Eric Cytrynbaum

Eric Cytrynbaum

My name is Eric Cytrynbaum and I'm a Professor of Mathematics at the University of British Columbia. I use this channel mostly to post video supplements for the courses I teach. Currently, the channel has videos relating to MATH 100 and 102 (two similar first year calculus course), MATH 256 (a second year ODE course for Engineers), and MATH 361 (a course on Mathematical Biology intended for Math Majors and students in other programs with an interest in both mathematics and biology). There might also be one or two videos related to a grad course I teach (Math 461/560).

During the COVID-19 pandemic, I was involved with the BC COVID-19 Modelling Group and produced numerous videos about our analysis. The KZread channel for the group is here: www.youtube.com/@bccovid-19modelling

I have plans in the near future to launch a new channel focussed on Mathematical Modelling. More on that when it launches.

Derivative notation

Derivative notation

The general product rule

The general product rule

Implicit differentiation

Implicit differentiation

Пікірлер

  • @nafiskarim3071
    @nafiskarim30712 ай бұрын

    It was just an awesome explaination..I really needed the step by step explaination.

  • @true_betman
    @true_betman4 ай бұрын

    What are you trying to explain?

  • @ericcytrynbaum
    @ericcytrynbaum4 ай бұрын

    This video makes a bit more sense if you watched the previous one on the course playlist to which it belongs. kzread.info/dash/bejne/Z4iMssajfcewdaw.htmlsi=HmdJL7OnTDgwEGi3

  • @YairCat
    @YairCat4 ай бұрын

    Incredible explanation, did it every single step of the way towards the solution!

  • @zuhairalsaffar7001
    @zuhairalsaffar70014 ай бұрын

    Sir, how could one thank you for your help and support me to overcome this subject thank you so much 💖 ❤ 💗 ♥ 💕

  • @user-dh6xq5oi3j
    @user-dh6xq5oi3j5 ай бұрын

    Thankyou

  • @Thereisnoname-_-
    @Thereisnoname-_-5 ай бұрын

    w eric

  • @elerimorales2506
    @elerimorales25066 ай бұрын

    Elegant and easy

  • @Vollendung5716
    @Vollendung57166 ай бұрын

    save my life before exam,thank you

  • @user-vc4dc8yg5p
    @user-vc4dc8yg5p8 ай бұрын

    Hello Eric,What software can be used to bifurcate the non-smooth vector field? Especially,filippov systems

  • @SwayamGhanghas
    @SwayamGhanghas8 ай бұрын

    Chl ht BKL

  • @yuvrajchadha1021
    @yuvrajchadha10218 ай бұрын

    🤣

  • @SwayamGhanghas
    @SwayamGhanghas8 ай бұрын

    Pdhne aaya hai ya comment dekhne ​@@yuvrajchadha1021

  • @yuvrajchadha1021
    @yuvrajchadha10218 ай бұрын

    @@SwayamGhanghas comment dekhne

  • @yuvrajchadha1021
    @yuvrajchadha10218 ай бұрын

    I can understand

  • @Daniel-li6gu
    @Daniel-li6gu8 ай бұрын

    you are the man Eric

  • @sumitroy5204
    @sumitroy52048 ай бұрын

    I can't understand 😢

  • @yessypincmun3980
    @yessypincmun39808 ай бұрын

    how about different frequency for example: x(t)=25-10sin(30t)+15cos(45t)+20sin(45t)+5cos(60t) rewrit as single sine

  • @ericcytrynbaum
    @ericcytrynbaum8 ай бұрын

    If you plot that function you’ll see it isn’t a simple sin function.

  • @asapvarg
    @asapvarg9 ай бұрын

    Very helpful, thank you!

  • @wesselverstelle8340
    @wesselverstelle834010 ай бұрын

    ai thanks legend!!

  • @Shreejaya
    @Shreejaya Жыл бұрын

    I can't get the slopes part & substracting part

  • @suparnadash1580
    @suparnadash1580 Жыл бұрын

    sometimes the nulclines has not been ploted. please explain the reosen?

  • @paulkelemen5087
    @paulkelemen5087 Жыл бұрын

    Very helpful. Thank you.

  • @citrarizqin
    @citrarizqin Жыл бұрын

    Thank you so much for the explanation, sir! This helps me a lot!

