Gauss Elimination Method Tutorial - Part 1: Basic Procedure | Numerical Methods with Python

[@mechtutorcom]

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[@ADITYASpeaks]

This is legit the best Gaussian Tutorial I could have possibly seen... Really helpful... great work ❣️❣️

[@no_cola]

Exactly what I was looking for. The best explanation I have seen

[@Wisdomfoundationlive]

Awesome video and editing bro👍

[@radha7492]

amazinggggg....the most helpful video...i was legit unable to understand from other videos, but your video made it so much easy..lots of love

[@priyanshitayal7637]

Truly the best explaination. I was struggling with this since 2 weeks. Thanks

[@nafizahamed8424]

Here i want say only one things this video is great. Wow

[@hamzaerraji1180]

man, you saved my life thank you

[@hemantagarwal1714]

#metoo

[@ZAIDSHAIKH-l7r]

Great explanation, thank you!

[@sontapaa11jokulainen94]

Thanks this really helped me visually understand the concept! Thank you from the bottom of my heart.

[@devin6329]

Love the explaination, It helps me a lot to understand the algorithm, thank you!

[@davidvinicius91]

Thank you so much! I hope that you continue to share more videos like this. This video helped me a lot.

[@AJ-et3vf]

Awesome video! Very helpful! So timely when I finally have decided to code Gaussian elimination ❤️

[@bapibasak2842]

Excellent explanation 👌👌👌

[@johnodland1154]

Great explanation, thank you!

[@jett1448]

Amazing and such a unique tutorial. Thx A Lot

[@naufalmuhadzdzib7338]

Very good explanation. Thank you so much.

[@ibrahimhegazi3955]

Hi I am a computer science student and i had a lovely hard project related to gaussian elimination, and I wondered as I am watching your video: how and when you started understanding the algorithms and its implementations by yourself. In other words, how many years did you spend on learning mathematics then on learning python as a programming language. And have you started with studying the math behind the scene or did you study the modules that will help you program this type of programs first. And as a new student i got another question, do you google for these algorithms or use trial and error. Because from my humble position right now, I am not confident that one day I might be creating algorithms while I am trying to solve a problem. As a final overall question, should I copy and understand your code for the now till I learn try and try more. It will be an honor for me if you answered my questions. And thanks for reading thin comment and for making this amazing video. Hope you the best.

[@mechtutorcom]

Dear Ibrahim, Thank you for your nice words. Like many students, I started learning math early school. But my main math skills were developed at High School thanks to my brilliant teachers. At the University, I studied Mechanical Engineering, which depends heavily on meth, especially calculus and linear algebra. I used numerical methods to solve different problems in fluid mechanics, theory of machines and heat transfer. During studying for my Master's degree, I studied numerical methods as a graduate course and also it was the basis of my Master's thesis. Later, it became the core of my research interests. At university and computer centers, I taught computer programming for engineering students, where I used numerical methods in examples and exercises. In textbooks, all these algorithms are explained in different forms: pseudocodes, flowcharts, math formulas or just textual explanations. In these videos, I tried to present those algorithms as simply as possible by using PowerPoint slides and animations. I was first interested in Python in late 2016. I used to use MATLAB, which is not free software and focuses more on engineering. In contrast, I found Python and its packages totally free and more general. I believe it is a matter of interest and experience, so I recommend that you study the algorithms in different areas of your study and transform them into working codes. By the time, I am sure that you will gain the experience to design and develop your own algorithms. Finally, the textbooks I usually use to prepare the videos are: 1) Applied Numerical Analysis, Curtis F. Gerald & Patric O. Wheatley, 7 ed. 2) Numerical Analysis, Richard L. Burden & J. Douglas Faires, 9 ed. 3) Schaum's Outline of Theory and Problems of Numerical Analysis, Francis Scheid. I sometimes use other books in case I need more details. I hope I could answer your questions Regards

[@ibrahimhegazi3955]

@@mechtutorcom What a long and lovely journey. Thanks alot for your time and your response. And thanks for the resources(books) at the end.

[@mm_film_trailer4458]

very clear explanation!!

