i never comment, but i just need to let you know, you literally just summarised into 8 mins, what was two, 1 hour lectures. Thank you and keep up the work good sir! The way you explained it was extremely intuitive.
Thanks so much. Very simple and and great explanation. I’m in a top uni in Egypt and we have a German professor who asks us complex questions to make sure we understand in depth and that video helps so much❤
Dude this is the best video I've seen on this subject. Its so funny cause these 80 year old professors think they're so intelligent but can barely put two comprehensible sentences together. However you did it in 8 minutes. Thanks!
you just earned a happy subscribe Im not even joking you saved my life ,I just turned 15 and studying calculus 3 at home my parent will not get me a tutor and when i reached this it was so porrly expland before i was stuck for days now i understand it and have well moved past it and working on later subtopics in clac 3 like Fubini's theorm .So again thank you soo much 🙏☝☝🙏🙏🙏🙏🙏🙏And i think everyone here can relate to you helping so much
Correct me if I am wrong ,Directional Derivativ e helps us to calculate the derivative along a vector say r=ai+bj ,iand j vectors are basis vectors ,r vector is given by moving a units along X direction ,and b units along Y direction ,δf/δx gives us how much the function changes per unit length of X ,and δf/δy gives us how much the function changes per unit length of Y, since it has moved a units along X direction the changes the function has undergone in X direction is a(δf/δx) ,similarly in y direction it's b(δf /δy) since the changes are different in each direction shouldn't the changes be a(δf/δx )i +b (δf/δy )j ? What I am trying to say is both δf/ δx; δf/δy are along 2 different direction ,just adding them doesn't feel right,shouldn't we mention i and j vectors along with them
I also thought the same thing, the problem is no one is explaining this, I searched a lot but no proper answers I mean after travelling about dx distance and found a change in height and then I go about dy distance and get another change in height, how could be the total change is the addition of them ?
Why would it be a(δf/δx )i +b (δf/δy )j? You can't multiply vectors like that since A and B are the vector components. I don't understand where you're coming from, but a dot product is not a vector so it cannot be that anyways.
If you mean where the formula comes from; basically for your function F plug in a line function of 1 variable t ihat goes through your point A you wanna differentiate at, and at t = 1 have it go through A + u, with u your unit direction vector. To get this derivitive along the line at a, evaluate using the chain rule at t = 0, and the formula matches. Alternatively, the idea is your locally scaling each coordinate by the derivative value of that coordinate and adding the total
I have a question, does the u vector in the dot product have to be a unit vector that has square magnitude = 1 or the component of the u vector can be anything we want?
The definition of the directional derivative is the rate of change per unit length. If we use a vector of magnitude L instead of a unit vector (which has magnitude 1), then we would instead be computing the rate of change per length L. That's fine as long as you understand that you're computing something different than the standard directional derivative!
A dot product is typically done with two column vectors as shown in the video. Using a row vector would be correct if it were matrix-vector multiplication instead.
1:55 here why multiply why not add? also please explain why a unit vector what happens if we use a non-unit vector? the output of the directional derivative is a scalar value what does that mean what does it tell us?
We use a unit vector because we want to find the change in function output per unit length. If we used a non-unit vector, then we would have to divide by the length of the vector to make sure we still got the change per unit length. The directional derivative is a scalar that describes the change in function value per unit length in a specific direction.
@@MuPrimeMath how does multiplying a unit vector to the gradient tells the slope in that unit vector direction? if its possible can you recommend a video that properly explains dot product with visualisation and also how it changes direction to particular vector
Haydn is naturally left-handed. He combs his hair from the right side. Math is usually from the analytical side of the brain, which controls the right side. So, his talent in math comes from his nondominant side of the brain. He uses his dominant right side to compose music. So, his talent in music comes from his right side of the brain, the creative side. Conclusion: he is a treasure with his brilliance.
![Megan Thee Stallion - Bigger In Texas [Official Video]](http://i.ytimg.com/vi/QxTkZTLWdo4/mqdefault.jpg)
keep it up, you have a special talent of explaining complex topics with simple terms
LEFT HANDED AND BEING A MATHEMATICIAN IS TRULY A GIFT
i never comment, but i just need to let you know, you literally just summarised into 8 mins, what was two, 1 hour lectures. Thank you and keep up the work good sir!
The way you explained it was extremely intuitive.
Damn, straight explanation with no “uhms”. How do other people do that
Nice, simple, and intuitive. Thanks!
Thanks so much. Very simple and and great explanation. I’m in a top uni in Egypt and we have a German professor who asks us complex questions to make sure we understand in depth and that video helps so much❤
Absolutely killed it, great video.
Thank you so much, very clear and concise!
Thank you for a very clear and straightforward explanation
Wow, such a clear and simple explanation!
Cleared my concepts in no time. Thanks a lot.
