Which path to learn differential?

DynV

DynV

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Well... Although my program prerequisite didn't have a single differential question, it turns out my studies uses some and doesn't teach about it (it teaches what I assume is what a student knowing about differential would need to learn).
khanacademy-courses-240802.png
is how I passed my program prerequisite, so I intend to study that way. Which would be the most efficient path to learn differential? If there's a path that would take **a little** longer, how longer do you think it would be and how longer on average, eg also study X it should take ~10% longer and you'd benefit a lot from that?

I wasn't sure where to ask this, feel free to move this thread.

Thank you kindly
 
DynV said:
Well... Although my program prerequisite didn't have a single differential question, it turns out my studies uses some and doesn't teach about it (it teaches what I assume is what a student knowing about differential would need to learn).
View attachment 38441
is how I passed my program prerequisite, so I intend to study that way. Which would be the most efficient path to learn differential? If there's a path that would take **a little** longer, how longer do you think it would be and how longer on average, eg also study X it should take ~10% longer and you'd benefit a lot from that?

I wasn't sure where to ask this, feel free to move this thread.

Thank you kindly
Click to expand...
An introduction to "differential" is generally covered in precalculus, just before introduction of "differentiation".
 
DynV said:
Well... Although my program prerequisite didn't have a single differential question, it turns out my studies uses some and doesn't teach about it (it teaches what I assume is what a student knowing about differential would need to learn).
View attachment 38441
is how I passed my program prerequisite, so I intend to study that way. Which would be the most efficient path to learn differential? If there's a path that would take **a little** longer, how longer do you think it would be and how longer on average, eg also study X it should take ~10% longer and you'd benefit a lot from that?

I wasn't sure where to ask this, feel free to move this thread.

Thank you kindly
Click to expand...
Are you planning to study - Calculus of Variance ( as in Finite Element Analysis) ?
 
I couldn't understand the following from my tutor which lead me to create this thread. If you'd like to follow along the lesson, it's the PDF linked by "texte de référence" on Module 3 | inf1421.teluq.ca.
Update 1
There's also the 4th module I couldn't even star to understand.
translated email
From: TUTOR@teluq.ca
Date: AUGUST 2024
Subject: RE: INF1421 module 3 start Case of univariate density
To: ME

Hello ME,

the partial derivative of the log-likelihood with respect to θ2 is obtained by differentiating each term of the log-likelihood with respect to θ2, then combining the results. The condition for maximizing the log-likelihood gives us an equation to estimate θ2.

I have not found a clearer method than manual calculation.

I have attached the derivation that I did by hand, following the rules. I hope it will be easier for you to follow.

I apologize for my handwriting.

Do not hesitate to let me know if you have any further questions.

Best regards,
TUTOR


From: ME
Sent: AUGUST 2024
To: TUTOR@teluq.ca
Subject: INF1421 module 3 start Case of univariate density

Hello TUTOR,

I am writing to you regarding the 3rd module of INF1421, specifically the start of the subsection Case of univariate density of section 3.2.3, on page 6. I am having difficulty understanding how we arrive at the derivative, i.e. from the 1st formula of

to the 2nd. Regarding the 1st element of the matrix, how come we have to keep 1 / θ˅2 but have to discard the rest of the fraction, i.e. the -1/2. Regarding the 2nd element of the matrix, where does the square (exponent 2) of the denominator of the 2nd part come from? Could you refer me to a page of a free site or a free document to better understand?

There are several pages left in the module so I might contact you again for that.

Thank you,
ME
Click to expand...
translation of attached
INF1421-Cas_de_densité_uni_variée_(section_3.2.3)-joint_réponse_tuteur-1-translated.jpg
only 4 attachments allowed, I'll make another post for the remaining 2 images.
attached
INF1421-Cas_de_densité_uni_variée_(section_3.2.3)-joint_réponse_tuteur-1.jpg
INF1421-Cas_de_densité_uni_variée_(section_3.2.3)-joint_réponse_tuteur-2.jpg
INF1421-Cas_de_densité_uni_variée_(section_3.2.3)-joint_réponse_tuteur-3.jpg
 
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Steven G said:
differential is a well known topic in math. One can only assume that the poster is asking about differentials
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The handwritten notes in the pictures are French. I suppose that differential is meant to be the translation of différentielle which is mainly the Leibniz notation of a derivative df(x)=f′(x)dx. df(x)=f'(x)dx . However, approaching derivatives from the side of differential forms is quite challenging for beginners. Personally, I like it since I prefer the Weierstraß formulation of differentiation f(x0+v)=f(x0)+Dx0⋅v+o(∥v∥). f(x_0+v)=f(x_0)+ D_{x_0}\cdot v + o(\|v\|) .However, starting with differentials, i.e. differential forms can be confusing. That's why I recommended the OpenStax book which is suited for beginners.
 
I like a lot following with videos and practice, hence the OP featuring Khan Academy. Although not as important IMO, Khan Academy also keep track of your progress; it even allow a tutor or teacher to link up to your account to keep an eye on you. While I appreciate all help, my question was mainly about the order of Khan Academy courses I should take for my goal.
 
I'm not a fan of video consumption. In my opinion, it sells only an illusion of understanding. You follow the presenter and agree with him if it is presented well. But did you learn anything? There might be a minority of people who can answer this positively but I think the majority only thinks they have learned something. There is no way around ...

DynV said:
... and practice ...
Click to expand...

You have to do math to learn math, ideally without videos or books. Most content of the videos I have watched I have forgotten the very next day.
 
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