Brian Sullivan
Brian Sullivan
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2D Linear Wave Simulation in Python - Leapfrog Integration
In this video we extend our previous 1D Linear Wave code to two spatial dimensions.
Slice notation for numpy arrays makes this a very quick conversion, and 3D axes in matplotlib make the solution easy to visualize.
Here is a link to the source code for the 1D Solution as well as the 2D solution (both codes are in the repository):
github.com/bpatricksullivan/1d_wave_leapfrog
If you missed earlier episodes in this series, here they are:
czcams.com/video/B4rziSNUpAA/video.html
czcams.com/video/4i_Qm_YMHjs/video.html
czcams.com/video/nIuVn14PyJw/video.html
czcams.com/video/VLl-03mSO4U/video.html
czcams.com/video/fTprfksvoXc/video.html
zhlédnutí: 3 048

Video

Testing Python Solution to the 1d Linear Wave Equation (Leapfrog Integration)
zhlédnutí 283Před 6 měsíci
Testing Python Solution to the 1d Linear Wave Equation (Leapfrog Integration)
1D Linear Wave Simulation in Python
zhlédnutí 583Před 7 měsíci
1D Linear Wave Simulation in Python
The Leapfrog Algorithm with Numpy Arrays and Slice Notation
zhlédnutí 191Před 7 měsíci
The Leapfrog Algorithm with Numpy Arrays and Slice Notation
The Wave Equation & the Leapfrog Algorithm Part 1
zhlédnutí 571Před 7 měsíci
Here is a link to the source code for the 1D Solution for this system as well as the 2D solution (both codes are in the repository): github.com/bpatricksullivan/1d_wave_leapfrog Here are links to the other episodes in this five part series: czcams.com/video/B4rziSNUpAA/video.html czcams.com/video/4i_Qm_YMHjs/video.html czcams.com/video/nIuVn14PyJw/video.html czcams.com/video/VLl-03mSO4U/video.h...
Introduction to Derivatives
zhlédnutí 150Před 10 měsíci
Introduction to Derivatives
Chain Rule Examples with Trig Functions
zhlédnutí 67Před rokem
Chain Rule Examples with Trig Functions
Chain and Product Rule Together: A parabola times a circle
zhlédnutí 22Před rokem
Chain and Product Rule Together: A parabola times a circle
Chain Rule Example: The "mount doom" function
zhlédnutí 34Před rokem
Chain Rule Example: The "mount doom" function
Chain Rule Example: Reciprocal of A Polynomial
zhlédnutí 167Před rokem
Chain Rule Example: Reciprocal of A Polynomial
Chain Rule: Cube Root of a Parabola
zhlédnutí 29Před rokem
Chain Rule: Cube Root of a Parabola
Chain Rule: Derivative of a Cuspy Cube Root
zhlédnutí 22Před rokem
Chain Rule: Derivative of a Cuspy Cube Root
The Harmonic Oscillator
zhlédnutí 143Před 2 lety
The Harmonic Oscillator
Derivative of Square Root X by Definition...Whoa!
zhlédnutí 128Před 2 lety
Derivative of Square Root X by Definition...Whoa!
Using the Limit Definition to Find the Slope of the Tangent Line
zhlédnutí 1,1KPřed 2 lety
Using the Limit Definition to Find the Slope of the Tangent Line
An Introduction to Derivatives
zhlédnutí 134Před 2 lety
An Introduction to Derivatives
Einstein Solids
zhlédnutí 3,7KPřed 3 lety
Einstein Solids
Multiplicity - How Many Microstates in a Macrostate
zhlédnutí 944Před 3 lety
Multiplicity - How Many Microstates in a Macrostate
Counting Heads and Tails- Multiplicity in Two State Systems
zhlédnutí 125Před 3 lety
Counting Heads and Tails- Multiplicity in Two State Systems
Adiabatic & Isothermal Processes Compared
zhlédnutí 64Před 3 lety
Adiabatic & Isothermal Processes Compared
Work and Adiabatic Processes
zhlédnutí 34Před 3 lety
Work and Adiabatic Processes
Work in Isothermal Processes
zhlédnutí 28Před 3 lety
Work in Isothermal Processes
Use the IMPORTHTML command to scrape webpage data to a spreadsheet.
zhlédnutí 259Před 3 lety
Use the IMPORTHTML command to scrape webpage data to a spreadsheet.
Pressure in a Straw
zhlédnutí 683Před 3 lety
Pressure in a Straw
What is Pressure?
zhlédnutí 38Před 3 lety
What is Pressure?
Reconstructing the Data with a Model Function
zhlédnutí 257Před 3 lety
Reconstructing the Data with a Model Function
Finding the Damping Coefficient with Log-Linear Fitting
zhlédnutí 1,8KPřed 3 lety
Finding the Damping Coefficient with Log-Linear Fitting
find period
zhlédnutí 275Před 3 lety
find period
locate peaks
zhlédnutí 2KPřed 3 lety
locate peaks
Load Range Data for a Damped Spring into a CoLab Notebook
zhlédnutí 272Před 3 lety
Load Range Data for a Damped Spring into a CoLab Notebook

