NumPy Tutorial (2022): For Physicists, Engineers, and Mathematicians

Check out my course on UDEMY: learn the skills you need for coding in STEM:
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This from-scratch tutorial on NumPy is designed specifically for those in physics, mathematics, and engineering. In the future, I will be making tutorial videos on all the essential python packages, so subscribe for more!
All code can be found here:
github.com/lukepolson/youtube...
0:00 Introduction
3:43 Array Operations
8:28 Indexing and Slicing (1 Dimension)
15:18 Calculus and Statistics
21:28 Examples
47:18 Multi-Dimensional Arrays
52:22 Functions on Multi-Dimensional Arrays
56:26 Linear Algebra: Matrix Operations
58:33 Linear Algebra: Systems of Equations
59:53 Linear Algebra: Eigenvalue Problems
1:02:02 Examples
1:28:42 Basic Datasets

[@francisrayquintana5119]

This dude, this channel: is a blessing.

[@vittoriociardiello9945]

Believe me, you are one of the most useful channels about python. Thank you so much. You would deserve much more subscriptions. What about a cython playlist?

[@indocesare14]

At university I've been taught Matlab but I always wanted to switch to python in order to get rid of licensing problems and fully embrace the "open-sourceness" of this programming language. This video is a blessing!

[@flynnxd8229]

Super useful and engaging! Looking forward to the scipy and matplotlib ones.

[@SubhadipDas1]

Your tutorial are very easy to learn yet very concise, informative and in-depth. Please keep making such contents.

[@ayushkumarsharma7019]

Even after 2 years this is the most fun and informative video for numpy that i needed , really loved those exercises. thank you for such an amazing content

[@Ali-pd2rl]

It's awesome mate! Your videos about these libraries really help me, and of course these are very useful in my major (physics). Thank you 🙏

[@davidhendriks1395]

Great video. Having some clear and complete tutorial on these topics is very useful!

[@nicoleworoniuk1544]

This is the best channel I have come across for python, as an engineering student, I am so grateful! Thank you !!

[@sietsebuijsman8523]

Very good tutorial, thank you! I was kind of figuring out Python by myself, but this helped me put everything in context. And this finally enables me to get rid of the for loops :'D

[@kekskekskeks112]

Wow, thank you so much! Because of your explanation at 29:44 I just understood those slice-operations, I allways struggled with, fell like scales from my eyes :D

[@abishaimathai6542]

I hope the algorithm blesses you. Best tutorial for NumPy on the internet hands down.

[@bismillahyusufu5121]

For sure, you're the best Python teacher I have met so far on KZbin. Thank you so much. God bless you

[@marioaguilar8735]

U got one more subscriber. Just found you by chance, and I appreciate. Great tutoria and very clear explanations!!!

[@sucksh97]

Amigo, eres un crack! me sirvió muchísimo el tutorial. Gran calidad de videos :)

[@amsal1998]

This video series is going to be great!

[@AndreasLvgaard]

This was really informative! You are a genius, thank you! I like the hands-on exercises/examples, which I followed along in my own desktop application (VSCode). And I learned that "trick" of how to get all x-values when dy/dx = 0. Incredible how something that looks hard can turn out to be so easy :D Using Python a lot in my engineering career and NumPy is essentiel in numerical calculations! I guess I will continue to look at your videos, starting with SciPy!

[@AishikDasgupta-pm5pl]

Thanks a lot mate. Please keep posting. I find these videos tremendously helpful for my Computational Nano electronics course.

[@VALedu11]

I have shared this link with almost 75 students of mine in the MAchine learning with PYthon class. You have made my job so much easier.. thanks a TON

[@AluminiumT6]

Completed today. Thanks for this great resource Luke!

[@frankkoslowski6917]

Nice and meaty tutorial. Have been going over it several times. Cross-referenced many ideas and principles with information from other sources. It can be said that If nothing else, the effort invested in studying the material, has produced good fluency in typing LaTex Script, and consequently, textbook-like IPython Notebook files. Thank You!

[@marounrizk]

So underrated, what a great channel ! Thank you from a physics engineering undergraduate.

[@carlossalgueirosa1821]

Awesome! There are no more word to say, your lecture is awesome!

[@NinjaMartin]

Man. So good. I really wish you the best, you are such a great teacher as well. Thanks for sharing your knowledge.

[@user-qo7vr3ml4c]

Referred to your scipy and numpy tutorials, excellent content. Thank you!!

