Computational errors in MATLAB, Wolfram, Derive, and TI-Nspire

[jeffer vitola]

hello remember not speak English and use a translator on line,

together some pictures to show some errors,from a simple integral or easy to those who are not as oscillatory integrals, when I worked and ask oscillatory integrals or approximate numerical answers, also when try plot a complex function on a small scale, the graph has cuts which is not correct because the complex function is continuous in these intervals,i want job *2 years ago texas instruments contact and wolfram alpha for these failures corrected, and I don't not *was hired as a consultant mathematician of his companies, as *i don't not they hired me, there are some mathematical problems of these programs, I do as a publication for knowledge general, I *not upload all the photos , low quality pictures so they could see on this forum. as the translator is bad clarify that I have not been hired by wolfram alpha or by texas instruments. never.*
jefferson alexander vitola (Bigsmile)

hola recuerden que yo no hablo ingles me toca usar un traductor en linea,, escribio en español you que la traduccion es muy mala. al no ser contratado como consultor matematico para texas instruments o wolfram alpha, entonces yo decidi publicar algunos errores que he encontrado desde hace you mas de 2 años entonces ahora lo voy a publicar como pasatiempo.att
jefferson alexander vitola (Bigsmile)

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[MarkFL]

Re: Some mistakes en matlab, wolfram alpha,derive 6 and calculator ti nspire cas

In your first image, in the Derive 6 window, you have:

$$\int\frac{(2x-1)e^{x^2}}{e^x}\,dx=e^{x^2-x}$$

With the exception of the omission of the constant of integration, we can see that this is correct, we we rewrite the integral as:

$$\int(2x-1)e^{x^2-x}\,dx$$

Use the substitution:

$$u=x^2-x\,\therefore\,du=(2x-1)\,dx$$

and we have:

$$\int e^u\,du=e^u+C=e^{x^2-x}+C$$

For the definite integral:

$$\int_{15.73}^{19}\frac{78541212}{8411}\sin\left(x^4 \right)\,dx$$

W|A returns:

0.529973

An online Simpson's Rule calculator gives (with $n=2^{16}$):

0.53022209468772

 

[jeffer vitola]

Re: Some mistakes en matlab, wolfram alpha,derive 6 and calculator ti nspire cas

In your first image, in the Derive 6 window, you have:

$$\int\frac{(2x-1)e^{x^2}}{e^x}\,dx=e^{x^2-x}$$

With the exception of the omission of the constant of integration, we can see that this is correct, we we rewrite the integral as:

$$\int(2x-1)e^{x^2-x}\,dx$$

Use the substitution:

$$u=x^2-x\,\therefore\,du=(2x-1)\,dx$$

and we have:

$$\int e^u\,du=e^u+C=e^{x^2-x}+C$$

For the definite integral:

$$\int_{15.73}^{19}\frac{78541212}{8411}\sin\left(x^4 \right)\,dx$$

W|A returns:

0.529973

An online Simpson's Rule calculator gives (with $n=2^{16}$):

0.53022209468772

forgive I was not clear in the first image at the top, it shows that the texas instruments calculator can not take the integral, but the same image compare with a program called derrive 6 which although they are the same texas instruments company computer program has a better structure in some fields of mathematics more than the calculator from the same company, on the other images do a comparison of the errors committed by one or other program or sometimes in all programs. is just a small sample that sometimes math programs contradict one another or that some are successful and others are not,or in the case of the same program wolfram alpha contradicts himself by giving some numerical approximation modes for oscillatory integrals despite being the same exercise raised from the beginning,my language is very limited in this language because as not handling and all I have to do it through a translator if you think I can write in Spanish explaining each image, because if you look closely compare a program on top of the same image and the other at the bottom of the same photograph, or sometimes it is the same program but show different solutions giving the same problem and not are good solutions.

this type of oscillatory integrals $$\int_{15.73}^{19}\frac{78541212}{8411}\sin\left(x^4 \right)\,dx$$, I me find designed a new numerical method to calculate and am in copyright to publish freely and that I what me recognized as the creator of the numerical method, I'm working on it.
clarify that your MarkFL solutions are perfect ,,,, what I mean is that mathematics programs sometimes contradict each other finding different solutions to the same problem and are not correct, or sometimes not even find a solution to a problem proposed. any questions write me.:)

att
jefferson alexander vitola(Bigsmile)

 

[MarkFL]

Okay, now I see what you are referring to with the first integral...my TI-89 Titanium returns the same result as your TI Nspire.

I did notice that the second integral returns wildly different results with the online Simpson's Rule calculator until the number of steps was made sufficiently large. It may be that with such rapidly oscillating functions some numeric integration algorithms will fail because care is not taken to ensure successive results do not differ by a small enough value.

If you have developed an algorithm that handles such oscillatory functions in a superior manner than that which is currently implemented by mainstream software, then I applaud your ingenuity!

 

[jeffer vitola]

Okay, now I see what you are referring to with the first integral...my TI-89 Titanium returns the same result as your TI Nspire.

I did notice that the second integral returns wildly different results with the online Simpson's Rule calculator until the number of steps was made sufficiently large. It may be that with such rapidly oscillating functions some numeric integration algorithms will fail because care is not taken to ensure successive results do not differ by a small enough value.

If you have developed an algorithm that handles such oscillatory functions in a superior manner than that which is currently implemented by mainstream software, then I applaud your ingenuity!

I hope as good contributions from the mistakes and failures that all users of this forum have found that the work programs in math and you know,,, is also including errors in different calculators and math programs,,,I'll be watching to see which errors and faults found all of you, in programs of math and calculators,,,att
jefferson alexander vitola(Bigsmile)

 

[jeffer vitola]

hello remember not speak English and use a translator on line,

together some pictures to show some errors,from a simple integral or easy to those who are not as oscillatory integrals, when I worked and ask oscillatory integrals or approximate numerical answers, also when try plot a complex function on a small scale, the graph has cuts which is not correct because the complex function is continuous in these intervals,i want job *2 years ago texas instruments contact and wolfram alpha for these failures corrected, and I don't not *was hired as a consultant mathematician of his companies, as *i don't not they hired me, there are some mathematical problems of these programs, I do as a publication for knowledge general, I *not upload all the photos , low quality pictures so they could see on this forum. as the translator is bad clarify that I have not been hired by wolfram alpha or by texas instruments. never.*
jefferson alexander vitola (Bigsmile)

hola recuerden que yo no hablo ingles me toca usar un traductor en linea,, escribio en español you que la traduccion es muy mala. al no ser contratado como consultor matematico para texas instruments o wolfram alpha, entonces yo decidi publicar algunos errores que he encontrado desde hace you mas de 2 años entonces ahora lo voy a publicar como pasatiempo.att
jefferson alexander vitola (Bigsmile)

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hi all, as I had said before I will continue publishing mistakes math programs, I recommend you look well put pictures that the integrals are simple but the program fails with the change of variable and can not develop and other computer does not understand the substitutions that are also including calculator ti-nsipre cas, and remember I use a translator online,,, greetings from Colombia,,,.,.att
jefferson alexander vitola (Bigsmile)

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att
jefferson alexander vitola (Bigsmile)