Vector Integral Calculus - Gradient Vector Field p2

[ura239]

THANX DONNY, LOVE YOUR VIDEOS!

[mysteryimpt]

Thank you for amazing video, could you kindly make the tree diagram gradient please?:) Thank you.

[abdulhamidalsalman]

Great lectures. Your videos not only helpful but also entertaining. I can't stop laughing when you get excited. I always tell my friends "Donylee is the Kung Fu Master of Mathematics" :)

[Quinctius]

very basic calculus but refreshing.

[daowz]

thank you so much !!! by the way .. ur English have gotten better since those first videos from calculus

[seamyb88]

you explain everything brilliantly... the people who criticize you dont realize that they can rewind the video back. you have helped me sooooo much. thank you man.

seamus (ireland)

:)

[sukardihenry]

nb.. super singaporean

[simplystimpy]

very good lecture. It might help to explain why we differentiate wrt lambda because if we want to find the instantaneous rate of change of phi from p0 to p, then we take the limit as lambda approaches 0 as this will be our infinitessimally small change in x,y,z. This works since lambda is the distance traveled in the direction of u.

[xurumeng]

Good clear lecture but he has irritating habit of punctuating every other sentence with an 'OK'. Because of his strong accent (Singapore or Malaysian), he should speak slower

[yort45]

you go pretty fast man. im pretty sure i understood what you were saying but why so fast? you seemed to jump around alot and add things later that may have been helpful at that point.

[espen180]

I wouldn't say that he's talking fast, but rather that he is really "engaged" in the subject. I think this is a good thing as it motivates the viewer. If you need a contrast to compare to, search for Algebra Help and watch the videos from youteachermathhelp.

[thefuturebird]

Your videos are all so clear and helpful. They are helping me to review many of these concepts!

[soulfuluniverse]

hello donylee,

this is a very good explanation of this subject. But I have to note that in your example of the boy who can move left and right you might have confused "two dimensional calculus" with "one dimensional calculus". And change of speed is usually denoted as "dx/d²t" or "dv/dt" where t is the scalar variable of time and x is a function the form of x: IR->IR, where the domain and range of the function x(t) are the set of real numbers.

[donylee]

Hello soulful,

Yup, I notice my mistake. dv/dx is not a good representation of the boys speed though I do believe there is such a thing as rate of change of velocity wrt to displace. dv/dt is a more accurate expression.

[donylee]

As for one or two dim calculus, I notice that the distinction is blurred depending on how you look at it. Calculus taking place with just x and y CAN be thought of as one dim calculus if you imagine x to be the perimeter and y to be the direction. Allowing x to vary, y varies only in ONE direction. On the other hand, it could be thought of as 2d is x and y does in fact form a plane.

Hmmm, have to think about that one!

[soulfuluniverse]

I think I know what you mean about the difficulty in explaining the difference in "dimensionality" ... I myself was only looking at it from a purely algebraic standpoint where dimension is defined as the maximum number of linearly independent vectors in a vector space.