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Eric Cytrynbaum
เข้าร่วมเมื่อ 16 ก.ย. 2013
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 TH-cam 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.
During the COVID-19 pandemic, I was involved with the BC COVID-19 Modelling Group and produced numerous videos about our analysis. The TH-cam 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.
Taylor polynomial calculation shortcuts - example 2
Taylor polynomial calculation shortcuts - example 2
มุมมอง: 138
วีดีโอ
Taylor polynomial calculation shortcuts - theory and an example
มุมมอง 8411 หลายเดือนก่อน
Taylor polynomial calculation shortcuts - theory and an example
Taylor polynomial - an application to calculating a series
มุมมอง 7411 หลายเดือนก่อน
Taylor polynomial - an application to calculating a series
Strategies for setting up applied optimization problems
มุมมอง 14811 หลายเดือนก่อน
Strategies for setting up applied optimization problems
Calculating the global maximum for a two-variable function
มุมมอง 27311 หลายเดือนก่อน
In this video, I demonstrate a method for finding the extrema for a function of two variables.
Logarithmic differentiation
มุมมอง 5811 หลายเดือนก่อน
In this video, I show how to use logarithmic differentiation to calculate the derivative of a function that has the form f(x)^g(x).
Phase lines as a qualitative tool for analyzing differential equations
มุมมอง 857ปีที่แล้ว
This video is the fourth in a series of videos introducing differential equations. I use the concept of a slope field to explain what a phase line is for autonomous differential equations (DEs) and how they can be used to quickly understand solutions to DEs without having to solve for an explicit formula for the solutions. In it I cover the definition of a steady state and stability of steady s...
Solving linear ODEs using a phase-line inspired method
มุมมอง 637ปีที่แล้ว
This is the fifth video in a series of (five) videos introducing differential questions. In it I use the phase line to reveal the similarity between all linear (first order) DEs and use that to come up with a method of solving them.
Some modelling applications that lead to linear (and one non-linear) differential equations
มุมมอง 388ปีที่แล้ว
This is the second video in a series about differential equations. In it, I discuss some of the places where differential equations appear in the context of modelling real systems.
Slope fields as a qualitative tool to understand solutions to differential equations
มุมมอง 595ปีที่แล้ว
This is the third in a series of videos introducing differential equations. In it, I discuss a first qualitative method (i.e. not looking for an exact solution) for analyzing differential equations called slope fields.
Verifying solutions to differential equations and using ansatzes
มุมมอง 1.1Kปีที่แล้ว
This is the first of a series of videos introducing differential equations intended for students in a first term calculus course. I talk about how to verify that a function is a solution to a differential equation and how to solve an equation using "an educated guess", referred to as an ansatz.
Sketching Graphs - Rational Power Functions
มุมมอง 212ปีที่แล้ว
In this video, I go through two graph sketching examples for power functions for which the power is a rational number (x^(1/3) and x^(2/3)).
Sketching Graphs - Critical points that are neither minima, maxima, nor inflection points.
มุมมอง 394ปีที่แล้ว
In this video, I go through a graph sketching example of a function that has a zero second derivative at a point that is not a minimum, a maxima, or an inflection point.
