Lessons I wish I had learned before teaching differential equations [pdf] (1997)
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Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#2Previous discussion from 2022...
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#3“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary
differential equations? I will hazard an answer: for the same reason why we see so little change
anywhere today, whether in society, in politics, or in science“
I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained.
There is also a certain veneration of the establishment and traditions. I remember on my first day of Classical Mechanics the 50+ year old teacher beamed with pride when he told us he used the same exact textbook when he was in school. As if it was written by the Shakespeare of textbook writing and nobody has managed to surpass it in decades. It' frankly should be an embarrassment
As he observed, other departments will step in an do much better. The best linear algebra class I had was a graduate course in the electrical engineering department
I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on. I really wish textbooks with open licenses would take over and they could be reworked and improved year after year by different people
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#4“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
Came here to quote the same exact part. The author is hilarious and savage but it seems appropriately. Amazing prose and sad state of affairs
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#5“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on
When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#6“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.
The problem isn't writing a better text, it's having departments willing to teach it, or to try alternate approaches at all.
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#7“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
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Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#8“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
Just out of curiosity, what was that classical mechanics textbook?
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#9“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“ I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep…
Khan Academy is excellent for Calculus however their material for Differential Equations is rather minimal since they don't really go into university level material.
Perusing online resources for Differential Equations shows that there doesn't seem to be much agreement on how to define the core subject, and there is no grounding on 'how we got here' to provide a path forward to people just starting out. My experience so far, at least.
Re: Lessons I wish I had learned before teaching differential equations [pdf] (1997)
#10Speaking of 2nd-order linear ODEs w/ const factor (a.k.a. mass-spring-damper systems), I wrote a blog post[0] deriving all possible general solutions in a concise matrix that makes it easily implementable in code.
The following is the complete solution in Lua:
function sprung_response(t,pos,vel,k,c,m)
local decay = c/2/m
local omega = math.sqrt(k/m)
local resid = decay*decay-omega*omega
local scale = math.sqrt(math.abs(resid))
local T1,T0 = t , 1
if resid0 then
T1,T0 = math.sinh(scale*t)/scale , math.cosh(scale*t)
end
local dissipation = math.exp(-decay*t)
local evolved_pos = dissipation*( pos*(T0+T1*decay) + vel*( T1 ) )
local evolved_vel = dissipation*( pos*(-T1*omega^2) + vel*(T0-T1*decay) )
return evolved_pos , evolved_vel
end