MathAndPhysics
MathAndPhysics
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Newton-Raphson Algorithm in Python | Finding real and complex roots systematically
The algorithm explained: th-cam.com/video/qlNqPE_X4ME/w-d-xo.html
In this video tutorial I show you how to implement the Newton-Raphson algorithm in Python. The basic algorithm is very straightforward to implement, but there are a few tricks and things to keep in mind. In the video I show how to numerically find the roots of a polynomial of 4th degree, but you can apply this technique to any function as long as you also know its derivative.
มุมมอง: 6 370

วีดีโอ

Lie derivative pt. 2: Properties and general tensors
มุมมอง 1.5K3 ปีที่แล้ว
Part 1: th-cam.com/video/vFsqbsRl_K0/w-d-xo.html Updated version with the sign error fixed (sort of). The previous version of this video contained an ugly sign error as pointed out by Magist. It should now be clear what the correct sign is. Unfortunately, I also had to cut out part of the video because it made too much use of the wrong sign. I might just rerecord this whole thing at some point ...
Compound interest and Euler's number
มุมมอง 9K3 ปีที่แล้ว
There is an intimate but surprising relation between the concept of compound interest, or, more precisely, the compounding frequency and the exponential function. Since the latter includes Euler's number e, there is a way to arrive at that number by a simple thought experiment about putting money into a bank account and collecting interest. The program you see my using is called "Write" and I g...
Study on a rainy day | Long Pomodoro session | 50/10 | with Sound
มุมมอง 3573 ปีที่แล้ว
The Pomodoro technique can increase your productivity when studying or working. As soon as the video starts you enter your first work period. Start working/studying until you reach the first break after 50 minutes. Then you can enjoy a 10 minute break. Do not continue working during that break. Drink some water, walk a few steps, get some fresh air, whatever you need to refresh yourself for the...
gnuplot Tutorial 8: Colorful datapoints + labelling tics from datafile
มุมมอง 7K3 ปีที่แล้ว
Palette Tutorial: th-cam.com/video/497TNXMUCG4/w-d-xo.html In this part of the gnuplot tutorial I show you how a neat trick how to get the labels for your tics directly from the datafile. Then we are going to color in some datapoints. I prepared a dataset corresponding to the monthly average temperature in some city over the course of a year. First I color the datapoints according to the temper...
Approximate the square root of any number with this formula (+ why it works)
มุมมอง 1.7K3 ปีที่แล้ว
I first saw this formula on reddit, but without any explanation how it could be derived and why it works. I was intrigued, because computing square roots by hand is a tedious process that is almost never necessary in the age of computers and calculators, but getting an approximate result within seconds can be very convenient. In the video I show the formula and give an example how it can be app...
Lie derivative of a vector field (flow and pushforward)
มุมมอง 13K3 ปีที่แล้ว
Part 2: th-cam.com/video/roFNj3k4Lmc/w-d-xo.html In this video I show you how you can derive the Lie derivative of a vector field. First, we look at a vector field on a manifold and develop the notion of an integral curve followed by the flow of the vector field. We can then move another vector along that flow, moving it to a different tangent space. To be able to compare tangent spaces we need...
gnuplot Tutorial 7: plotting for LaTex documents using epslatex
มุมมอง 16K4 ปีที่แล้ว
Scientific papers are usually created using LaTex. If you want to include plots in your paper gnuplot has a specific terminal called epslatex that allows you create vector graphic plots with LaTex style labels to include in your LaTex documents. For this video it is assumed that you are somewhat familiar with LaTex. I am using Overleaf (overleaf.com) as my LaTex editor of choice but the method ...
Are these the same? | Mechanics Puzzle
มุมมอง 1574 ปีที่แล้ว
Reddit post: www.reddit.com/r/physicsmemes/comments/hzthd5/corporate_needs_you/ This mechanics puzzle might have you think that these mechanical systems behave the same. But do they really? Watch the video to find out! The font used in the video and thumbnail is called Inconsolata by Raph Levien. It's a beautiful monospaced font and if you do any programming at all and are looking for a differe...
