Calculus 3: Divergence and Curl (2 of 26) What is the Gradient?

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In this video I will explain what is the gradient, del operator f(scalar).

Next video in the series can be seen at:

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This has got to be the best video on an introduction to vector calculus out there, thank you so much!

Cadmin

until I start to apply calculus in my post-grad study, I realize that I really need some simple but detailed instructions and illustrations. here I find what I need!!

weixiao

As usual, van Beizen to the rescue!
Every exam period brings a new wave of desperate students to complement the good teachers on the net.
Thanks again :)

taladiv

@6:07, it is important to mention when Z = X^2 + Y^2 = 1, X = .707 and Y =.707, or square root 2 over 2. Then when you plug in for X and Y, you get root 2 i + root 2 j, which the magnitude (slope at that point) is 2.

fcp

I think The point between should be (1/sqrt2, 1/sqrt2)

RiaziMohandesi

Thanks, this teacher tell us the concepts well in a intuitive way 😊, it helped me a lot

zzzyout

@ 6:07 the point in between should be (√2/2, √2/2), and hence the slope magnitude would be 2

ASIR

Between (0, 1) and (1, 0) on a circular path is (sqrt(2)/2, sqrt(2)/2) not (sqrt(2), sqrt(2))

terjeoseberg

I would really like to Thank you a lot for taking such a pain to provide such a beautiful & in depth explanation...

sarangdharkumar

At time 04:32, i think it is better to say :In the direction of The Maximum increase in function, not Maximum increase in slope, or better to say :In the direction of maximum slope.

RiaziMohandesi

First of all, thank you for a great video series. However, I am lost for the intro video for gradient.
When writing f=f(x, y, z), f is a function of (x, y, z) R^3->R, where x, y, z are independent "input" variables and f(x, y, z) is a dependent "output" variable, for example velocity field f at position (x, y, z), which is not x, y or z. However, in the example f = x^2 + y^2, the meaning of f seems changed to be z or f(x, y)? Considering a level curve of f(x, y, z)=C, it will be a cylinder not paraboloid. Did I miss anything?

yangqian

how the point between the (1, 0) and (0, 1) on the circular line comes equal to (√2, √2)?
just on the basis of my imagination i think it should be (1/√2, 1/√2).

And this value of x and y can also give magnitude of vector sum equal to 2
Please correct me if i am wrong
And thanks for the great explaination

GursimranSingh

This was very helpful for me. Thank you very much for your effort.

manueljenkin

But the function of x, y and z will lead to a 4th dimension and I don't know how to visualise the function in 4th dimension.

spurti

I have a doubt. Sir chose (√2, √2) and said magnitude is 2(slope).

Firstly, how can (√2, √2) have the same z value as (1, 0) and (0, 1)?

If z is not the same, slope is neither the same right?

And how did you calculate the magnitude? Is it the √((2x^2)+(2y^2)) ?

Then the magnitude of the √2, √2 case will be 4 right?

I'm confused. Thanks in advance.

mohammadsabithali

I have a question that's been bugging me for a while now. what would be the gradient of f where f(x, y, z)= 1/p. It doesn't give anything about what P represent but since f is a function of three variables, I am guessing p is also a function of the same three variables. So would you use chain rule in problems like this, to find the gradient?

Bearfair

The points you have labeled (1, 0) and (0, 1) should be labeled (1, 0, 1) and (0, 1, 1), shouldn't they?

dggrossman

Sir

Michel Van Biezen. How is the ' magnitude of the gradient' defined? This has always confused me. Is it the magnitude of the sum of the magnitudes of the two partial derivatives in the x and y direction, if say z=f[x.y] I would be most grateful if you would care to clarify this for me . Thanks.

barryhughes

Thank you sooo much !! by the way, isn't it the point (sqrt(2), sqrt(2)) not on 3-dimentional figure which includes (0, 1) and (1, 0).
Isn't it we cannot calculate slope of that point because there is no figure

YuriKim-bbwx

How is magnitude of 2sqrt (2) i` + 2sqrt (2) j' equal to 2??? It is 4 right?? plz explain the part at 6:16

SidharthShambu

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