I thought poisson's equation was expressed as: <
Poisson's Equation
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Re: Poisson's Equation
#92I consider Pagerank to be a discrete variation of the poission equation.
Re: Poisson's Equation
#93Earlier quoted context omitted.
I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…
Interesting to think a bit about student/teacher ratios (STR). The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world,…
The flip is an emergent property of the 1 Million to 1 student teacher ratio.
Re: Poisson's Equation
#94We referred to this method of numerically solving Poisson's equation by successively averaging values, as the method of relaxation.
Re: Poisson's Equation
#95I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) It amazes me just how many key topics were so inaccessible to the majority of the class at engineering school. I base this on observations from group study sessions and the hyper-aggressive test curves. I knew lots of people who never got the hang of div/grad/curl, or a Jacobians, or eignenvectors, or Z-transforms... These are k…
> rather than add a curve to a test that makes a 23 out of 100 an "A" grade.
For people wondering why fresh college grads they interview somehow have 4.0 averages yet can’t code FizzBuzz during an interview, this is the answer.
It’s also why good hiring managers do not even bother to look at GPAs listed on CVs. They are so inflated as to be totally meaningless.
Re: Poisson's Equation
#96I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) It amazes me just how many key topics were so inaccessible to the majority of the class at engineering school. I base this on observations from group study sessions and the hyper-aggressive test curves. I knew lots of people who never got the hang of div/grad/curl, or a Jacobians, or eignenvectors, or Z-transforms... These are k…
> rather than add a curve to a test that makes a 23 out of 100 an "A" grade. For people wondering why fresh college grads they interview somehow have 4.0 averages yet can’t code FizzBuzz during an interview, this is the answer. It’s also why good hiring managers do not even bother to look at GPAs listed on CVs. They are so inflated as to be totally meaningless.
That's not true at all. When someone drops 200 resumes on your desk and says, "Find 10 candidates to interview by tomorrow", you need some initial sort criteria.
The truth, my criteria were: #1: university, #2: GPA, #3: keywords. Sure, I was bitten a few times (I hired an MIT master's student who was utterly helpless), but over the course of years doing this, some patterns emerge, and high-GPA absolutely correlates with good candidates.
Sure, there might be a 2.0/4.0 who is a whiz, but sorry charlie, I'm not gonna picky your resume, so apply yourself or start your own company, because a low GPA means you don't give a shit or have some other problem.
Re: Poisson's Equation
#97Earlier quoted context omitted.
Don’t forget APL. I can’t say for sure but I imagine this \ operator came from there.
It's not some obscure symbol; it's just division. It just so happens that we typically "divide" matrices from the left when solving equations like this (and matrix "division" isn't commutative) so instead of `a/b` it's `b\a`.
Yes I know. It’s a solve operator…it’s equivalent to division only in the infinite precision world.
The \ operator differs from the / operator in that it doesn’t compute an inverse … it solves the system of equations. Solver algorithms are more numerically stable ( in that you’re much less likely to have large errors due to wacky input data).
Re: Poisson's Equation
#98Earlier quoted context omitted.
Sure! But it's a bit surprising that they do not use the language-provided linear solver and write simply f=A\b
Wait, how does this work? I'm really rusty, what would the f, A and b correspond to here?
using LinearAlgebra, SparseArrays
N = 10
D1 = sparse(Tridiagonal(ones(N-1),-2ones(N),ones(N-1)))
Id = sparse(I,N,N)
A = kron(D1,Id) + kron(Id,D1)
Re: Poisson's Equation
#99Earlier quoted context omitted.
> rather than add a curve to a test that makes a 23 out of 100 an "A" grade. For people wondering why fresh college grads they interview somehow have 4.0 averages yet can’t code FizzBuzz during an interview, this is the answer. It’s also why good hiring managers do not even bother to look at GPAs listed on CVs. They are so inflated as to be totally meaningless.
That's not true at all. When someone drops 200 resumes on your desk and says, "Find 10 candidates to interview by tomorrow", you need some initial sort criteria. The truth, my criteria were: #1: university, #2: GPA, #3: keywords. Sure, I was bitten a few times (I hired an MIT master's student who was utterly helpless), but over the course of years doing this, some patterns emerge, and high-GPA absolutely correlates w…
I agree that GPA is useful as a binary indicator—if it’s abominably low, like a 2.0 in your example, it’s a red flag. But a 4.0 is no more predictive of being a good hire than, say, a 3.3. It’s also very school-dependent. Some places inflate grades a lot more than others.
In my own anecdotal experience, I omitted my GPA entirely from my CV when looking for jobs straight out of college and got interviews at every single place I applied. It’s not nearly as important as a lot of people think.
Re: Poisson's Equation
#100> This oval (called a separatrix) has the special property that no wind flows through it at all. It acts just like a solid surface. We have already assembled a reasonably accurate simulation of how air flows around an ellipse in some confined space like a wind tunnel! My understanding of airflow simulation (undergrad-level at best) is that the correct boundary condition is almost without exception the no-slip one: ai…
You are correct! The simulation as written does not handle the no slip condition. The simulated "air" is inviscid and irrotational. You would need to tackle a few more things in order to have a really accurate simulation.