ti-cas CARDS

The " cards methods " propose a catch in fast hand of the principal functions of the TI-89 and TI-92 Plus / TI V200 for the most current uses of the mathematical activity of a pupil of college.

They also give consultings on the use of the most current functions.

See also the METHODS heading giving you a support in the resolution of certain mathematical problems.

Numerical calculation
- Calculate with entireties: arithmetic, enumeration: - Decomposition in product of factors first; - PPCM, PGCD. Euclidean Division; - Enumeration: arrangements, combinations
Calculus
- Develop, factorize an expression: - Expand, Factor; - Replace a variable by a value in an expression
- Solve an inequation: - Inequations
- Solve a system of equations: - Systems not admitting a single solution; - nonlinear Systems; - Systems depending on a parameter
- Calculate in the whole of the complex numbers: - Seize a complex or symbolic system use; - usual Operations; - Factorize, solve in C; - Make display the roots of an expression in polar form
Analyze
- Define and study a recurring continuation.: - Regulate the machine in sequence mode; - Define the continuation; - Display the first terms of the continuation; - Represent the continuation graphically; - Construction step by step of the terms of the continuation
- Represent conical definite by a Cartesian equation.: - Example with a hyperbole

Numerical calculation
- Calculate with entireties: arithmetic, enumeration: - Decomposition in product of factors first

To break up an entirety into products of factors first, function Factor is used.

The screen is an example with 3750 and factorial of 100.

One can use the decomposition in factors first to look at if a number is first.

ISPRIME allows this kind of checking and returns TRUE or FALSE according to whether its argument is first or not.

- PPCM, PGCD. Euclidean division

LCM(A,B) and GCD(A,B) respectively calculate the ppcm and the #pgcd of two entireties has and B.

INTDIV(a,b) and MOD(a,b) the quotient and the remainder of the division of A by B calculate respectively.

- Enumeration: arrangements, combinations

The number of arrangements of p elements taken among N #A(n,p) is calculated with the function nPr, the number of combinations It p,n) with #nCr.

Calculus
- Develop, factorize an expression: - Expand, Factor; - Replace a variable by a value in an expression

One uses the operator [ | ] " knowing that ".

The condition can be a list.

This operator also causes to specify the field of a variable, which induces

- Solve an inequation: - Inequations

The systems of formal calculation generally have a weakness in the field of the resolution of the inequations.

Examples:
2x+1<5x-7 and x²-3x+2>0
First is solved, but not the second. And yet, x²-3x+2 has 2 simple roots!
It should be noted that this screen comes from the download 1.00 of the TI-89 and 1.01 of TI-92 Plus / TI V200.

The function SOLVE allows the processing of formal calculation. Defer you to the page " Progs/Fcts " to obtain a program of resolution.

- Solve a system of equations: - Systems not admitting a single solution

Example 1: 4x-2y=1 and -2x+y=-3
" FALSE " indicates that the system does not have a solution.

Example 2: 4x-2y=1 and -2x+y=-1/2

In the case of a system admitting an infinity of solutions, the answer given can be read:
y is arbitrary, and x=(2y+1)/4

- nonlinear Systems

One can solve in an exact way certain nonlinear systems.

Here: x²-2x+y²-4y+5=4 and x+y-2=0

- Systems depending on a parameter

It is possible to solve systems depending on parameters. However, certain values of the parameters can make nonvalid the displayed solutions. It is to the user that it returns to be ensured of the field of validity of the solutions.

- Calculate in the whole of the complex numbers: - Seize a complex or symbolic system use

Symbol I makes it possible to seize a complex number symbolically.

It should be noted that the character of underscore _ makes it possible to specify that a variable is element of C.

- usual Operations

In addition to the usual algebraic operations (Factor...) one obtains by the small #MATH the principal functions of handling of the complex numbers.

CONJ: combined
REAL: real part
IMAG: imaginary part
ABS: modulate
ANGLE: argument

- Factorize, solve in C.

To factorize in C, one uses command CFACTOR, equivalent to Factor in R, which requires 2 arguments: the expression and the variable compared to which one wishes to carry out calculation.
Command CFACTOR tries to give a factorization with coefficients approached in the event of failure for exact values.

Function CSOLVE requires 2 arguments: an equation, and the variable compared to which one wishes to carry out calculation.

- Make display the roots of an expression in polar form.

Example with x²+x+1=0

SOLVE(x²+x+1=0,x) allows to obtain the 2 roots of this expression. To have these roots in the form of list (this is particularly useful in programming), CZEROS is used. It should be noted that the first parameter is not an equation, but an expression equalizes to 0.

POLAR makes it possible to display a complex expression with the polar format.

It was possible to configure the small mode with the polar format of display.

Analyze
- Define and study a recurring continuation.: - Regulate the machine in sequence mode

The configuration of limps MODE is to be carried out only if you wish to explore the curve representative of the continuation.

To carry out calculations on the terms of a continuation, you have the command WHEN.

- Define the continuation

Here, one opened the application " Y= ". See that the continuation is noted u1. The fact of opening this application will enable us to explore the curve representative of the continuation.

It would have been possible to define the continuation with command #WHEN:
WHEN(n=1,1,1+2/u(n-1)) ® u(n)
When (n=1... 1... if not... 1+2/u(n-1)

Caution: on TI-92.9ÌI, it is necessary to carry out a change of variable.

- Display the first terms of the continuation

The application TABLE display the terms of the continuation.

With command WHEN, there would be pû directly to calculate the terms by u(1), u(2)...

- Represent the continuation graphically

For an optimal zone of display, place in application WINDOW, then choose " Zoomfit " in Zoom.

- Construction step by step of the terms of the continuation

To build the terms of the continuation step by step, it is necessary to open the application " Y= " and the menu [ F7 ] AXES as the first screen shows it.

Rock then in application #GRAPH. To pass in mode TRACES by supports on [ F3 ], then to press several times the cursor to build " snail ".

- Represent conical definite by a Cartesian equation.: (application available only on TI-89 and TI-92 Plus / TI V200); - Example with a hyperbole

After having placed the machine in mode 3D, seize the expression in the screen Y=.

FORMAT limps makes it possible to specify the style of layout.

After swing in application GRAPH, calculations before display of the layout are carried out.

These calculations are relatively slow. To suspend them, press [ ON ].

To understand the method used by the machine, you in your instruction manual defer.