How logic becomes intuitive through real-life examples
มุมมอง 2.6K4 ปีที่แล้ว
Formal logic can be hard to grasp when not illustrated by real-life examples. In fact, the same task can be either very hard or extremely easy depending on the context in which it is presented. The Wason selection task is a well documented example of such a phenomenon. The font used in the video and thumbnail is called Inconsolata by Raph Levien. It's a beautiful monospaced font and if you do a...
gnuplot Tutorial 6: Palette
มุมมอง 8K4 ปีที่แล้ว
Demo script: gnuplot.sourceforge.net/demo/pm3dcolors.html The sixth part of the gnuplot tutorial series is very specific: I take an in-depth look at the palette feature that is used whenever part of your plot is colored in according to some data value. There are different features to help you achieve the color gradient that you want and that highlights your data in the best possible way. The fo...
Newton-Raphson method | Animated and explained | Algorithm for finding roots of a function
มุมมอง 45K4 ปีที่แล้ว
The Newton-Raphson method or Newton-Raphson algorithm is a way to numerically determine the roots of some function. It relies on an initial guess where a root of the function might be and then gives an iterative process to find the root. Choosing different starting points one can find all the roots of the function. The algorithm works for real and complex functions. The animation in the first h...
gnuplot Tutorial 5: Heatmaps, Vector Fields and the "every" command
มุมมอง 22K4 ปีที่แล้ว
See the different palette options: gnuplot.sourceforge.net/demo/pm3dcolors.html In this video I show you how you can create heatmaps (also sometimes called contour plots, although we are not actually drawing contours) and plots of vector fields in gnuplot. This plotting technique lends itself to visualizing physical potentials (think of electrostatic or gravitational potential) and correspondin...
Kramers-Kronig Relations | Motivation and Derivation | Linear Response Theory
มุมมอง 8K4 ปีที่แล้ว
The Kramers-Kronig relations are an important part of linear response theory. Mathematically, they relate the real and imaginary parts of some complex function that is analytic in the upper half plane. The Fourier transform of the linear response function, or susceptibility, happens to be such a function, which is why the Kramers-Kronig relations are so interesting. After introducing linear res...
How to evaluate this sum?
มุมมอง 3795 ปีที่แล้ว
This infinite series looks a little bit like the geometric series, but unless the geometric series its value is not well known to most Mathematicians and Physicists. It can be derived from the geometric series though via a neat little trick that is shown in the video. A note on the little "subtlety" when differentiating the sum: While the differential operator is a linear operator and the infin...
gnuplot Tutorial 4: Animated gifs and STATS (statistical summary)
มุมมอง 20K5 ปีที่แล้ว
gnuplot Tutorial 4: Animated gifs and STATS (statistical summary)
gnuplot Tutorial 3: Curve Fitting, SSR and WSSR (unweighted and weighted)
มุมมอง 33K5 ปีที่แล้ว
gnuplot Tutorial 3: Curve Fitting, SSR and WSSR (unweighted and weighted)
gnuplot Tutorial 2: linestyles, better plots, symbols, fonts & pngcairo
มุมมอง 51K5 ปีที่แล้ว
gnuplot Tutorial 2: linestyles, better plots, symbols, fonts & pngcairo
gnuplot Tutorial 1: basic Plotting tips & tricks, errorbars, png output
มุมมอง 235K5 ปีที่แล้ว
gnuplot Tutorial 1: basic Plotting tips & tricks, errorbars, png output
How Special Relativity saved Electrodynamics (an example)
มุมมอง 9K5 ปีที่แล้ว
How Special Relativity saved Electrodynamics (an example)
Legendre Transformation explained (with Animation)
มุมมอง 72K6 ปีที่แล้ว
Legendre Transformation explained (with Animation)
Introduction to Planck Units
มุมมอง 11K7 ปีที่แล้ว
Introduction to Planck Units
4 ways of solving the Overlapping Clock Hands Problem
มุมมอง 9K7 ปีที่แล้ว
4 ways of solving the Overlapping Clock Hands Problem

ความคิดเห็น

  • @edvi-m5t
    @edvi-m5t 20 วันที่ผ่านมา

    thank you!