Komentáře

  • @savazeroa
    @savazeroa Před 4 dny

    Dang i came up with this myself at school

  • @Keith_Untitled
    @Keith_Untitled Před 5 dny

    Noicr

  • @ts37924
    @ts37924 Před 8 dny

    Thank you so very very much

  • @bob-pq6ef
    @bob-pq6ef Před 9 dny

    Excellent thank you

  • @formieboy2615
    @formieboy2615 Před 16 dny

    Correct me if I'm mistaken, I'm new to this, but shouldn't it be lim h->1 since we're trying to see how the slope will react as we bring it closer to the x value of 1?

  • @SM_Price
    @SM_Price Před měsícem

    This is an extraordinarily helpful video. Thank you!

  • @happyfish3961
    @happyfish3961 Před 2 měsíci

    Hi (:

  • @MRT-co1sd
    @MRT-co1sd Před 2 měsíci

    So to get the correct derivative do you just take the average of the right and left slope?

  • @mmgedi
    @mmgedi Před 2 měsíci

    Wow, as the width of the rectangle tends to zero, the height of the rectangle tends to the slope of the original function. In other words, that infinitesimal sliver becomes the tangent line at that specific instant of time. Thank you so much!

  • @yashashreemhase8429
    @yashashreemhase8429 Před 2 měsíci

    It works 💯

  • @sudeeppaul3403
    @sudeeppaul3403 Před 3 měsíci

    this video is just awesome. Thank you, mate❤❤

  • @UnknownSENKu
    @UnknownSENKu Před 3 měsíci

    thanks

  • @TehLionz
    @TehLionz Před 3 měsíci

    Great Video!!! btw Drew is silly and not listening

    • @bpatricksullivan
      @bpatricksullivan Před 3 měsíci

      Thanks! I guess I did have a Walter White thing going on in 2019. Drew, listen up!

    • @TehLionz
      @TehLionz Před 3 měsíci

      @@bpatricksullivan drew did listen up and I did change the comment bc of drew

  • @sitaraloth
    @sitaraloth Před 3 měsíci

    Very helpful, thank you

  • @henrytzuo8517
    @henrytzuo8517 Před 4 měsíci

    Thank you !! Very Clear!!

  • @AdamKubanek
    @AdamKubanek Před 4 měsíci

    Thank you so much I needed exactly this, taught me so much about sheets and the SIR model . Needed it for my mathematics essay Lifesaver.

  • @sadornsamdi3263
    @sadornsamdi3263 Před 4 měsíci

    I have bien looking for such a video for quite à long time thank you

  • @rizvi1512
    @rizvi1512 Před 4 měsíci

    AMAZING !!!!!!

  • @arlenestanton9955
    @arlenestanton9955 Před 5 měsíci

    A house of bees, is called a hive.

  • @richleprecon718
    @richleprecon718 Před 5 měsíci

    Hello! How could I change the boundaries condition to produce an absorbing boundary ? Thanks alot!

