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.

Let’s start with the Disk Method. We just select that option in the menu:

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 .

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 😉

 

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!

TiNspire and Finances/Business : Compute Taxes, Time Value

TiNspire users can easily solve Finance and Business related problems STEP BY STEP using the Finance Made Easy at

https://www.tinspireapps.com/?a=FME  .

The  extensive Time Value section of the menu shows Simple Interest, Future and Present Value, Compounded Interest, Annuities, NPV , IRR and MIRR (further down)

Lets start off with a basic tax (i.e. VAT) problem where we have to add 30% to $1000 to get $1300 .

Vice versa ,  we can also subtract interest from a given amount (i.e. pay check)  by entering a negative % , see below:

Auxiliary / Characteristic Equation to Solution of Differential Equation – Step by Step – using the TiNSpire CX

Auxiliary Equation Solution using the Tinspire CX

Finding the Solution given Auxiliary (also called Characteristic) Equation of a Differential Equation is a fun exercise using the Differential Equation Made Easy app .

Just select option 5 :

Then enter the auxiliary equation (of any order)  as shown below

Solve 2×2 System of Equation – Step by Step – using TiNSpire CX

When solving

x-5y =6
3x+2y=1

with the TiNspire CX CAS  you can either use the Substitution or the Elimination Method.

Let us demonstrate how to use the Substitution Method using the STEP BY STEP EQUATION SOLVER first:

Now, to use the Elimination Method select option 1,8 :

Below watch the Steps  to solve the system of equations using the Elimination Method:

It always works! Always get correct solutions. And you get to select YOUR method of choice.

 

 

Gamma and Beta Function – Step by Step – for the TiNSpire CX

To compute the Gamma Function – Step by Step – using the TiNspire CX start the Differential Equation Made Easy app at https://www.tinspireapps.com/?a=DEQME  , go to menu option EXTRAS and select GAMMA FUNCTION. You will be prompted to enter value for n as shown below.

Entering in example n=9 yields 8! or 40320 as the Gamma Value.

You may also enter .5 – value such as 4.5 or 9/2 into the Gamma Function, see below.

The Beta Function can easily be computed using the Gamma Function upon entering two values x and y for the Beta Function. Just select BETA FUNCTION under the EXTRAS menu.

Below we are entering x=5 and y = 4 to get the correct Beta Function value of 1/280 :

As you can see the Gamma and Beta Functions can be computed easily using the Differential Equations Made Easy. Values are computed step and step and are always correct. Even for large values of x and y and n .