  • @gradozero8140
    @gradozero8140 Жыл бұрын

    Is it possible to write a ramp than increases from 0 whenever f(x) it's 0?

  • @ericcytrynbaum
    @ericcytrynbaum Жыл бұрын

    I’m not sure what you mean.

  • @gradozero8140
    @gradozero8140 Жыл бұрын

    @@ericcytrynbaum Thank you, I would like to create an Heaviside H(x) function that creates an increasing ramp whenever another function f(x) composed by irregular impulses is = 0. This is for tracking the timing between the impulses (the maximum of the ramp=time between the two specific impulses). However, I'm struggling in trying to make the ramp starting from 0, because the easiest way is to make the Heaviside = x whenever f(x) is equal 0, but in this case, the ramp starts from the actual value of x and not from 0. I would have to subtract something but I don't know what, because this is not known in advance, and if I would already know the spacing between the impulses, I wouldn't need the ramp ...

  • @ericcytrynbaum
    @ericcytrynbaum Жыл бұрын

    @@gradozero8140 If the impulses are at times t_i, then maybe you want something like this: g(t) = sum over i of (H(t-t_i)-H(t-t_{i+1}))(t-t_i) ?

  • @gradozero8140
    @gradozero8140 Жыл бұрын

    @@ericcytrynbaum Thank you very much. It seems this fits well for regular impulses. But if the impulses are not regular, I'm trying to find a rule to make the ramp starting from 0 whenever f(x)=0 like H(x)=[f(x) <1, 1], however this is good with a fixed value of H(x) like H(x)=[f(x) <1, 1] (going to 1 when f(x) is =0) but setting up a ramp seems impossible. If I refer to the variable x, like that, H(x)=[f(x) <1, x], H(x) doesn't start from 0, but when f(x)=0 H(x) starts from the actual value of x. I should subtract something, but not x, otherwise it will not increase ... I'm wondering if it's possible to create such a piecewise function

  • @MinecraftWithRichy
    @MinecraftWithRichy Жыл бұрын

    your videos are so clear thank you for working it out so thoroughly.

  • @humahdi4317
    @humahdi4317 Жыл бұрын

    Dear Eric, could you please provide me with tutorial about plotting two bifurcation parameters of Hopf or any explanation from you is highly appreciated

  • @calvinjackson8110
    @calvinjackson8110 Жыл бұрын

    You did not argue in detail why the first limit as t goes to infinity is zero.

  • @tonychen3306
    @tonychen3306 Жыл бұрын

    Hi! Thank you for the awesome video! Would you mind sharing the Desmos notebook? I would like to try out what would repeated eigenvalue look like. Thanks!

  • @tfl_supers5362
    @tfl_supers5362 Жыл бұрын

    Mate I’m in oxford and my lectures on this are shit

  • @mankanwarsingh1616
    @mankanwarsingh1616 Жыл бұрын

    great explanation

  • @user-bx1hl7zx6s
    @user-bx1hl7zx6s Жыл бұрын

    Thank u very much

  • @maylingliu
    @maylingliu Жыл бұрын

    Thank you so much!

  • @alishahocane6490
    @alishahocane6490 Жыл бұрын

    Thanks

  • @lazywarrior
    @lazywarrior Жыл бұрын

    very cool

  • @The_bengali_political_analyst
    @The_bengali_political_analyst Жыл бұрын

    Excellent!

  • @Mahlodi_Makobe
    @Mahlodi_Makobe Жыл бұрын

    appreciate this video so so much

  • @kumuduninilanthi9223
    @kumuduninilanthi9223 Жыл бұрын

    why did you put a limit -1/2 to 1/2 instead of 0 to 1? if it is not a step function we just put f(x)=1 or something but how do we put value for f(x) if it was a step function? (for final answer )

  • @jormaq7851
    @jormaq7851 Жыл бұрын

    I like your videos, but I have a question. What do the green dots you get with the PERIODIC command at the HB point mean? and what information do they give me about the system? Thanks. I expect more xppaut videos

  • @ericcytrynbaum
    @ericcytrynbaum Жыл бұрын

    They denote a periodic solution. Their heights (one above, one below the steady state) are the min and max X value reached by the oscillation and the green dots indicate that the periodic solution is stable.