Sketching Graphs - Minimum, Maximum, or Inflection point
มุมมอง 603ปีที่แล้ว
Sketching Graphs - Minimum, Maximum, or Inflection point
More derivatives using logarithms - the general power rule and (x^x)'
มุมมอง 836ปีที่แล้ว
More derivatives using logarithms - the general power rule and (x^x)'
Finding the derivative of an inverse function
มุมมอง 881ปีที่แล้ว
Finding the derivative of an inverse function
Implicit differentiation - infinite slopes on relations
มุมมอง 885ปีที่แล้ว
Implicit differentiation - infinite slopes on relations
Exponential functions and their derivatives
มุมมอง 895ปีที่แล้ว
Exponential functions and their derivatives
Intro to working with functions in a spreadsheet
มุมมอง 841ปีที่แล้ว
Intro to working with functions in a spreadsheet
The lac operon, bistability and non-dimensionalization
มุมมอง 3012 ปีที่แล้ว
The lac operon, bistability and non-dimensionalization
How to derive the Kolmogorov Forward Equations for a bimolecular reaction
มุมมอง 5152 ปีที่แล้ว
How to derive the Kolmogorov Forward Equations for a bimolecular reaction
Summary of Kolmogorov Forward Equation calculations
มุมมอง 1.5K2 ปีที่แล้ว
Summary of Kolmogorov Forward Equation calculations
Satisfying initial conditions when using Separation of Variables
มุมมอง 8213 ปีที่แล้ว
Satisfying initial conditions when using Separation of Variables
Finding general solutions to PDEs using Separation of Variables
มุมมอง 1.9K3 ปีที่แล้ว
Finding general solutions to PDEs using Separation of Variables
Did someone double check this?
Thanks, Eric for the useful video, can you help me track periodic(stable and unstable) solutions and plot a time series of the periodic solutions emerging from HB points. I am working on the Normal form of the Hopf bifurcation model, I got four HB points, each having emerging periodic solutions (green and open blue circles), I want to track each orbit and plot X vs T graphs to identify the pattern types that each HB point gives and also plot two-parameter diagram from those four HB points, Please help.
Very nice to learn this Kepler's problem, forerunner to the Calculus. Thank you.🌹
It was just an awesome explaination..I really needed the step by step explaination.
What are you trying to explain?
This video makes a bit more sense if you watched the previous one on the course playlist to which it belongs. th-cam.com/video/5TXPdjMdJEI/w-d-xo.htmlsi=HmdJL7OnTDgwEGi3
Incredible explanation, did it every single step of the way towards the solution!
Sir, how could one thank you for your help and support me to overcome this subject thank you so much 💖 ❤ 💗 ♥ 💕
Thankyou
w eric
Elegant and easy
save my life before exam，thank you
Hello Eric,What software can be used to bifurcate the non-smooth vector field? Especially，filippov systems
Chl ht BKL
🤣
Pdhne aaya hai ya comment dekhne @@yuvrajchadha1021
@@SwayamGhanghas comment dekhne
I can understand
you are the man Eric
I can't understand 😢
how about different frequency for example: x(t)=25-10sin(30t)+15cos(45t)+20sin(45t)+5cos(60t) rewrit as single sine
If you plot that function you’ll see it isn’t a simple sin function.
Very helpful, thank you!
ai thanks legend!!
I can't get the slopes part & substracting part
sometimes the nulclines has not been ploted. please explain the reosen?
Very helpful. Thank you.
Thank you so much for the explanation, sir! This helps me a lot!
Is it possible to write a ramp than increases from 0 whenever f(x) it's 0?
I’m not sure what you mean.
@@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 ...
@@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) ?
@@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
your videos are so clear thank you for working it out so thoroughly.
Dear Eric, could you please provide me with tutorial about plotting two bifurcation parameters of Hopf or any explanation from you is highly appreciated
You did not argue in detail why the first limit as t goes to infinity is zero.
u look at it
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!
Mate I’m in oxford and my lectures on this are shit
great explanation
Thank u very much
Thank you so much!
Thanks
very cool
Excellent!
appreciate this video so so much
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 )
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
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.
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.
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
Hi, I want to find Poincare section plane coefficients. Can you guide me on how this software is helpful in my concern?
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
Excellent explanation. Thank you so much!
👏
Thank you, this video lecture gives me a huge help. Also, the explanation is clear!
Come back
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?
I included the minus sign in the function (4-t) so your suggestion would be correct if you changed that to (t-4).
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!
Yes, as long as the integral is over one full period, the answer is the same.
@@ericcytrynbaum Great, thank you!
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
Try arctan(3/4) or arcsin(3/5).
@@ericcytrynbaum can you explain why it's arctan or arcsin? I'm not understanding
@@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.
@@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
Why not maximise the matlab window before recording?
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.
make some more videos for this series Sir. Its a request.
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.