[@radha7492]

i didn't like it; i just loved it bosssss🥰🥰🥰🥰🥰

[@expertmundoquantico870]

An excelent class, thanks

[@souadmassi7683]

Do you have an online course about Matlab and how to use it to prgram any problem? Tips about this software, please

[@mechtutorcom]

I have several tutorials in this channel about numerical methods with MATLAB/Octave, but I haven't made yet a full online course about it specifically. Thanks.

[@souadmassi7683]

@@mechtutorcom Thank you sir for your reply. Please, make an online course about Matlab and how to program with it? Because you are so talented in programmimg. All the best

[@rozakcenter]

Thank you sir, from Indonesia

[@Дильназ-и5ъ]

Thank you very much. I thought that I will never understand that.

[@abouzidmohamed7646]

Great explanation

[@mechtutorcom]

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[@morganvoldemort675]

One if the top left number is zero? do you skip it?

[@mechtutorcom]

I think you mean by "the top left number" the pivot element. If any pivot element during the eliminations is zero, its whole row is replaced with another from the next rows by using the "Partial Pivoting." It is explained in Part 2: kzbin.info/www/bejne/n2jJaoN4mpKdlbs Thank you for the comment.

[@shubhampatel578]

I am using PyCharm. when I tried to import array and zeros, it showed me error. Can you please explain this?

[@mechtutorcom]

I think you have a problem in importing Numpy. Numpy doesn't come with Python by default. You have to install it to your file system so the Python can import it. I published a video about the installation of the packages of scientific computations: kzbin.info/www/bejne/hZvKk4yBh9SSh80 In that video, the versions of Python and the packages are old, but the installation methods are still the same. I hope you find my answer helpful. Thanks for your comment.

[@IndiraPuteri]

Hi. I think the factor should be a[i,k]/a[k,k], right?

[@mechtutorcom]

The factor depends on which row is multiplied by the factor before the subtraction. In this video, the factor a[k,k]/a[i,k] was multiplied by each one of the lower rows, then the row was subtracted from the pivot row above. If the pivot row itself is to be multiplied by the factor every time, then the factor should be a[i,k]/a[k,k], as you mentioned. Both methods are correct since they should yield the same solution. I hope I could answer your question.

[@IndiraPuteri]

Thank you so much. Your explanation help me understand the code. Another thing, why did you use normal index on the elimination phase, but you use python index on the substitution phase? I already learn your explaination in the video, but i still dont get it. Would you please explain it?

[@mechtutorcom]

@@IndiraPuteri You are always welcome. I used the normal index (1,2,...,n) in the theory part for both elimination and back-substitution because it is the one used in almost all books of linear algebra and numerical analysis. I wanted to make it the same as the common references. But, during coding, I applied the array index system of the computer language. Array indexes in Python are (0,1,...,n-1) while in MATLAB they are similar to normal. You can notice that more clearly in the manually solved example. I hope I could explain the point.

[@IndiraPuteri]

@@mechtutorcom Hi. I just create a video on NGE method with Python, for my students. It is inspired by this video. Thank you so much. I divide in to two part. I hope you Will have time to look at it.

[@poojagupta-do4nr]

thanku

[@sidalifero6271]

thanks a lot

[@holyshit922]

Maybe it would be better to multiply one row per iteration only In first iteration first row can be multiplied only In second iteration second row can be multiplied only etc That would be better in my opinion

[@daniellequaye9010]

When I used this code, I keep getting error messages

[@iosuegea9607]

I think you had a little error in line 13, isn't it? It should have been if a[ik]!=0: continue

[@AdminNST]

if a[i,k] == 0:continue That's the right way to do it.

[@Deban.jannnn]

10:30

[@AdminNST]

I don't know English badly, but what is FACTOR?

[@AdminNST]

only interested in this interval

[@boycomment4324]

Hi! Thank you for this helpful video. I wonder if I can ask for your email address. I currently doing a python code which I learned from this video. I would like to send you my python file and maybe you can help with to fix the errors on it?

[@carsonbartlett2724]

the division is incorrect, it should be a(i,k)/a(k,k)

[@mechtutorcom]

The elimination can be performed in two ways; by subtracting the pivot row (k) from the current eliminated row (i) or by subtracting the row (i) from the pivot row (k). The division factor should be changed accordingly. Please, watch the parts of stepwise calculation and the final run of the code. Thanks for the comment.

[@ayoube_baalla]

Thanks a lot