    • @bpatricksullivan
      @bpatricksullivan Před 3 měsíci

      Great question. This is a complex topic. "open outflow boundary conditions", "zero gradient boundary conditions", or "absorbing boundary conditions" are all terms you can use to learn about ways people have approached this problem. They all have flaws. It is a very desirable boundary condition in many real world systems, but it presents significant difficulties in implementation.

  • @mynamesgus4295
    @mynamesgus4295 Před 5 měsíci

    thanks for this !

  • @syedamahwish4235
    @syedamahwish4235 Před 5 měsíci

    Best explanation I have seen of the SIR model! I have watched so many videos to understand this

  • @whatitmeans
    @whatitmeans Před 5 měsíci

    3Blue1Brown has a beautiful video about this topic, but your explanation is much more intuitive. Congrats.

  • @danlule1
    @danlule1 Před 6 měsíci

    Thanks a lot! This is the best explanation of complex math to someone who has no understanding of calculus.

  • @samueldeandrade8535
    @samueldeandrade8535 Před 6 měsíci

    The example was not good. Like, not good at all.

  • @Yguy
    @Yguy Před 6 měsíci

    I don't understand why such an important explanation was not in my book. Nice explanation though, Keep it up!

  • @lanog40
    @lanog40 Před 6 měsíci

    I’d like to check making some custom wave simulations over the summer, so this will help!

  • @SuadM2
    @SuadM2 Před 6 měsíci

    Nice job! I look forward to witnessing similar efforts applied to the 2D shallow water equations.

    • @bpatricksullivan
      @bpatricksullivan Před 6 měsíci

      Thanks! I have a few projects higher in my queue for courses I am teaching, but the Saint-Venant Shallow Water Equations are on my list.

  • @mustafayigitkartal4257
    @mustafayigitkartal4257 Před 6 měsíci

    This is great, I'm glad the algorithm brought me here 👍

    • @bpatricksullivan
      @bpatricksullivan Před 6 měsíci

      Thank you so much! I am glad the algorithm brought you here as well! I have a lot more similar content in my pipeline over the next few weeks. Please let me know any topics you'd like to see covered within computational physics, data science, data visualization, Python programming, or adjacent areas.

  • @beaverbuoy3011
    @beaverbuoy3011 Před 6 měsíci

    Nice

    • @bpatricksullivan
      @bpatricksullivan Před 6 měsíci

      Thank you! Let me know anything related you'd like to see covered in a video.

  • @lNightmarel
    @lNightmarel Před 7 měsíci

    his voice is 🗿✨

  • @hoteny
    @hoteny Před 7 měsíci

    Thanks. Even tho I am free from calc-1 now, it was a good watch.

  • @jagroopahluwalia
    @jagroopahluwalia Před 7 měsíci

    thanks mate, you explained it better than my teacher

  • @EE-Spectrum
    @EE-Spectrum Před 7 měsíci

    Brilliant! Thanks so much.

  • @benbearse4783
    @benbearse4783 Před 7 měsíci

    The way that let me understand integrals the best is that the anti derivative of a function is literally the area formula for under the graph. Like take y=x for example. The distance between any point is X and the height of any point is Y which equals X. This forms a triangle because it’s just a straight diagonal line. The formula for the area of a triangle is bh/2 so base (x) times height(x) divided by 2 =(x^2)/2 Which I thought was really cool. This continues for every other possible line The area for under a quadratic is 1/3(bh) where base is still x and height is x^2 (hence y=x^2) so (x^3)/3 is the area

    • @lyricass7810
      @lyricass7810 Před 4 měsíci

      Your intuition is so much better than 3blue and this video, I don't understand why you didn't get single like, thanks for commenting bro your comment made my day, but I still don't understand how adding infinitesimally small rectangles is equal to taking anti derivative of a integral function f(x) 🥲. Why finding anti derivative will do the work of adding infinitesimally small rectangles? And how ? If you have intuition for this please let me know bro 🥲.