[@leonardofacchin1452]

Like many others before me, I'm just chiming in in order to thank you for these outstanding tutorials. It's not hard to find numpy tutorials on the internet, but most of them are either very basic because of the target audience (and so they can't push the student hard enough) or deeper but still mostly amounting to a showcase of methods, functions and syntax. What I like about yours is that they can be challenging at times for a newbie but still very much rooted in the scientific problem-solving mindset and that makes them priceless and fun to watch and try out.

[@bot5am]

Exactly what you said. Chiming x 2

[@scienceaj2907]

Amazing stuff and one of the best teachings I’ve ever seen ❤️

[@connorbrown5267]

For my entire undergrad and masters I avoided coding like the plague, always disliked matlab and used maple a few times for checking christoffel symbols in black hole studies, other than that I am extremely inept, this tutorial saved my life, looking forward to trying all of your other videos, from one PhD student to another, god bless you

[@guitar0wnz]

Good luck man, did the same thing. Didn't feel comfortable coding until I was out of college knowing that deadlines and everything were finally behind me. Now that I'm out though I realize what an amazing resource it is. Bet you'll have a badass thesis down the line

[@annakquinn7084]

Good luck with your student loans

[@alboz1327]

@@annakquinn7084 ???????? What kind of comment is that

[@annakquinn7084]

@@alboz1327 real ones based on reality

[@albertonovati8033]

@@annakquinn7084 the comment doesn't make sense. Why bringing up student loans, what does this have to do with anything in a python video

[@Michallote]

Just a small remark: at 31:31 we have not found 'exactly' the locations where dydx = 0. We have just found the minimum interval available where dydx = 0 is bound to be. This is important because imagine our number of points wasn't ideally as big as 10000, in most cases we don't have the luxury of having analytic functions. And in most cases this makes it sensitive to discretization errors. So in reality one additional step would suffice to get the most precise answer. This already gives us the number of sign changes in the interval. So we could simply use interpolation to find zeros between the x[interval],x[interval+1] to get a precise answer.

[@akshatrastogi9063]

This is one of the best numpy tutorial for engineers on youtube!

[@lecturesfromleeds614]

Brilliant presentation! You pretty much covered everything important for doing computational mathematics

[@lookaway8496]

such a great teacher you are! I am learning a lot here

[@user-le1el4fy4t]

very nice and in depth presentation. You deserve appreciation and subscription. Thanks

[@user-vi1tw1xw7r]

This has been fantastically helpful, thanks. I've used python a lot for the last 5 years or so for many projects, but hadn't properly acquainted with numpy. I'm currently exploring analysing captured audio signals for equipment testing, so playing with numpy and fft a bit. The array multiplication tip for finding zero crossing points is just brilliant. I've just implemented it as another way to get a frequency measurement. 👍

[@irvinggaspar1531]

I've learned a lot of thing with your videos rather than in Computer physics classes, thank u Bro

[@d3f3kt57]

I am migrating from Matlab to Python. Your videos are a blessing. Thanks

[@samuelnjau8086]

The illustration and speed is just amazing😎

[@abdullahalmehadi6152]

These tutorials are really great ! Thanks man !

[@mayabelemezova1548]

Thanks a lot and for questions we have to think of. At that places you stop and think :"Am I really remember all the elements? And did I know how exactly to use them?" All the tricks are not just for the exact implementation of the rules , it was to teach with the way of thinking! Thank you!

[@brucewernick6542]

This stuff is pure gold. The curvefit video was excellent. Then the turkey cooking demo caught my eye. Now, you have me playing with numpy, scipy, matplotlib and sympy. Fantastic tools for engineers. I tried Jupyter but I don't see the benefit. There seems to be a big overhead when you consider that Python can be run from the most basic plain text editor.

[@alex_blade2001]

Thanks a lot for all this video. It helped me a lot in my final year project. 😊

[@maksudulhossainjewel378]

It's gonna hit a million in no time!

[@anweshbhattacharyya7763]

Bro you are a gift for data science & machine learning.

[@markushaysnielsen4885]

This is amazing! I’m sharing this with everyone I know :-)

[@ErikS-]

better than most of the other video tutorials on numpy that I have seen...

[@ameerbaloch9894]

thank you so much for these videos. please keep up the good work

[@AnatolVZ]

Amazing algorithm for roots!! I have watched 3 times and I cetch the idea!! You are cool!!!

[@frankservant5754]

Very concise explanations thanks you are a lifesaver

[@e-Technik]

Thanks a ton. Please keep making your videos. Just excellent.

[@Millapez]

thank you Mr.P, as a PhD geology student entering into python this video is amazing,

[@bensepter8500]

These videos are great, man.

