Archive for April, 2016

Solve Differential Equation using LaPlace Transform with the TI89

Saturday, April 30th, 2016

Lets solve y”-4y’+5y=2e^t y(0)=3 , y'(0)=1
Go to F5 1 and enter the D.Eqn as shown in the image,
just press enter and see how the solution is derived , nicely laid out, step by step using Differential Equations Made Easy.

The support I get from TI89.com has been phenomenal !!!!

Saturday, April 23rd, 2016

I initially found TI89.com through the education.ti.com website because I was looking for an app which could help me understand Calculus equation better.

I initially bought the Calculus made easy 2 years ago and was just very fascinated how much this app helped me understand calculus problems better. If it wouldn’t have been for Calculus Made Easy I probably would have never passed Calculus I and II. Everything was very detailed and laid out in steps which makes it easy to follow.

Now several years later I own 5 of the TI89 apps apps made easy and I couldn’t be happier.

Statistics & Probability has been one of the hardest classes so far for me and I wished I would have bought the app sooner because it definitely helps seeing the equations before solving it.

The support I get from TI89.com has been phenomenal and I am never left in the dark with help in regards to questions.

Thanks so much for the support and developing this app because if it wouldn’t have been for TI89.com I probably would have struggled through most of my math studies.

How to perform a Z-Test Step by Step on the TI 89 using Statistics Made Easy

Wednesday, April 6th, 2016

Here is a sample problem:
A student who works in the blood lab plans to test the hypothesis that the mean cholesterol level of men is less than 230 mg/dL. The population variance of cholesterol level is assumed to be (40 mg/dL)^2. The student tested nine men for cholesterol levels
and found the following values (mg/dL): 164, 230, 335, 272, 261, 248, 235, 192, and 203.

Since we are given the variance , we use the Z-Test.
Since we are given the data, we may just enter them in the 2. row using list notation {..} .

Next just press enter to view everything you need: test statistic, p-value, conclusion, even type 2 error and power of test can be found.

Very easy to use, yet very powerful!

How to solve a Bernoulli Equation using Differential Equations Made Easy with the TI 89

Tuesday, April 5th, 2016

To solve x*(dy/dx) + y = 1/y^2 there are several options to do so.

F1 G : Bernoulli or F1 A : Linear in y or F1 D: N*y’+M=0 , try them all to get the same
solution in different ways.

To use the F1 G : Bernoulli , first rewrite x*(dy/dx) + y = 1/y^2
as (dy/dx) + y/x = 1/x * 1/y^2
Thus enter P=1/x and Q=1/x and n=-2

Press ENTER many times to observe how the proper substitution and integrating factor is found :

How to solve 1. order Differential Equations using Differential Equations Made Easy with a TI89

Tuesday, April 5th, 2016

How to solve the 1. order Diff Eqn: (3y+2t-2)dt + (10y+3t-1) dy = 0 with y(-1)=2

Just replace every t by x and enter the D.E. and initial conditions under F1 C as shown.

To view more steps on how to solve an exact Diff Eqn enter it
under F1 6 .

Voila!!

How to get STEP BY STEP solutions using the TI89 Titanium Calculator

Saturday, April 2nd, 2016

How to get STEP BY STEP solutions using the TI89 Titanium Calculator

A) TI89 has a Computer Algebra System

You probably know that the TI 89 Titanium calculators are very powerful due to their built-in Computer Algebra System, called CAS.

This allows us to solve equations such as a*x + b = c for x or a or b or c. To accomplish this, just enter the following command into the HOME screen:

solve( a*x+ b = c, x) and press ENTER . Or type in solve( a*x+ b = c, b) when solving for b. The TI 83 / 84 calculators, however, cannot solve those

equations symbolically as they have no built-in CAS. For that reason, programs such as STEP BY STEP EQUATION SOLVER(www.Ti89.com)

can run on the TI 89 but not on the TI 83 / TI84 calculators. Interestingly, the TI 83 and TI 84 calculators are the most prominent calculators in the USA.

Prices between TI83/84 and the TI-89 Titanium calculators don’t differ significantly. You could google : Graphing Calculator TI89 Walmart, or simply

Walmart calculators or Graphing Calculator TI 89 Amazon.