  • @Amy_D_Cruz
    @Amy_D_Cruz หลายเดือนก่อน

    Quite helpful... Thank you sir❤

  • @GK-TUBE-u4h
    @GK-TUBE-u4h หลายเดือนก่อน

    Thank you for the step by step explanation

  • @mr.sepulka
    @mr.sepulka 2 หลายเดือนก่อน

    11:30 and then suddenly gravity defied appears

  • @timsmith9942
    @timsmith9942 4 หลายเดือนก่อน

    Хорошее видео!

  • @danielvolinski8319
    @danielvolinski8319 4 หลายเดือนก่อน

    I copied the python code, I run it in two different platforms successfully, but I always get a lot of "Iteration 0", the counter doesn't change!

  • @SampleroftheMultiverse
    @SampleroftheMultiverse 5 หลายเดือนก่อน

    13 This process’s load deflection curve is sawtooth like in your video Mechanical properties related to a unique variation of Euler’s Contain Column studies. It shows how materials (representing fields) naturally respond to induced stresses in a “quantized“ manor. This process, unlike harmonic oscillators can lead to formation of stable structures. The quantized responses closely models the behaviors known as the Quantum Wave Function as described in modern physics. The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems. The model shows the known requirement of exponential load increase and the here-to-for unknown collapse of resistance during transition, leading to the very fast jump to the next energy levels. This is shown by the saw-tooth graph’s bifurcation during the quantum jump. In materials the process continues till the load passes the ultimate tensile strength. Fields are not bounded by these conditions. th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=waT8lY2iX-wJdjO3

  • @joelsilverman4361
    @joelsilverman4361 5 หลายเดือนก่อน

    Great video made defining a custom palette very easy

  • @sinuture
    @sinuture 7 หลายเดือนก่อน

    I must admit this video is very helpful and splendid. But I cannot understand why none is referring to the annoying mouth sounds.

  • @Eta_Carinae__
    @Eta_Carinae__ 7 หลายเดือนก่อน

    Hi. Usually when we talk of transformations (Fourier, Laplace), these are usually a change of basis of the function (the former into sinusoids and the latter into damped sinusoids). These transforms are intuitive enough to grok. I'm wondering: the coordinates that we're in after taking the Legendre transform are of what exactly?

  • @geraldmarewo8234
    @geraldmarewo8234 7 หลายเดือนก่อน

    This is a very good presentation.

  • @asef_1986
    @asef_1986 8 หลายเดือนก่อน

    Thanks a lot for these tutorial series. It was really helpful for me. I just have one question. Can you also explain how we can use subfigure using \input{} command? The normal subfigure command works only when you use \includegraphics{} command, but it wouldn't work for \input{}. Thanks a lot.

  • @ultrametric9317
    @ultrametric9317 8 หลายเดือนก่อน

    It just amazes me how a simple idea can be tarted up with notation and made to seem impenetrable. I will never understand the modern ethos in math. Thank god everything I need is from earlier days and most of this noise can be ignored.

  • @timmattack
    @timmattack 9 หลายเดือนก่อน

    Still working today !! For an algorithme class projetct, i have to search for the shortest path in a graph of n points. Anyway, here comes the moment where you want to display your result, and with my friend we were like "It could be so great if you could display the points you take one by one". Thanks to this tutorial, i know how to organize my file, and what commands to use to create a *maginficient* gif that shows the path point by point xdd Thank you so much for your tutorial !!

  • @douglasstrother6584
    @douglasstrother6584 9 หลายเดือนก่อน

    "A graphical derivation of the Legendre Transform" by Sam Kennerly (12 April 2011) and "Making sense of the Legendre transform" by Zia, Redish & McKay, American Journal of Physics, vol. 77, (7), July 2009 present enlightening discussions on the Legendre Transform.

    • @chenyang_wu
      @chenyang_wu 3 หลายเดือนก่อน

      I have to go back and hit the thumb for you! These resources are truly incredibly useful and crystal clear. Thanks for sharing!

  • @zecuse
    @zecuse 9 หลายเดือนก่อน

    Due to symmetry of a clock, the 90°, 180°, & 270° hand positions also occur 11 times in 12 hours. This ends up coming out to 44 occurrences every 12 hours which equates to about 16 minutes and 21.818181 seconds.