    • @benbearse4783
      @benbearse4783 Před 4 měsíci

      @@lyricass7810 Thank you! I really appreciate what you said. Honestly, I’m just glad that my comment could help at least one person. When it comes to the logic behind why the anti derivative gives the area could be best explained saying that, the derivative of a function is found by dividing the function by a tiny change dx, while the area is found by multiplying it by tiny changes dx(which by multiplying tiny change in x by the formula for y getting the area for the rectangle under that little instance of the graph), ultimately undoing what the derivative did. Hope this helps! If not i can try and clarify for you.

    • @lyricass7810
      @lyricass7810 Před 4 měsíci

      @@benbearse4783 thanks for the reply bro, I would say I understood 50 percent 😂, can you clarify clearly please. How anti derivative will take care of adding infinitesimally small rectangles with different areas 🥲. Thanks in advance,

    • @bruhifysbackup
      @bruhifysbackup Před 3 měsíci

      ​@@lyricass7810And that is where fundamental theorem of calculus steps in.

  • @ebog4841
    @ebog4841 Před 7 měsíci

    ribbit

  • @gravitystorm58
    @gravitystorm58 Před 8 měsíci

    Loved the video, great explanation! I have a question though; when you divide by dx and then take the limit, on the right side of the equation you’d have something of the form 0/0, does this matter?

    • @bpatricksullivan
      @bpatricksullivan Před 7 měsíci

      That is one of the most significant results of calculus. Often we have ratios of infinitesimals which we can evaluate in the contexts of limits, and although both numerator and denominator approach zero, they approach zero at different rates, and as a result the ratio remains finite and non-zero.

  • @slowfern
    @slowfern Před 8 měsíci

    very helpfull

  • @WillSmith-ui1pb
    @WillSmith-ui1pb Před 8 měsíci

    Good shyt my nigga. Real shit You a Physics God.

  • @stevves4647
    @stevves4647 Před 9 měsíci

    This video is gold!

  • @themonrovian8441
    @themonrovian8441 Před 9 měsíci

    After doing an entire physics degree I never saw an explanation as clear as this for illustrating the fundamental theorem of calculus. Bravo sir 👏

  • @myonn0319
    @myonn0319 Před 9 měsíci

    This should be in every calculus textbook!

  • @BilalAhmed-on4kd
    @BilalAhmed-on4kd Před 10 měsíci

    I have a q about this, we must've added the limit as dx->0 before the last step So we have Lim dx->0[g(x+h)-g(x)]=f(x)dx So when we divide by dx we have { Lim dx->0[g(x+h)-g(x)] }/dx=f(x) So what we actually have now is that the numerator applies only on the numerator of the lhs,which is not exactly what the derivative of a function is

  • @toddmiller6232
    @toddmiller6232 Před 10 měsíci

    Just wonderfully tasty

  • @Yue27s
    @Yue27s Před 10 měsíci

    Real thanks bro, you can explain it in really simple term, i dont know is that simple, real thanks!

  • @marcusmarcula
    @marcusmarcula Před 10 měsíci

    Thanks for taking the time to make these videos.

    • @marcusmarcula
      @marcusmarcula Před 10 měsíci

      you on mathstack or twitter by chance?

    • @bpatricksullivan
      @bpatricksullivan Před 10 měsíci

      No. I've written answers for Socratic, but not Math Stack Exchange or Twitter yet. I will look into it.

  • @JavierBonillaC
    @JavierBonillaC Před 10 měsíci

    That is really very good.Every single rectangle has as a height the original function and as width dx. So if the slope is constant (say a horizontal line) the area will alyas be dx times 1. I seem to understand. thank you so much for this super interesting video.

  • @amirfaris5526
    @amirfaris5526 Před 11 měsíci

    sir, where is part 2?

  • @aneeshaperera6680
    @aneeshaperera6680 Před 11 měsíci

    Thank you for clear explanation

  • @toddmiller6232
    @toddmiller6232 Před rokem

    We should rule out outliers because they're sus.