B) TI89 calculators excel in Calculus

May be the most important advantage of the TI 89 Titanium over the TI-83 and TI-84 calculators is in Calculus: Derivatives, Integrals and Limits can be

computed symbolically with ease using the TI-89 Titanium calculator. For example, integral(x^2,x,c) will correctly find x^3 / 3 + c . Or, if you like to have some fun you could

enter integral(g^2, g, p) to find g^3 / 3 + p . A TI-89 Titanium Derivative example would be d(x^3,x) = 3x^2 and d(x^3,x,2) finds the 2. derivative of x^3 .

The TI 89 is the best Limits Calculator, try this: Limit(sin(x)/x,x,0) to correctly get 1. If that does not convince you that the TI89 calculators

are the best Limits Calculator then enter this : limit((sin(x+h)-sin(x))/h,h,0) to correctly get its derivative cos(x) using the limit definition of the derivative.

Now that is powerful and it is the underlying reason why the TI 89 Titanium calculator app CALCULUS MADE EASY is such a powerful beast rivaling

WolframAlpha, Mathematica and Maple. This app takes full advantage of the CAS allowing for STEP by STEP solutions to both integrals and derivatives:

Just enter the function and press ENTER a few times to see all rules and steps involved! Considering you can carry the TI89 calculator with you, you practically

always have your personal tutor available, and that any time of day!

C) TI89 calculators excel in Differential Equations too

CALCULUS MADE EASY extends its STEP BY STEP solutions through Multivariable Calculus covering 4 years of Calculus. Thus, Step by Step Implicit

Differentiation, Step by Step Polar and Parametric Equations, Step by Step Partial Derivatives and Step by Step Lagrange Multipliers are all integrated. Even

Differential Equations can be solved Step by Step on the TI 89 Titanium using this app. Nevertheless, it is limited to the introductory method to solving Differential

Equations called Separation of Variables. In case you are looking for more advanced techniques such as Integration Factors, Variation of Parameter,

Undetermined Coefficients, Wronskian , Runge Kutta, LaPlace Transforms or you need to solve Higher Order, Bernoulli, Exact or Non-Exact or Linear Differential

Equations then the DIFFERENTIAL EQUATIONS MADE EASY app will provide you with STEP BY STEP solutions on the TI89 Titanium calculator.

D) Step by Step solutions in Math, Science and Business

In fact, STEP by STEP apps for the TI89 Titanium calculator are available at www.TI89.com for all areas of Mathematics, Science and Business: Geometry,

Algebra , Trigonometry, PreCalculus , Statistics, Number Theory , Numerical and Complex Analysis, Physics, Chemistry, Business, Finances, even Portfolio & Markets.

Visit TI89.com to see the full listing of the 20+ STEP BY STEP apps available for the TI 89 Titanium Calculator. In fact, the Step by Step apps are also available for the

Voyage 200 calculator which also has the built-in CAS. The programmers at TI89.com take a lot of pride in their apps and gladly update them based on users feedback.

Trial versions are available and allow free testing of the apps.

E) TI89 old and new, RAM versus ROM

Lastly, we should mention that the TI89 Titanium is the modernized version of the original TI-89 calculator. While they both have CAS and are identical in functionality,

the newer TI89 Titanium calculator looks sleeker and has much more RAM as well as ROM. The TI89 Titanium calculator allows running more than 20 STEP BY STEP apps.

Apps are stored in ROM (the calculators hard drive) and are copied to RAM when executed and removed afterwards.

Implicit Differentiation Calculator Step by Step

Saturday, April 2nd, 2016

STEP BY STEP Implicit Differentiation with examples – Learn how to do it in either 4 Steps or in just 1 Step.

A) You know how to find the derivatives of explicitly defined functions such as y=x^2 , y=sin(x) , y=1/x, etc .

What if you are asked to find the derivative of x*y=1 ? This is an Implicitly defined function (typically a relation) as y is not alone on the left side of the equation.

Well, one way would be to rewrite it as an explicit function by dividing both sides by x to get y=1/x and we know its derivative dy/dx = -1/x^2 using quotient rule.

Well, this Houdini “trick” does not always work. You couldn’t use it for x^2*y+y^3*x=6. So how can we find its derivative?

