NO WAY. Your example equation is again the exact same as my homework problem AGAIN. Maybe you're in cahoots with James Stewart. In any case, you're making my MV Calc class way too easy. Thanks! :)
Your voice is so calming when you explain things, it's probably because every other mathematician on youtube is a guy. Keep up the good work! I will be referring to your videos more often :)
@@kristakingmath .Thank you, perhaps you may go a little further and just confirm what I discern to be true. Is the magnitude of gradient vector of a surface represented by the 'projected' length of it on the x, y plane ? If it is then I am content, it's not that easy when your are self taught. Thanks, in hope of reply.
I have a question - everyone says "and the maximum rate of increase is - and the length of the gradient vector" but this length is of varying size - why is that ? shouldn't we normalize it to 1 first ?
the directional derivative and the direction in which f increases rapidly at a point should be in the same video. Since they usually ask about both in the same question.
What is the direction of maximum increase of scalar field at a specific point. Is it equal to gradient of the scalar field or it is equal to “ grad function / | gradient functions | “
So please correct me if I am wrong.......the gradient vector is the sum of the two partial derivative vectors in the x,y plane and it's value is the magnitude of the sum of these two vectors? If this is the case then is this magnitude the actual slope of the surface at this point...ie...the tangent? I would be so grateful if you could clarify....and thanks for the videos.
The gradient is often used interchangably with slope, however the gradient is the partial derivatives in any dimension (in this case 2) but as vectors, meaning they can be expressed in terms of unit vectors.
Can you do a video on exactly why the gradient of a scalar field is the magnitude and direction of the maximum increase of that scalar field at any given point in that scalar field? Is there a proof?
There's definitely a proof somewhere, and I'd have to dig into it in order to make a video for it, but proofs are something I'd like to start doing at some point. In the meantime, I'd search around a little bit for this if you're interested! :)
I haven't been able to find a good, clear explanation yet - which surprises me. If I find one or derive one, I'll send it your way. Seems to me there may be a very important concept in there that may open up a new understanding for me and may help me during my study of tensors - which has come to a halt till I get past this nagging curiosity. On the other hand, it may end up being simple and of no greater consequence.
Krista King I'm looking forward to them with bated breath!! Internet high five! Do you have a PHD in math? You must be a teacher in real life, if not you should be!
what a legend! so quick and to the point, no more harder than it needs to be
Hi, your videos have helped me so much with my calculus class during the pandemic and I just really appreciate your content
The best Teacher of all time.
Thanks Krista!
Perfect for my short attention span.
It was pretty helpful, though I am confused on just why we know that is the direction of the maximum rate of change.
NO WAY. Your example equation is again the exact same as my homework problem AGAIN. Maybe you're in cahoots with James Stewart. In any case, you're making my MV Calc class way too easy. Thanks! :)
still helping students 7 years after it was posted, thank you ms King XD
Thank you so much for the amazing explanation. love your videos. I don't know what would I do without your videos.
+Mohammed Al-Bashiri Aw thanks! I'm glad they're helping.
I couldn't find a video regarding "Gradients and level curves". Do you have a video regarding this subject with another name?
+Mohammed Al-Bashiri Unfortunately I don't have a level curves video at the moment, but it's on my list!
I see. Thank you :)
Your voice is so calming when you explain things, it's probably because every other mathematician on youtube is a guy. Keep up the good work! I will be referring to your videos more often :)
thanks! i'm so glad you like the vids!
Thank you so much. Finally some has explained " the magnitude" of the gradient vector.
Glad it helped, isobar! :)
@@kristakingmath .Thank you, perhaps you may go a little further and just confirm what I discern to be true. Is the magnitude of gradient vector of a surface represented by the 'projected' length of it on the x, y plane ? If it is then I am content, it's not that easy when your are self taught. Thanks, in hope of reply.
You're the best, Krista!
Aw thanks! Right back at ya!