[@sarojmandloi7974]

Thank you very much for providing this type of content to us.

[@shrimaykher2978]

Man you are amazing!! Great work

[@richardbennett4365]

I like watching this man, because he is thorough and is great with examples in his teaching, but his language is unique!!! He is LOUD. He yells to learn you the material. He also repeats himself, and he is a big fan of the imperative mood in English. He's always commanding the listener to do something or remember something. He's so funny 🤣😅🤣.

[@gedavaa1]

Dear Mr. P Solver, I am very thankful for your Python tutorial videos. I have learnt much more things. Thank you again.

[@User-jr7vf]

do you know what software he is using in the video?

[@kaushikgupta8722]

Perhaps the best explanation!!

[@prietjepruck]

Thanks for this great tutorial.

[@kevinesh]

U r the GOAT. I already liked it and I still don't even see it. Do you think it would be possible a serie in Optimization Methods using numpy numba, etc?

[@alvarobyrne]

zooming in: at 13:51 you did something most coding teachers don't take into account, which is zooming in; you yourself forget to zoom in at the beginning of your excellent tutorials , but they could be much better if you remembered to zoom in at the beginning of them; ha ha. you know, some of your thousands of spectators use glasses to watch your tutorials, 13:51, thnkyou very much for your channel for your attention and thanks in advance for zooming in, ;) Ah! and removing the side bar, hiding it: everything that increases screen real state

[@TatouVlogs1]

I need more, you're wholesome.

[@user-ml9ib1lm3r]

Amazing tutorial thank you very much !!

[@thomasking5894]

great young teacher here. fine fast ideas for my use of numpy in my elliptic curve work.thanky P. Solver

[@nobody2937]

Excellent Tutorial .... Thank you ...

[@attajilani]

Impressive, wonderful python skills.

[@anilawasiya3642]

omg awesome content I am learning for my passion in physics

[@develxper7931]

This dude is an absolute legend

[@renzy4584]

Amazing!! Some real stuff!!

[@KylianMbappe07303]

54:45 for =anyone who didnt understand, learn aprtial derivatives and integration multivariable one is constant while other is changing and vise versa

[@renukavelu1701]

I enjoyed learning!! Please do more such tutorials. If possible, please share the codes too:)

[@renukavelu1701]

could you explain why this code doesn't work for the last part of the 1st exercise? x[dydx==0]

[@pratyushprakashpatra7062]

@@renukavelu1701 Because it's never exactly equal to 0. We have to find the value for which it is closest to 0

[@Arkantosi]

I never compliment people but...this dude is fantastic.

[@frankkoslowski6917]

ravel(), compared to flatten(), will often be faster since no memory is copied, but you have to be more careful about modifying the array it returns. flatten() always returns a copy. ravel() returns a view of the original array whenever possible.

[@rio_agustian_]

28:00 Wow, that's an amazing trick! Last semester I had a computational physics exam. If I know this sooner, probably my grade would be better

[@richardbennett4365]

😅

[@caiolaytynher5994]

First things first, your channel is really great, I'm an engineering student learning python and you are making that process so much easier. That being said, did you know that you don't need any library to answer question 2? Just use a list comprehension! sum([i for i in range(0, 10_001) if i % 4 != 0 and i % 7 != 0])

[@MrPSolver]

Very neat! Though I suspect this may be faster with numpy, as list comprehension (which is essentially just a for loop) can be slow in python. I would try this for 10 million numbers and see which method works faster.

[@caiolaytynher5994]

@@MrPSolver In my tests, there is no significant improvement other than 1 ms, 100,000,000 was enough to take the runtime to over 7 s. If someone test this and find a significant improvement, I'll like to see cuz even myself thought that with numpy would be faster, lol.

[@user-ek6rf7dw5d]

At 24:31 , is there any advantage of using the * operator rather than a plain logical & operator? Both give the same result, but, coming from a programming background, I feel using a boolean operator make the meaning of the operation much clearer. Other operator, like | , don't match so cleanly to a multiplication.

[@hsh7677]

Thank you!!

[@upgraduate]

Very good tutorial, thank you! I

[@anupkulkarni6986]

Hey man ,you got one new subscriber 😊

[@rasin9391]

love the camera dude

[@onadav]

great! I am back to python thanks to you. what about the Maxwell equations?

[@athalm8289]

Thank you, Luke. Can you upload the meshgrids diagram , thanks!

