in the following example

[1,2,3;4,5,6]T - Transpose the matrix

Inverse of a matrix

Note : The matrix needs to be square

[1,2;3,4]^-1

Determinant

det( [1,2,3;4,5,6;7,8,9] ) - Return the determinant of a matrix

Identity Matrix

Here is a quick way to enter an identity matrix. Saves entering all the 0's and 1's

identity(3) - Returns a 3 x 3 identity matrix

Normal (length) of a vector

norm( [1,2,3] ) - returns the norm of a vector

Dot product

dotP( [1,2,3] , [4,5,6] ) - Return the dot product of two vectors

Showing your working

We are often asked to show our working in our exams/tests. The easiest way to work with matrices is to use the rowSwap and mrowAdd functions. It is also a good idea to use the "Ans" key (2nd (-) button) to save re-entering the matrix for each step.

You need to remember that the "last" value entered is the row that will be replaced

rowSwap( Ans , 1 , 2) - Swap row 1 and 2

mrowAdd( 3, Ans , 1 , 2) - Row 2 is replaced with row 2 + 3 times row 1

Subtraction of a row can be done by using -1 as the first element in the mrowAdd function

Conclusion

There are many more functions that the TI89 is capable of. But these are the ones that I have found most useful in Stage 1 Mathematics. As I proceed through the year, I will no doubt find even easier ways to do things and will post them as I find them.

My next job is to write a summary of functions for my Statistics course

1 comment:

Elliott said...

Thanks for the awesome tips! I am doing quad equations right now and those commands will help a lot with factoring and solving!