## Uniform and Discrete Distribution using the TiNspire CX

Given a Discrete Probability Distribution such as the one shown below make sure that the sum of the given probabilities is 100% or 1 . If you own a TiNspire CX you can enter the distribution in the top two boxes of the Statistics Made Easy App available at www.TiNspireApps.com .

Once done you get the expected value , variance : step by step.
Optional is the value of N which allows to compute P(X>N) , P(X<N) etc

For a uniform distribution , you enter the given interval [a,b] and the value c which lies on [a,b] . You will then find P(X<c) and P(X>c)

## 2. Fundamental Theorem of Calculus using the TiNspire – Step by Step

Applying the Fundamental Theorem of Calculus using the TiNspire – Step by Step – can easily be done using Calculus Made Easy at www.TiNspireapps.com . Here is an example:

Just enter the given function f(t) which is the integrand.

Next, enter the upper bound of the given definite integral.

Then , Calculus Made Easy provides you with the Theorem and also applies it to show the correct answer.

Steps for the computation can be seen below: First the integrand is integrated and evaluated using the given bounds . Lastly, differentiation yields that final answer.

## NEW: Newton Method, Cholesky Decomposition, Jacobi Method, Simpson Rule and more using the TiNSpire CX

The Numerics Made Easy app at www.TinspireApps.com was updated to also solve the following concepts:

Secant Method to find zeros of a function
Jacobi Method to solve A*X=B
Cholesky Decomposition
Newton Method for Interpolation
Orthogonal Polynomials: Legendre , Hermite, Chebyshev and Leguerre
3-8 Simpson Rule
Newton Cotes

## TiNspire : Volume of Solids of Revolution using Disk, Washer and Shell Methods

Computing the Volume of a Solid of Revolution using the TiNspire CX CAS can easily be done – step by step – using the Calculus Made Easy at www.TinspireApps.com .

Here is how.

Then this pops up :

Now, enter the given function in the top box and the given interval below. Automatically, the answer will show in the bottom with correct integral setup and the correct answer.

Similarly, when using the Washer Method for two functions we have:

Finally, the Shell method works the same way :

In conclusion, the just like all other Calculus topics finding the Volume of Solids of Revolution using the Disk , Washer and Shell Methods can be done easily using Calculus Made Easy at www.TiNspireApps.com .

## Gauss Seidel Method – Step by Step – using the TiNspire CX CAS

Say we have to solve the following system of equations using the Gauss Seidel method.

We just launch the Numerical Analysis Made Easy app at www.TiNspireApps.com , go to Menu option A 2 and enter the problem as shown below using matrix A and matrix B:

and

until we finally arrive at the last step :

## TiNspire Users in Finnland comments

Kuulin koulussa 3 ihmisen ryhmän puhuvan Calculus kurssista miten hän läpäisi kurssinsa sovelluksen, avulla joka näytti kaikki välivaihe ratkaisut.
Luokkakaveri oli puhunut myöskin ohjelmasta, jonka nimi oli Calculus made easy, mikä näytti kuulemma välivaihe ratkaisut.

Yhden matikan kurssin reputtaneena ja toisenkin ehkä myöskin, turhautumiseni matematiikka kolmannen matikan Calculus kurssiin alkoi olemaan stressaavaa.
Päätin ostaa Calculus Made easy ohjelma TI-Nspire CX CAS laskimeen, tämä ohjelman avulla olen onnistunut tekemään kotitehtäviä jotka, ovat olleet haastavia minulle!
Erittäin hyödyllinen ohjelma niille jotka eivät ole keskiverto tasoa matikan laskemisessa.

## Tinspire CX : Black Scholes Pricing – Step by Step

The Black Scholes Option Pricing may be used to compute the fair market value of options, its computation requires some level of mathematical analysis. If you own a Tinspire CX you can easily compute the Black Scholes Put and Call pricing – step by step – using the Portfolio Made Easy app at https://www.tinspireapps.com/?a=PIME . Just follow the steps below.

Select 1: Black Scholes : Call & Put Price

Enter the expiration date (in days), the stock price , its volatility (in %) , the strike price and the risk-free rate (in%)

Notice how the value are plugged into the Black Scholes formula. Notice how the 60 days are automatically divided by 365 days to turn the 60 days into a fraction. Additionally, the volatility and the risk-free rate re expressed as decimals.

After computing the parameters d1, d2 and the values of the normal distribution the Call price C is determined, here C = 49.4468

Lastly , the Put Price is computed, here P=37.937

The computation is easily accomplished simply by entering the given values, and it is always correct 😉

## TiNspire: LaPlace Transforms of a Piecewise-Defined Function

Laplace transform over Piecewise def. Function

Example:

f(1) = 3 defined over 0<= t <2

f(2) = t  defined over t >= 2

To find the LaPlace Transform use Differential Equations Made Easy at

https://www.tinspireapps.com/?a=DEQME  and select LAPLACE TRANSFORM OF PIECEWISE DEFINED FUNCTION and enter as follows:

We use infinity since the function f2 is not bounded. If it was bounded by for example 10 then we would have entered as [0,2,10]

## Ti-Nspire : Step by Step Definite Integrals

Computing definite Integrals using the 1. Fundamental Theorem of Calculus can be achieved using Calculus Made Easy at https://www.tinspireapps.com/?a=CME

Use option 8 in the INTEGRATION menu

Enter function f(x) and bounds [a,b] as shown below

View the Integration steps, here, the Power Rule is applied.

Lastly, plug the bounds into the above Antiderivative, subtract and that’s it!