[@user-we6mf5bn4m]

This is Awesome !! Science girls should be in looove

[@mariomuysensual]

You are amazing dude

[@TheGmr140]

very helpful video, thanks for this. very nice

[@nicholas.hutton]

Thanks for having the chapters built into the video. I do have a question though. Do you see a benefit to learning math applications of python like this instead of using Matlab? My school gives us an edu license and I don't know where to spend my time learning.

[@MrPSolver]

Despite having access to both, I would still choose learning python over Matlab, mostly because there are so many resources available online for python. That being said, from what I understand, the two languages are very similar. If you spend a lot of time learning one, it should transfer over to the other (not the notation, per se, but the general way you approach problems). But for all intents and purposes, python has everything you need for an undergraduate degree. When I was in undergrad, my school also offered a full Matlab license, but I chose to learn python instead. Also when working with others people's code after you've graduated (grad school, industry) you'll notice that A LOT of code will be written in python.

[@Piipolinoo]

Without any doubt: python. Matlab is proprietary bullshit and there is a reason Mathworks (the maker of matlab) is giving out free educational licenses to universities: just to trap you in their ecosystem. Stay clear from matlab unless you actually have to.

[@rubayetalam8759]

at 22:50 if endpoint=True in linspace() why should we consider the N+1 value?

[@robbietorkelsonn8509]

x = np.linspace(1,10,100) f=vectorize(lambda x: 1/x**2 * np.sin(x)) dxdy=gradient(f(x), x) that is where the vectorize comes in

[@nahblue]

In the eigenfunction problem, what do we do to make sure the bounardy conditions are fulfilled? They seem to be, but we don't do anything for it. Edit: it "comes from the matrix shape"; the first line of the matrix is just "-2f1 + f2" (with f0 missing). I see it now :)

[@diegofernandez8881]

Thanks, and please continue (:

[@ddiq47]

1:12:20 what is the difference between this swap function and just transposing the matrix?

[@dejenewoldeyes4184]

I am struggling define function to uniform random distribution, to count the the number of point in circle from the rectangle.

[@maksudulhossainjewel378]

Can you please explain this part E = np.swapaxes(E, 0, -1)? Why is -1 the element or inner axis?

[@baburaosimma9784]

You have used np.cumsum() and sum() for doing the integration ..which one is we follow for integration ?

[@eu-cj3oj]

In Question 3(tougher), how to know that meshgrid should have variables as (t, z) or (z, t)? Because this interchanges the plot for z=0 and t=0.. which one is correct way?

[@idotsameret5144]

your channel is over the top and your are better then my python prof, so thanks . can you also uplode a video about pandas ? to much lab results in a csv file . and again many thanks

[@shivpratapsingh5766]

You are a legend

[@sabagolshahi]

Hi Luke! Thanks for the awesome to-the-point video. I've got a question for you wrt the last part of the first question which was to find the roots. Although the method is clever, it seems there can be some concerns regarding the result. Does this method assume that none of the discrete elements of x are the roots? because if this becomes the case, it seems that the point will be neglected (due to the < 0 condition) which does not seem so elegant. If we change the condition to

[@sabagolshahi]

Moreover, in question 4, I believe there is no match between the what you asked and what you plotted which I find not that nice. Moreover, I think the last formula in the question ( E(t)=Integral.... ) is not a correct formula and is weird. IMO, there was no need to use t' here since E is a function of t. In the solution, all t variables could be replaced by t' and then the t' replaced by kt.

[@MichaelJGruber]

If none of the consecutive values is 0 then none of the x positions is a root. Assuming the evaluated function is continuous, there has to be one in between (by the intermediate value theorem), and any of the two x positions is an approximation within the accuracy given by the original spacing. This is accepted, of course, and without further information you can at best take the mean of the two positions in order to double the "precision". The same precision argument is true for the case where you (numerically) hit a zero. You are correct that

[@kennethstephani692]

Epic video!!!

[@michellebaltazar2447]

Thank you so much!!!

[@vasanthibns3992]

Hey! Thank you so much for the video! As a beginner, I found this really helpful! 13:59 when I tried doing names[first_letter_j] I got an error saying that "TypeError: Only integer scalar arrays can be converted to a scalar index" 31:30 Here the function appears to have derivative = 0 between 2 and 6, but we have values 1.472 and 4.613. Is the method really working? Can you please clarify this?

[@kevinsweeney2809]

Can you please make a video where you write code for a nudged elastic band calculation? You use nudged elastic band methods to calculate the structure and energy of transition state(s) for a reaction. The classic example for a nudged elastic band calculation is determining the structure and energy of the transition state for H2 splitting.