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Exploring Maths
Приєднався 12 чер 2022
Flow in a Rectangular Channel | Fourier Series & Laplace's Equation
Chapters:
00:00 Introduction
00:45 2D Problem
05:40 3D Problem
08:00 Solving Laplace's Equation
13:10 Calculating Fourier Series
17:00 Surprising Infinite Sums
00:00 Introduction
00:45 2D Problem
05:40 3D Problem
08:00 Solving Laplace's Equation
13:10 Calculating Fourier Series
17:00 Surprising Infinite Sums
Переглядів: 611
Відео
Matched Asymptotic Expansions & Boundary Layers | Theory and Sample Problem
Переглядів 2203 місяці тому
Explaining the method of matched asymptotic expansions, and demonstrating it on an example problem.
Predator-Prey Population Models || Lotka-Volterra Equations
Переглядів 28 тис.2 роки тому
An introduction to the Lotka-Volterra population models and analysing their solutions in the phase plane.
HARD River Crossing Maths Problem | Can You Solve It?
Переглядів 752 роки тому
A challenging differential equation problem.
Which Monopoly Properties are the Best? | Understanding Markov Chains
Переглядів 1,2 тис.2 роки тому
Using Markov chains to help us win at Monopoly Look out for new videos every Friday Let me know if there are any topics you'd like me to explore in future videos
Excellent video! I've been trying to follow along and derive the equations, one thing that I'm not sure off is at ~8:40, where you write the boundary conditions after seperating the variables. Why is it f(-/+w) = -g(y) and not 0
Ah, good question. If you look at 7:55, the values of the particular solution on the boundaries (left hand side) aren't all 0. So we need the general solution (right hand side) to balance those out, so that it works when we add the 2 solutions together
@@exploringmaths9336 Yes, thank you that makes a lot of sens! And thank you again for this great video
Lovely video, I wish I could do science communication that well myself
Isn't the fact that the eigenvalues have no real component enough to determine that the trajectories don't spiral in or out?
That is the case here, but it can't be guaranteed in general. Because we have linearised the system, we're ignoring any higher order terms. Have a look at what happens in the example dx/dt = y, dy/dt = y^3 - x.
@@exploringmaths9336 OK thanks - I wasn't thinking of that.
Thank you for sharing this videos. Looking forward to watching "Phase planes" videos!
Thank you my friend. Currently studying to enter into grad school for Quantitative Bio. The journey has been challenging but it is people like you who make the challenge seem surmountable... and loads of fun! Please make others! Perhaps SIR model of disease transmission, Levins meta-population model, Tillman's model of resource competition, or Holling's disc equation. Best wishes fellow nerds!
I saw your video about Lotka volterra, i'm studying biology and it helped me to understand a bit more. I thought I'd be supercool if you could do another video on dynamic systems, or dynamic equilibrium, or maybe idk what's the math concept underlying that kind of models in ecology. It'd be perfect for people not so close to maths but to biology to clarify the ideas behind population and community dynamics.
Thanks for this. I'm not clear how the overlap term arises. Could you clarify this, please?
Looking again, I assume the overlap term fixes up the x=0 boundary condition exactly and the x=1 boundary condition as epsilon -> 0
can you provide me these slides ?
This is one of the best explanations ive seen! Keep doing what your doing!
Likely the best video on introductory Predator-Prey models!
how do you show the ODE's existance and uniqueness?
A professor from a reputed institute taught us this in class in the most time confusing, complicated way. Thank you for simplifying it <3
Was it Berkeley
I feel this pain Mine doesn’t understand that incomplete worksheets aren’t lecture notes and his handwriting is worse than any doctor’s I encountered in 10 years of pharmacist practice before going into engineering
Awesome!!!!!!!!!! Thank you
Excellent
Amazing
nice video
👍