  • @Onlinefizik
    @Onlinefizik 10 หลายเดือนก่อน

    Great 👌

  • @meyou4912
    @meyou4912 10 หลายเดือนก่อน

    Bro best visual explanation of why e shows up.

  • @bagusaldyguna2839
    @bagusaldyguna2839 11 หลายเดือนก่อน

    tysm buddy

  • @lilamdan
    @lilamdan 11 หลายเดือนก่อน

    Might be depended on the type of the clock

  • @rikbagdi8103
    @rikbagdi8103 11 หลายเดือนก่อน

    how to save data as .dat file

  • @aminiphysics
    @aminiphysics ปีที่แล้ว

    thanks to your tutorial series,it's grate

  • @ricardoaer
    @ricardoaer ปีที่แล้ว

    Terrific! Thanks so much

  • @jonatanpaschoal7362
    @jonatanpaschoal7362 ปีที่แล้ว

    Done

  • @budapest233
    @budapest233 ปีที่แล้ว

    The tutorial was well done, thank you! I wonder though why I shouldn´t use Excel or anything similar for these kind of tasks, where everything you´ve prompted the (80´s-90´s) hard way can be literally done with 2-3 mouse clicks? I´m not trolling, I´m really curious! Is there something GNUPLOT offers later on, with advanced techniques, that can´t be done anywhere else much simpler? Will it be worth for me learning this? I´ve just downloaded it for a test run.

  • @jorgemontano7494
    @jorgemontano7494 ปีที่แล้ว

    very nice it is extremly useful to do quickly graphs with terminal

  • @i-ska
    @i-ska ปีที่แล้ว

    Loop has been proven impossible in Collatz conjecture, it was cracked by the same person who cracked the double slit experiment. That proved that the big bang and particle model are both wrong, wonder why those in the big money big bang & particle industries controlling the media are not backing the proof th-cam.com/video/cbzF7C0l23A/w-d-xo.htmlsi=IMwZDe06D46fxEhg

  • @julioreyram
    @julioreyram ปีที่แล้ว

    Helped me sink down a bunch of concepts that I've been reading but wasn't able to connect all together. Really nice how you threaded the story! Thx <3

  • @vidyapith6046
    @vidyapith6046 ปีที่แล้ว

    Gnuplot in Bengali th-cam.com/play/PLjVF8cuDkJFsSz6Dbct3-fz8JN881D9Gq.html&si=DKOhgfBTPWyGcdke

  • @Optimal_Living01
    @Optimal_Living01 ปีที่แล้ว

    This video was better at conveying the message better than 3b1b in respect to manim lol

  • @MiguelAngelLopezP
    @MiguelAngelLopezP ปีที่แล้ว

    I’m glad to say that it’s not a dream, the bank is currently paying me 13% I guess it just depends on the country. For reference inflation is currently at 6%

    • @MathAndPhysics
      @MathAndPhysics ปีที่แล้ว

      Yes, the world has definitely changed since I made this video.

    • @anunuevesiete
      @anunuevesiete ปีที่แล้ว

      Same, I’m getting 15%, crazy isn’t it?

  • @1495978707
    @1495978707 ปีที่แล้ว

    0:50 To be very explicit, that means this transformation must be *invertible*. Saying that we can get the original function back is not as clear of a statement. Not only that, but the Legendre Transformation is it’s own inverse! The term for such a transformation is an involution. This is part of why it makes so much sense to use the Legendre transformation in thermodynamics, you use one simple transformation to get between any of the representations of your system

  • @MamtaSingh-d3s7d
    @MamtaSingh-d3s7d ปีที่แล้ว

    Sir, can you please post a video on how to do density plotting/distribution curved/filledcurves in gnuplot?

  • @adrijaroy4172
    @adrijaroy4172 ปีที่แล้ว

    What is the expression of lie derivative of the matric tensor??

  • @beccacross7880
    @beccacross7880 ปีที่แล้ว

    what is x_0?

  • @danbakana
    @danbakana ปีที่แล้ว

    Your explanation was very good. However, I still have a question. I understood that the Legendre transformation is like a parameterization of the function f(x) by its derivative at x, f'(x), but I don't understand why g(p) = ±x. Did you arrive at this result or establish it? If you established it, why?