Thank you! so how would you do to find the MINIMUM rate of change?
minus the graient ve tor.. so signs will change and yiu go in opposite direction. i. e date of least change
Studying for final tomorrow! My savior!
Good luck on the final!
thanks so much for your videos. they really have helped a lot.
+Aaron Ivy Awesome! Thanks for letting me know.
YOU'RE AWESOME!
I like your way of explanation. thank you
I have a question - everyone says "and the maximum rate of increase is - and the length of the gradient vector" but this length is of varying size - why is that ? shouldn't we normalize it to 1 first ?
thank you so much krista
You're welcome! :)
thank you thank you thank you. You are the best.
You're welcome, Dli, I'm so glad it helped! :)
Thank you for the heart ❤️
the directional derivative and the direction in which f increases rapidly at a point should be in the same video. Since they usually ask about both in the same question.
Hey ! Could you please make a video on explaining 'why does the gradient give maximum change ' ?
Yes! This is what I’m looking for!
perfect way to explain..love your at the first checkout..
Keep it up
and thanks a lot for such a great help
Already Subscribed you :)
Goddamn ! Hot stuff! It is the best explanation on the net so far!
YOU SAVE MY LIFE
What is the direction of maximum increase of scalar field at a specific point.
Is it equal to gradient of the scalar field or it is equal to “ grad function / | gradient functions | “
How do i find direction where the rate of change is zero?
Is rate of change the same of angular coefficient?
Very helpful! Thank you so much!!
Glad I could help! :D
So please correct me if I am wrong.......the gradient vector is the sum of the two partial derivative vectors in the x,y plane and it's value is the magnitude of the sum of these two vectors? If this is the case then is this magnitude the actual slope of the surface at this point...ie...the tangent? I would be so grateful if you could clarify....and thanks for the videos.
The gradient is often used interchangably with slope, however the gradient is the partial derivatives in any dimension (in this case 2) but as vectors, meaning they can be expressed in terms of unit vectors.
So is the direction (0,1) or (1,0)?
technically isnt the "absolute value" of the gradient vector function representing the magnitude of the vector?
Yes
You make maths hot, thanks.
Mam can you explain HCF and LCM
Is the direction 0,1 from the origin or from the point 1,0?
+robashton47 From the origin
Can you do a video on exactly why the gradient of a scalar field is the magnitude and direction of the maximum increase of that scalar field at any given point in that scalar field? Is there a proof?
There's definitely a proof somewhere, and I'd have to dig into it in order to make a video for it, but proofs are something I'd like to start doing at some point. In the meantime, I'd search around a little bit for this if you're interested! :)
I haven't been able to find a good, clear explanation yet - which surprises me. If I find one or derive one, I'll send it your way. Seems to me there may be a very important concept in there that may open up a new understanding for me and may help me during my study of tensors - which has come to a halt till I get past this nagging curiosity. On the other hand, it may end up being simple and of no greater consequence.
Thank you!
Life saver!
Thanx a lot for your effort:)
Awesome explanation Krista! Are you related to Morghan King?
Thanks! No I'm not related.
Thanks a lot!
You're welcome! Glad it could help!
Engineering major here hoping you have videos on advanced statistics, diff. eq's, and linear algebra. . .please tell me you do!
I have a little on Diff Eq's, but nothing yet for advanced stats or LA. Hoping to make them in the future, though!
Krista King I'm looking forward to them with bated breath!! Internet high five! Do you have a PHD in math? You must be a teacher in real life, if not you should be!
thank you!
You're welcome, Asaad! :D
you rock , please come and replace my lecturer
+Frassie28 LOL, thanks!
thank you
you're welcome! :D
Awesome !
:)
Midterm time LETSSS GOOOO
I hope the midterm went great, Gustavo! :)
WHat is a gradient vector??
Thank you :)
+Udith Ashoka You're welcome!
wow! Its amazing !!!!
thanks great vid
Thanks!
will you marry me?
The best Teacher of all time.
Thanks Krista!
thank you