Great explanation! Thank you
That was amazing explanation really thank you
Thank you for not making it complicated.
Dude this is the best video I've seen on this subject. Its so funny cause these 80 year old professors think they're so intelligent but can barely put two comprehensible sentences together. However you did it in 8 minutes. Thanks!
You made me clear
Your explanation is so clear, thank youu.
u just made this make sence thank you thank you
you just earned a happy subscribe
Im not even joking you saved my life ,I just turned 15 and studying calculus 3 at home my parent will not get me a tutor and when i reached this it was so porrly expland before i was stuck for days now i understand it and have well moved past it and working on later subtopics in clac 3 like Fubini's theorm .So again thank you soo much
🙏☝☝🙏🙏🙏🙏🙏🙏And i think everyone here can relate to you helping so much
Amazing. Masha allah. Can you explain how your thought process work or how you approach problems. So we can follow it and get some good GPA
Correct me if I am wrong ,Directional Derivativ e helps us to calculate the derivative along a vector say r=ai+bj ,iand j vectors are basis vectors ,r vector is given by moving a units along X direction ,and b units along Y direction ,δf/δx gives us how much the function changes per unit length of X ,and δf/δy gives us how much the function changes per unit length of Y, since it has moved a units along X direction the changes the function has undergone in X direction is a(δf/δx) ,similarly in y direction it's b(δf /δy) since the changes are different in each direction shouldn't the changes be a(δf/δx )i +b (δf/δy )j ?
What I am trying to say is both δf/ δx; δf/δy are along 2 different direction ,just adding them doesn't feel right,shouldn't we mention i and j vectors along with them
I also thought the same thing, the problem is no one is explaining this, I searched a lot but no proper answers
I mean after travelling about dx distance and found a change in height and then I go about dy distance and get another change in height, how could be the total change is the addition of them ?
Hi, not sure I got your point. I think he scales the partial derivatives by x zero and y zero that are what you call a and b
Why would it be a(δf/δx )i +b (δf/δy )j? You can't multiply vectors like that since A and B are the vector components. I don't understand where you're coming from, but a dot product is not a vector so it cannot be that anyways.
If you mean where the formula comes from; basically for your function F plug in a line function of 1 variable t ihat goes through your point A you wanna differentiate at, and at t = 1 have it go through A + u, with u your unit direction vector. To get this derivitive along the line at a, evaluate using the chain rule at t = 0, and the formula matches.
Alternatively, the idea is your locally scaling each coordinate by the derivative value of that coordinate and adding the total
Thank you so much! But are the contoure lines u?
This was such a good video
it is such an excellent explaination!
ولك ثانكيو بكد جمالك☹️💔
Very, very clear!
Clearly explained !!
I have a question,
does the u vector in the dot product have to be a unit vector that has square magnitude = 1 or the component of the u vector can be anything we want?
If we want the directional derivative to represent the change in function value per unit length, then u needs to be a unit vector!
@@MuPrimeMath Thanks a lot! 😊
Perfect !
excellent
Thank you
I have a question, how to achieve an expansion for the floor function?
math.stackexchange.com/questions/764467/full-series-expansion-of-the-floor-function
@@MuPrimeMath thank you so much
Superb man
THANK YOU! finally
If we use a vector of big magnitude instead of using unit vector, would the change be accurate?
The definition of the directional derivative is the rate of change per unit length. If we use a vector of magnitude L instead of a unit vector (which has magnitude 1), then we would instead be computing the rate of change per length L. That's fine as long as you understand that you're computing something different than the standard directional derivative!
Thanku 🙏sir
Wonderful Sir
dig it!
In 2:40 I think x0 and y0 must be in row vector not column
A dot product is typically done with two column vectors as shown in the video. Using a row vector would be correct if it were matrix-vector multiplication instead.
thx man
Nice
I don't understand why gradient is the direction of maximum change
helal len iyi anlattın
Dude why do I have the feeling that this guy is left handed...
1:55 here why multiply why not add?
also please explain why a unit vector what happens if we use a non-unit vector?
the output of the directional derivative is a scalar value what does that mean what does it tell us?
We use a unit vector because we want to find the change in function output per unit length. If we used a non-unit vector, then we would have to divide by the length of the vector to make sure we still got the change per unit length.
The directional derivative is a scalar that describes the change in function value per unit length in a specific direction.
@@MuPrimeMath how does multiplying a unit vector to the gradient tells the slope in that unit vector direction?
if its possible can you recommend a video that properly explains dot product with visualisation and also how it changes direction to particular vector
Why do you write with that hand?
Haydn is naturally left-handed. He combs his hair from the right side. Math is usually from the analytical side of the brain, which controls the right side. So, his talent in math comes from his nondominant side of the brain. He uses his dominant right side to compose music. So, his talent in music comes from his right side of the brain, the creative side. Conclusion: he is a treasure with his brilliance.
1st