How to teach Help students achieve their goal by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01This is the most important of all points.
Don't set goals for your students.
Ask students what they want to do, and help them achieve that goal.
If they don't know what to do, give suggestions of interesting things they could do.
Once they have a goal, just help them learn everything that is needed to achieve that goal
This is because the universe of potentially useful things that can be learnt is infinite, and no human can ever learn everything.
The only solution, is to try and learn only what seems necessary to reach your goal, and just try to reach your goal instead.
This approach is called backward design.
Also, setting overly ambitious goals, is a good idea: the side effects of ambitious goals are often the most valuable thing achieved.
How to teach Advertise your material by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Once you have crated something awesome, you have to advertise it, otherwise no one will ever find it.
This means:
- Then ask them if they want to talk about anything.
- whenever someone asks as question on an online forum, answer it, and link to the section of your material that also answers that question.The material will answer many of their future questions.
Eventually, people will find you on the front page of Google searches, and then you will know that you've truly made something useful.
How to teach Talk with individuals, not to groups by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Everything you want to teach is already online.
And if it is not, then you are wasting your time saying it face-to-face instead of creating such online resource.
The only goal of meeting students is talking to them individually or in small groups to:
- understand what they feel
- transmit your passion for the subject
and letting them do the same amongst themselves.
If you talk to a large group, you will only reach / understand a very small percentage of the group, so your time is wasted.
It is better to deeply understand what 25% of the students feel and adapt the course material, than to talk to everyone at once, and have only 5% understand anything.
Finding a complete basis such that each vector solves a given differential equation is the basic method of solving partial differential equation through separation of variables.
The first example of this you must see is solving partial differential equations with the Fourier series.
Notable examples:
- Fourier series for the heat equation as shown at Fourier basis is complete for and solving partial differential equations with the Fourier series
- Hermite functions for the quantum harmonic oscillator
- Legendre polynomials for Laplace's equation in spherical coordinates
- Bessel function for the 2D wave equation on a circular domain in polar coordinates
Directly modelled by group.
For continuous symmetries, see: Lie group.
Mnemonic: it gives out the amount of fluid that is going in or out of a given volume per unit of time.
Ciro Santilli thinks that maybe the government does not need to provide those, but it needs to regulate the fuck out of them, notably control over censorship in those platforms: the deplatforming of Donald Trump.
Related:
This section is about functions that operates on arbitrary sets.
MOOCs are a bad idea. We don't want to simply map the pre-computer classroom to the Internet. The Internet allows, and requires, fundamentally new ways to do things. More like Stack Overflow/Wikipedia. More like OurBigBook.com.
Being naughty and creative are correlated by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Order of the highest derivative that appears.
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
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