  • @renzostefanmp7937
    @renzostefanmp7937 ปีที่แล้ว

    This is the best video I've encountered on the Lie derivative. Thanks a lot, I'm sad because I didn't find your channe earlier. Gonna binge watch all these videos to see if I can pass tomorrow's exam.

  • @SomeJu4n
    @SomeJu4n ปีที่แล้ว

    Would be nice if you also show a case where the method is very sensitive to the initial guess, an even results in an infinite cycle of iterations that never converges. Just imagine a function F(x) that has a non-zero local minimum or maximum... you can pick an initial guess Xo (near the location of this local min/max) such that the tangent has nearly 0 slope...this tangent will almost be parallel to the x axis....and therefore its extension will definitely intersect the x-axis, but very far away from the initial guess....then you may have had the root close to Xo, but the method got you far away immediately. You can even construct a function F(x) such that there is a first guess Xo that after the first iteration results in another guess X1, and a second iteration takes X1 back to Xo....and the method cycles between these two values...never converging to the actual root. You can then show that even in this case, with initial guesses that end up in an infinite cycle...you can still re-try with a new guess....the average of all the X's in the cycle....and eventually the root will be found.

  • @bimDe2024
    @bimDe2024 ปีที่แล้ว

    This tutorial series is gold.

  • @gern0tk
    @gern0tk ปีที่แล้ว

    Why do banks not compund continuously? I mean it's sounds complicated but all they really need to do is evaluate the Euler function once per year and pay me the interest I deserve.

  • @sushi2slushy
    @sushi2slushy ปีที่แล้ว

    nothing governs p/r both equals to 1, so this is hard fitted outcome?

    • @MathAndPhysics
      @MathAndPhysics ปีที่แล้ว

      I put them both to 1 at the end because I wanted to extract just the e from p*e^r. Also, I think the example of starting with 1€ and an interest rate of 100% is very intuitive, but you could of course run this with any numbers p and r and use the general formula. The point I wanted to make at the end is that this simple problem with nice integer numbers has a solution that contains an irrational number. It is just math but to me it surely feels like a bit of magic.

    • @sushi2slushy
      @sushi2slushy ปีที่แล้ว

      @@MathAndPhysics hey thanks for the reply! i think what really got me to understand this is that for ANY interest_rate, the maximum interest approaches e^interest_rate (with regular -> ~infinite frequent payments)

    • @HUGOPEREZ12345
      @HUGOPEREZ12345 10 หลายเดือนก่อน

      ​@@MathAndPhysicswhy not I=P(1+r)^t ?

  • @axellejeune4709
    @axellejeune4709 ปีที่แล้ว

    where can i find the website on wich you made your aniamtion with electrons, ... ?

  • @alcatel1s508
    @alcatel1s508 ปีที่แล้ว

    7:78

    • @alcatel1s508
      @alcatel1s508 ปีที่แล้ว

      qSL unsupported Support invalid debitCard 's bawaatwwxxx opskatww vkb vboeatwwooe??? IBAN smartCash SEPA Online Kontis ⁰∅⁰

  • @alcatel1s508
    @alcatel1s508 ปีที่แล้ว

    qSL my fav rpiZërô WH reflection gestic controll mtp-||| GOOjprt esc/pos

  • @buhtastic
    @buhtastic ปีที่แล้ว

    Thank you for tutorial

  • @soumyaranjandash1026
    @soumyaranjandash1026 ปีที่แล้ว

    please tell me how I can remove the cb scale at right hand side and show only plot

  • @yrus7802
    @yrus7802 ปีที่แล้ว

    Great❤

  • @Thefan141
    @Thefan141 ปีที่แล้ว

    I tried this, and it didn't work for me. Latex told to convert my eps file into a pdf. Does anybody know what I did wrong?

  • @antoine3362
    @antoine3362 ปีที่แล้ว

    thank you michael 🕺🏻

  • @MarkLapasa
    @MarkLapasa ปีที่แล้ว

    After hitting limitations with Excel, I've added gnuplot to my toolbox thanks to your tutorial series!