  • @martinelosudietz6795
    @martinelosudietz67952 жыл бұрын

    I didn't find this particular equality elsewhere. Thanks for sharing, i found it really useful for understanding the response to armonic loads acting on dynamic systems.

  • @irisc3485
    @irisc34852 жыл бұрын

    Hi Eric, juts wondering for the ode file, why do I have this "illegal expression: X " "Error allocating or compiling X’ " when I put it into XPP

  • @javeriaayub6203
    @javeriaayub62032 жыл бұрын

    Hi, I want to find Poincare section plane coefficients. Can you guide me on how this software is helpful in my concern?

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    I've never tried using xpp for Poincare maps and related calculations but maybe this page will help: www.math.pitt.edu/~bard/bardware/tut/xppphase.html

  • @luisfernando262
    @luisfernando2622 жыл бұрын

    Excellent explanation. Thank you so much!

  • @jj6407
    @jj64072 жыл бұрын

    👏

  • @robertparaynojr4259
    @robertparaynojr42592 жыл бұрын

    Thank you, this video lecture gives me a huge help. Also, the explanation is clear!

  • @therealtucks
    @therealtucks2 жыл бұрын

    Come back

  • @_framer
    @_framer2 жыл бұрын

    Thanks for the video! In the first example, would the last term of heaviside functions (u3-u4) be subtracted instead of added onto the equation since it is dropping at t=3?

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    I included the minus sign in the function (4-t) so your suggestion would be correct if you changed that to (t-4).

  • @gilbert4004
    @gilbert40042 жыл бұрын

    At around 1:30, you could have integrated from -1/2 to 0, and plugged in +1 for your f(x), correct? Just making sure I understand. Great vid!

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    Yes, as long as the integral is over one full period, the answer is the same.

  • @gilbert4004
    @gilbert40042 жыл бұрын

    @@ericcytrynbaum Great, thank you!

  • @Klaus_Gamlng
    @Klaus_Gamlng2 жыл бұрын

    I’ve tried calculating your theta multiple times, and I never get 0.64 radians, the closest I got was 0.68. Not sure what I’m doing wrong

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    Try arctan(3/4) or arcsin(3/5).

  • @Klaus_Gamlng
    @Klaus_Gamlng2 жыл бұрын

    @@ericcytrynbaum can you explain why it's arctan or arcsin? I'm not understanding

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    @@Klaus_Gamlng sin(theta)=opposite/hypotenuse so to get theta, apply arcsin to both sides. arcsin is the same as sin^(-1). The sides of the triangle are 3/5, 4/5, and 1 with the 3/5 being opposite the angle theta. So sin(theta)=(3/5)/1. Or you could also use tan(theta)=(3/5)/(4/5)=3/4. Those both give you the same answer.

  • @Klaus_Gamlng
    @Klaus_Gamlng2 жыл бұрын

    @@ericcytrynbaum I thought sin(theta)=o/h because of SohCahToa? I may just be overthinking it, but I'm trying to work on some calc 4 homework, and im just having a hard time

  • @hms3021
    @hms30212 жыл бұрын

    Why not maximise the matlab window before recording?

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    That’s a good question/suggestion. I have no idea why I didn’t do that. Will keep it in mind for the future. Thanks.

  • @anjanballav9348
    @anjanballav93482 жыл бұрын

    make some more videos for this series Sir. Its a request.

  • @ericcytrynbaum
    @ericcytrynbaum2 жыл бұрын

    I'm glad the videos I've made are useful for you. Unfortunately, I'm unlikely to make more of these for the time being. Perhaps next year when I once again teach the course I made them for.

  • @brayanalexanderruiz3097
    @brayanalexanderruiz30972 жыл бұрын

    la buena panita 😍😍😍

  • @article1372
    @article13722 жыл бұрын

    Huh, this is funny, I found this video by googling it,

  • @fikky.b8246
    @fikky.b82462 жыл бұрын

    same it was the first video that popped and im meant to have watched it.

  • @bhanusharma8684
    @bhanusharma86842 жыл бұрын

    Hello Eric. Your videos are really helpful. I am working on Pred-Prey model with 3dimension equations. Could you please make some videos on how to do phase plane analysis for 3d or more dimension system? Kindly reply