First, we have to recall and use the fact that y as the dependent variable depends on x, so we could rewrite the equation as x^2*y(x)+(y(x))^3*x=6 .

This equation format convinces us i.e. to use chain rule for (y(x))^3 yielding 3*(y(x))^2*(dy/dx) where dy/dx=y'(x) is the derivative of y with respect to x.

Altogether, when applying product rule (f*g)’ = f’*g + f*g’ we get : 2x*y(x)+x^2*(dy/dx) + 3*(y(x))^2*(dy/dx)*x+(y(x))^3=0 (This is STEP 1)

Since we are after dy/dx , we have to factor it : (dy/dx)*[x^2
+ 3*(y(x))^2] + 2x*y(x) + (y(x))^3=0 (This is STEP 2)

And we have to subtract the non dy/dx to other side: (dy/dx)*[x^2
+ 3*(y(x))^2] = – 2x*y(x) – (y(x))^3 (This is STEP 3)

Lastly, we just have to divide by the non dy/dx on the left side: dy/dx = (- 2x*y(x) – (y(x))^3 ) / [x^2 + 3*(y(x))^2] (This is STEP 4)

Congrats, you just mastered Implicit Differentiation Step by Step (in 4 Steps to be precise) !!!!!

Lets revert back to y instead of y(x) : dy/dx = (-2x*y-y^3)/(x^2 + 3*y^2) to make our final derivative look less complicated. VOILA!!!

Remember that this derivative evaluated at (x,y)-points gives the slope at those points and we can draw conclusion about in/decreasing, extremaetc.

B) Lets go back to x*y=1 . Try to find its derivative using the 4 Implicit Differentiation Steps outlined above and compare it to the derivative found earlier.

Continue reading after performing the STEP BY STEP Implicit Differentiation!

STEP 1 : 1*y + x*dy/dx = 0 by Product Rule.

STEP 2 + 3: x*dy/dx = -y no factoring here and subtract the non dy/dx.

STEP 4 : dy/dx = -y/x DONE. Now how does -y/x match -1/x^2 ? Algebra helps here: Since y=1/x : -y/x = -(1/x)/x = -1/x^2 and everything that starts well ends well ðŸ˜‰

C) IMPLICIT DIFFERENTATION in only 1 STEPS ? Is this Possible???? Yes it is ….

To accomplish this, we have to subtract whatever is on the right side over the left side. In our example above, we get x^2*y+y^3*x-6=0, lets name this F=0 . Easy enough.

Now we use: dy/dx = -Fx/Fy thatÂ¡Â¯s our little formula.

Fx = is the derivative of the left side where x is our variable and the y’s are treated as constants (Think of y as y=10) . In our example, Fx= 2*x*y+y^3

Similarly, Fy = is the derivative of the left side where y is our variable and the x’s are treated as constants. (Think of x as x=10) . Fy = x^2 + 3y^2*x

After this prep work , we find dy/dx = -Fx/Fy = -(2*x*y+y^3)/(x^2 + 3*y^2*x)

Now, how cool is this ? Implicit Differentiation in only 1 STEP plus a bit of prep work.

Can you do Implicit Differentiation in 1 step for x*y=1 ? Or x*y -1 = 0

Here is how: Fx = y , Fy = x . Thus, dy/dx = -Fx/Fy = -y/x Done.

D) SUMMARY: Make an implicitly defined function explicit, if possible, by solving for y and differentiate it as such.

If impossible, do Implicit Differentiation in 4 Steps as outlined in B) .

And if you are not afraid of finding the partial derivatives Fx and Fy then do Implicit Differentiation in just 1 step. Though, your teacher may not like it as the typical 4 steps in B) are not included and your final solution looks if copied.

E) And here comes your Implicit Differentiation Calculator showing Step by Step solutions.

Make sure to use the correct TI Connect Software

Saturday, April 2nd, 2016

There are two similar looking TI Connect software products, but only “TI-CONNECT SOFTWARE” allows the transfer of TI89 apps. Download it here: TI-CONNECT SOFTWARE DOWNLOAD
Note its yellow-blue colored logo.

However, the so called “TI CONNECT CE SOFTWARE” allows file transfers to the TI-84 calculator only.